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Uma das características que nos distinguem de outros seres vivos é nossa cultura. Entretanto, como comportamentos não fossilizam, é difícil reconstruir o passado para gerar insights sobre por que nos tornamos o que somos hoje. Juntamente com dados etnográficos e experimentais, os modelos matemáticos têm sido utilizados para abordar a questão sobre como nossos comportamentos foram moldados pela evolução. Esta tese está dividida em duas partes. Na primeira parte, discutiremos sobre seleção multinível e sobre como o framework matemático chamado Two-level Fisher Wright (TLFW) pode nos ajudar a entender a evolução da cooperação em populações humanas. Após descrevermos o problema da cooperação através do uso de ferramentas de teoria dos jogos, revisamos algumas das teorias atuais sobre por que a cooperação evoluiu. Em seguida, empregamos o framework TLFW ao problema da emergência de altruísmo em populações de caçadores-coletores, considerando uma situação em que o conflito entre grupos direciona a seleção. Na segunda parte, abordamos o tópico de diversidade linguística e apresentamos a importância de se estudar a competição entre línguas para ajudar a preservá-las. Traçando um paralelo entre a evolução das línguas e a evolução de normas sociais, introduzimos um modelo para analisar a persistência de dialetos, quando existe competição com uma língua padrão nacional. One of the features that distinguish human beings from other living species is our culture. However, since behaviors do not fossilize, it is difficult to reconstruct the past to get insights about why we are who we are. Along with ethnographic and experimental data, mathematical models have been used to address the question of how our behaviors were shaped by evolution. This thesis is divided into two parts. In the first part, we will discuss multilevel selection and how the mathematical framework Two-Level Fisher-Wright (TLFW) can help us to understand the evolution of cooperation in human populations. After describing the problem of cooperation by using game theory, we review some of the present theories about why cooperation has evolved. Then, we apply the TLFW framework to the problem of the evolution of altruism in populations of hunter-gatherers, considering a situation in which group conflict drives selection. In the second part, we discuss language diversity and present the importance of studying the competition between languages for helping to preserve them. By drawing a parallel between the evolution of language and social norms, we introduce a mathematical model to analyze the persistence of dialects competing against a national standard language.

Background Osteoporosis is an underdiagnosed condition, and its seriousness is not considered until severe complications arise. This study aimed to evaluate general dentists’ knowledge about osteoporosis and their ability to identify patients with this disease by assessing mandibular cortical width (MCW) and mandibular cortical index (MCI) on panoramic dental radiographs using a visual method. Methods In this cross-sectional study, an email questionnaire regarding the diagnosis and prevention of osteoporosis was sent to 20,773 dentists in 2016. Those who completed the questionnaire were invited to participate in radiomorphometric training and then to analyze the MCI and MCW of 114 panoramic radiographs of postmenopausal women who underwent both panoramic radiography and bone densitometry. Based on the radiomorphometric indices and while blinded to the densitometry results, the dentists determined whether they would indicate densitometry for these patients. Results The response rate was 2.3%: 485 dentists completed the questionnaire, and 50 evaluated panoramic radiographs using the MCW and MCI. All of them reported some knowledge about osteoporosis, but 41.6% demonstrated a misleading conceptualization of the disease. Approximately 90% reported minimal access to this information during graduation, and only 27.0% were exposed to the topic during their postgraduate studies. Interest in osteoporosis prevention was expressed by 70.7% of the respondents, and interest in learning the radiomorphometric indices was expressed by 99.0%. The sensitivity in the detection of low bone mineral density through the MCW and MCI was 52.9%, and the specificity was 64%. Conclusions Brazilian dentists demonstrated insufficient knowledge about osteoporosis and a low ability to detect osteopenia or osteoporosis by applying radiomorphometric indices.

In supervised learning, training and test datasets are often sampled from distinct distributions. Domain adaptation techniques are thus required. Covariate shift adaptation yields good generalization performance when domains differ only by the marginal distribution of features. Covariate shift adaptation is usually implemented using importance weighting, which may fail, according to common wisdom, due to small effective sample sizes (ESS). Previous research argues this scenario is more common in high-dimensional settings. However, how effective sample size, dimensionality, and model performance/generalization are formally related in supervised learning, considering the context of covariate shift adaptation, is still somewhat obscure in the literature. Thus, a main challenge is presenting a unified theory connecting those points. Hence, in this paper, we focus on building a unified view connecting the ESS, data dimensionality, and generalization in the context of covariate shift adaptation. Moreover, we also demonstrate how dimensionality reduction or feature selection can increase the ESS, and argue that our results support dimensionality reduction before covariate shift adaptation as a good practice., Comment: Neural Comput & Applic (2022)

Energy fraud is a critical economical burden for electric power organizations in Brazil. In this paper we present the application of cutting-edge Machine Learning algorithms, namely XGBoost and Isolation Forest, for prediction of irregularities in electrical energy consumption. By using a Logistic Regression model as a benchmark, we show that the use of XGBoost results in a significant improvement in the F1-score for fraud predictions in two different scenarios: with and without inspection history features. Moreover, we also propose the use of the Isolation Forest algorithm for detection of anomalies in electrical energy consumption. We show that this approach may be useful in the case of lack of inspection history features, surpassing dummy classifiers.

Nesta tese desenvolvemos modelos de apreçamento de ativos financeiros baseados no conceito de influência social, analisamos também algumas das consequências destes modelos e comparamos com os modelos correspondentes clássicos. Por meio das funções de utilidade generalizadas exponencial e quadrática, deduzimos o CAPM com influência social. Obtivemos que o coeficiente beta da fórmula do CAPM depende de uma aversão ao risco efetiva do mercado que depende da distribuição de riqueza dos agentes do mercado. Supondo que distribuição de riqueza dos agentes do mercado segue uma distribuição de Pareto, fomos capazes de conectar, aversão ao risco média efetiva do mercado, volatilidade e distribuição de riqueza dos agentes, estabelecendo a previsão empírica de que a volatilidade aumenta com a concentração da distribuição de riqueza dos agentes do mercado, a qual foi corroborada por meio de análise estatística. Através da função generalizada tipo potência são feitas algumas considerações sobre alguns \"puzzles\" econômicos bem conhecidos (o \"Equity Premium Puzzle\" e o \"Riskfree Rate Puzzle\") que mostram que a modelagem da influência social pode ter impacto no esclarecimento destes \"puzzles\". In this thesis we develop pricing models for financial assets based in the concept of social influence, we analyze too some of consequences of this models and we compare with the corresponding classical models. By means of the exponential and quadratic generalized utility functions, we deduce the CAPM with social influence. We obtained that the coefficient beta from the formula of the CAPM depends of a market effective risk aversion that depends of the wealth distribution of the market agents. Supposing that the wealth distribution of the market agents follows a Pareto distribution, we were able to connect, market effective average risk aversion, volatility and wealth distribution of the agents, establishing the empirical forecasting that the volatility grows with the concentration of the wealth distribution of the market agents, which was corroborated by means of statistical analysis. Through the generalized power function are made some considerations about some economic puzzles well-known (the Equity Premium Puzzle and the Riskfree Rate Puzzle) that show us that the modeling of the social influence can to have impact in the clarification these puzzles.

The moral foundations theory supports that people, across cultures, tend to consider a small number of dimensions when classifying issues on a moral basis. The data also show that the statistics of weights attributed to each moral dimension is related to self-declared political affiliation, which in turn has been connected to cognitive learning styles by the recent literature in neuroscience and psychology. Inspired by these data, we propose a simple statistical mechanics model with interacting neural networks classifying vectors and learning from members of their social neighbourhood about their average opinion on a large set of issues. The purpose of learning is to reduce dissension among agents when disagreeing. We consider a family of learning algorithms parametrized by δ , that represents the importance given to corroborating (same sign) opinions. We define an order parameter that quantifies the diversity of opinions in a group with homogeneous learning style. Using Monte Carlo simulations and a mean field approximation we find the relation between the order parameter and the learning parameter δ at a temperature we associate with the importance of social influence in a given group. In concordance with data, groups that rely more strongly on corroborating evidence sustain less opinion diversity. We discuss predictions of the model and propose possible experimental tests.

Moral Foundation Theory states that groups of different observers may rely on partially dissimilar sets of moral foundations, thereby reaching different moral valuations. The use of functional imaging techniques has revealed a spectrum of cognitive styles with respect to the differential handling of novel or corroborating information that is correlated to political affiliation. Here we characterize the collective behavior of an agent-based model whose inter individual interactions due to information exchange in the form of opinions are in qualitative agreement with experimental neuroscience data. The main conclusion derived connects the existence of diversity in the cognitive strategies and statistics of the sets of moral foundations and suggests that this connection arises from interactions between agents. Thus a simple interacting agent model, whose interactions are in accord with empirical data on conformity and learning processes, presents statistical signatures consistent with moral judgment patterns of conservatives and liberals as obtained by survey studies of social psychology., Comment: 11 pages, 4 figures, 2 C codes, to appear in Advances in Complex Systems

We study the dynamics of the adoption of new products by agents with continuous opinions and discrete actions (CODA). The model is such that the refusal in adopting a new idea or product is increasingly weighted by neighbor agents as evidence against the product. Under these rules, we study the distribution of adoption times and the final proportion of adopters in the population. We compare the cases where initial adopters are clustered to the case where they are randomly scattered around the social network and investigate small world effects on the final proportion of adopters. The model predicts a fat tailed distribution for late adopters which is verified by empirical data., Comment: 14 pages, 8 figures, revised text, a new section with empirical evidence has been added

Within an agent-based model where moral classifications are socially learned, we ask if a population of agents behaves in a way that may be compared with conservative or liberal positions in the real political spectrum. We assume that agents first experience a formative period, in which they adjust their learning style acting as supervised Bayesian adaptive learners. The formative phase is followed by a period of social influence by reinforcement learning. By comparing data generated by the agents with data from a sample of 15000 Moral Foundation questionnaires we found the following. 1. The number of information exchanges in the formative phase correlates positively with statistics identifying liberals in the social influence phase. This is consistent with recent evidence that connects the dopamine receptor D4-7R gene, political orientation and early age social clique size. 2. The learning algorithms that result from the formative phase vary in the way they treat novelty and corroborative information with more conservative-like agents treating it more equally than liberal-like agents. This is consistent with the correlation between political affiliation and the Openness personality trait reported in the literature. 3. Under the increase of a model parameter interpreted as an external pressure, the statistics of liberal agents resemble more those of conservative agents, consistent with reports on the consequences of external threats on measures of conservatism. We also show that in the social influence phase liberal-like agents readapt much faster than conservative-like agents when subjected to changes on the relevant set of moral issues. This suggests a verifiable dynamical criterium for attaching liberal or conservative labels to groups., 31 pages, 5 figures

In this work, we propose a Bayesian online reconstruction algorithm for sparse signals based on Compressed Sensing and inspired by L1-regularization schemes. A previous work has introduced a mean-field approximation for the Bayesian online algorithm and has shown that it is possible to saturate the offline performance in the presence of Gaussian measurement noise when the signal generating distribution is known. Here, we build on these results and show that reconstruction is possible even if prior knowledge about the generation of the signal is limited, by introduction of a Laplace prior and of an extra Kullback–Leibler divergence minimization step for hyper-parameter learning.

We study evolution of cooperation in a population structured in a large number of groups of variable size, connected by random migration at rate $m$. Social interactions, including cooperation and competition occur only inside the groups. Assuming that groups are large, we define a parameter $\lambda$ that measures the strength of the local regulation, i.e., the rigidity of group sizes. Individuals are of two possible genotypes, one typically assumed to produce a non-cooperative phenotype and the other a phenotype that is cooperative with all members of its own group. Gene action may be additive, producing fitness functions that are linear in the number of cooperators in a group, or not. Assuming weak selection, we obtain the following two contrasting conclusions. (1) ``Hamilton regime'': If $\lambda << m$, then cooperative behavior can spread under a certain condition, which in the additive, i.e., linear, case is precisely Hamilton's rule. The general version of this condition is also relatively easy to apply and is based on Wright's classical beta distribution for the frequency of alleles in infinite island models. We call it the ``beta version of Hamilton's rule''. (2) ``Taylor regime'': If $m << \lambda$, then cooperation that is costly to the actor is eliminated by selection.

We observe that the Taylor-Frank method for making kin selection models when fitness $w$ is a nonlinear function of a continuous actor's phenotype $y$ and the average phenotype $z$ in its social environment requires $w(y,z)$ to be differentiable (as a function of two variables, i.e., jointly in $y$ and $z$). This means that even if $w(y,z)$ is non-linear globally, locally it must be close to linear, meaning that its graph must be well approximated by a plane. When more than two individuals interact, this assumption is only satisfied when the marginal fitness of the actor is a linear function of the fraction of individuals in its social environment that share its phenotype. This assumption sometimes fails for biologically important fitness functions, for instance in microbial data and the theory of repeated n-person games. In these cases, the Taylor-Frank methodology cannot be used, and a more general form of direct fitness must replace it, to decide when a social mutant allele can invade a monomorphic population.

article i nfo Article history: Initial receipt 5 June 2013 Final revision received 2 February 2014 Unlike other vertebrates, humans cooperate in large groups with unrelated individuals. Many authors have argued that the evolution of such cooperation has resulted from reciprocity and other forms of contingent cooperation. This argument is not well supported by existing theory. The theory of contingent cooperation in pairs is well developed: reciprocating strategies are stable when common, and can increase when rare as long as population structure leads to modest levels of relatedness. In larger groups, however, it is not clear whether contingent cooperation can increase when rare. Existing work suggests that contingent strategies cannot increase unless relatedness is high, but depends on unrealistic assumptions about the effects of population structure. Here we develop and analyze a model incorporating a two level population structure that captures important features of human hunter-gatherer societies. This model suggests that previous work underestimates the range of conditions under which contingent cooperation can evolve, but also predicts that cooperation will not evolve unless (1) social groups are small, and (2) the relatedness within ethnolinguistic groups is at the high end of the range of empirical estimates.

Low-density parity-check codes with irregular constructions have been recently shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of simple irregular codes. We use the replica method to find a phase transition which coincides with Shannon's coding bound when appropriate parameters are chosen. The decoding by belief propagation is also studied using statistical physics arguments; the theoretical solutions obtained are in good agreement with simulations. We compare the performance of irregular with that of regular codes and discuss the factors that contribute to the improvement in performance., Comment: 20 pages, 9 figures, revised version submitted to JPA

A variation of Gallager error-correcting codes is investigated using statistical mechanics. In codes of this type, a given message is encoded into a codeword which comprises Boolean sums of message bits selected by two randomly constructed sparse matrices. The similarity of these codes to Ising spin systems with random interaction makes it possible to assess their typical performance by analytical methods developed in the study of disordered systems. The typical case solutions obtained via the replica method are consistent with those obtained in simulations using belief propagation (BP) decoding. We discuss the practical implications of the results obtained and suggest a computationally efficient construction for one of the more practical configurations., 35 pages, 4 figures

We review the application of statistical mechanics methods to the study of online learning of a drifting concept in the limit of large systems. The model where a feed-forward network learns from examples generated by a time dependent teacher of the same architecture is analyzed. The best possible generalization ability is determined exactly, through the use of a variational method. The constructive variational method also suggests a learning algorithm. It depends, however, on some unavailable quantities, such as the present performance of the student. The construction of estimators for these quantities permits the implementation of a very effective, highly adaptive algorithm. Several other algorithms are also studied for comparison with the optimal bound and the adaptive algorithm, for different types of time evolution of the rule.

Reputation systems seek to infer which members of a community can be trusted based on ratings they issue about each other. We construct a Bayesian inference model and simulate approximate estimates using belief propagation (BP). The model is then mapped onto computing equilibrium properties of a spin glass in a random field and analyzed by employing the replica symmetric cavity approach. Having the fraction of trustful nodes and environment noise level as control parameters, we evaluate the theoretical performance in terms of estimation error and the robustness of the BP approximation in different scenarios. Regions of degraded performance are then explained by the convergence properties of the BP algorithm and by the emergence of a glassy phase., Comment: 20 pages, 14 figures

We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter quantified by the mutual information. We define the information excess as a measure of deviation from a maximum entropy distribution. The idea of marginal invariant dependence measures is also discussed and used to show that empirical linear correlation underestimates the amplitude of the actual correlation in the case of non-Gaussian marginals. The mutual information is shown to provide an upper bound for the asymptotic empirical log-likelihood of a copula. An analytical expression for the information excess of T-copulas is provided, allowing for simple model identification within this family. We illustrate the framework in a financial data set., Comment: to appear in Europhysics Letters

We study opinion dynamics in a population of interacting adaptive agents voting on a set of complex multidimensional issues. We consider agents which can classify issues into for or against. The agents arrive at the opinions about each issue in question using an adaptive algorithm. Adaptation comes from learning and the information for the learning process comes from interacting with other neighboring agents and trying to change the internal state in order to concur with their opinions. The change in the internal state is driven by the information contained in the issue and in the opinion of the other agent. We present results in a simple yet rich context where each agent uses a Boolean Perceptron to state its opinion. If there is no internal clock, so the update occurs with asynchronously exchanged information among pairs of agents, then the typical case, if the number of issues is kept small, is the evolution into a society thorn by the emergence of factions with extreme opposite beliefs. This occurs even when seeking consensus with agents with opposite opinions. The curious result is that it is learning from those that hold the same opinions that drives the emergence of factions. This results follows from the fact that factions are prevented by not learning at all from those agents that hold the same opinion. If the number of issues is large, the dynamics becomes trapped and the society does not evolve into factions and a distribution of moderate opinions is observed. We also study the less realistic, but technically simpler synchronous case showing that global consensus is a fixed point. However, the approach to this consensus is glassy in the limit of large societies if agents adapt even in the case of agreement., 16 pages, 10 figures, revised version

We employ the Bayesian framework to define a cointegration measure aimed to represent long term relationships between time series. For visualization of these relationships we introduce a dissimilarity matrix and a map based on the Sorting Points Into Neighborhoods (SPIN) technique, which has been previously used to analyze large data sets from DNA arrays. We exemplify the technique in three data sets: US interest rates, monthly inflation rates and gross domestic product growth rates., 13 pages, 8 figures, extended version submitted to Physica A

We investigate the Heston model with stochastic volatility and exponential tails as a model for the typical price fluctuations of the Brazilian S\~ao Paulo Stock Exchange Index (IBOVESPA). Raw prices are first corrected for inflation and a period spanning 15 years characterized by memoryless returns is chosen for the analysis. Model parameters are estimated by observing volatility scaling and correlation properties. We show that the Heston model with at least two time scales for the volatility mean reverting dynamics satisfactorily describes price fluctuations ranging from time scales larger than 20 minutes to 160 days. At time scales shorter than 20 minutes we observe autocorrelated returns and power law tails incompatible with the Heston model. Despite major regulatory changes, hyperinflation and currency crises experienced by the Brazilian market in the period studied, the general success of the description provided may be regarded as an evidence for a general underlying dynamics of price fluctuations at intermediate mesoeconomic time scales well approximated by the Heston model. We also notice that the connection between the Heston model and Ehrenfest urn models could be exploited for bringing new insights into the microeconomic market mechanics., Comment: 20 pages, 9 figures, to appear in Physica A

We employ the methods presented in the previous chapter for decoding corrupted codewords, encoded using sparse parity check error correcting codes. We show the similarity between the equations derived from the TAP approach and those obtained from belief propagation, and examine their performance as practical decoding methods.

An exact solution to a family of parity check error-correcting codes is provided by mapping the problem onto a Husimi cactus. The solution obtained in the thermodynamic limit recovers the replica symmetric theory results and provides a very good approximation to finite systems of moderate size. The probability propagation decoding algorithm emerges naturally from the analysis. A phase transition between decoding success and failure phases is found to coincide with an information-theoretic upper bound. The method is employed to compare Gallager and MN codes., Comment: 7 pages, 3 figures, with minor corrections

We investigate the performance of parity check codes using the mapping onto Ising spin systems proposed by Sourlas. We study codes where each parity check comprises products of K bits selected from the original digital message with exactly C checks per message bit. We show, using the replica method, that these codes saturate Shannon's coding bound for $K\to\infty$ when the code rate K/C is finite. We then examine the finite temperature case to asses the use of simulated annealing methods for decoding, study the performance of the finite K case and extend the analysis to accommodate different types of noisy channels. The connection between statistical physics and belief propagation decoders is discussed and the dynamics of the decoding itself is analyzed. Further insight into new approaches for improving the code performance is given., Comment: 32 pages, 12 figures, to appear in PRE

We study the online dynamics of learning in fully connected soft committee machines in the student-teacher scenario. The locally optimal modulation function, which determines the learning algorithm, is obtained from a variational argument in such a manner as to maximise the average generalisation error decay per example. Simulations results for the resulting algorithm are presented for a few cases. The symmetric phase plateaux are found to be vastly reduced in comparison to those found when online backpropagation algorithms are used. A discussion of the implementation of these ideas as practical algorithms is given.

The ways in which natural selection can allow the proliferation of cooperative behavior have long been seen as a central problem in evolutionary biology. Most of the literature has focused on interactions between pairs of individuals and on linear public goods games. This emphasis has led to the conclusion that even modest levels of migration would pose a serious problem to the spread of altruism through population viscosity in group structured populations. Here we challenge this conclusion, by analyzing evolution in a framework which allows for complex group interactions and random migration among groups. We conclude that contingent forms of strong altruism that benefits equally all group members, regardless of kinship and without greenbeard effects, can spread when rare under realistic group sizes and levels of migration, due to the assortment of genes resulting only from population viscosity. Our analysis combines group-centric and gene-centric perspectives, allows for arbitrary strength of selection, and leads to extensions of Hamilton's rule for the spread of altruistic alleles, applicable under broad conditions.

In this study we have used fluorescence spectroscopy to determine the post-mortem interval. Conventional methods in forensic medicine involve tissue or body fluids sampling and laboratory tests, which are often time demanding and may depend on expensive analysis. The presented method consists in using time-dependent variations on the fluorescence spectrum and its correlation with the time elapsed after regular metabolic activity cessation. This new approach addresses unmet needs for post-mortem interval determination in forensic medicine, by providing rapid and in situ measurements that shows improved time resolution relative to existing methods.

This thesis presents three main contributions to the understanding of machine learning models by making use of statistical physics tools. First, we investigate the possible relation between the renormalisation group and restricted Boltzmann machines trained with two-dimensional ferromagnetic Ising data, pointing out possible misleadings in preliminary proposals to explicitly construct this bridge. Secondly, we examine the convergence behaviour of stochastic gradient descent in high-dimensional two-layer neural networks. By building up on classic statistical physics approaches and extending them to a broad range of learning rate, time scales, and hidden layer width, we construct a phase diagram describing the various learning scenarios arising in the high-dimensional setting. We also discuss the trade-off between learning rate and hidden layer width, which has been crucial in the recent mean-field theories. Thirdly, we study both Bayes-optimal and empirical risk minimization generalisation errors of the multi-class teacher-student perceptron. We characterise a first-order phase transition arising in the Bayes-optimal performance for Rademacher teacher weights and observe that, for Gaussian teachers, regularised cross-entropy minimisation can yield to close-to-optimal performance. Esta tese apresenta três contribuições principais para a compreensão de modelos de aprendizado de máquina por meio de ferramentas de física estatística. Primeiramente, investigamos a possível relação entre o grupo de renormalização e máquinas de Boltzmann restritas treinadas com dados amostrados do modelo de Ising ferromagnético bidimensional, apontando problemas em propostas preliminares para construir explicitamente essa ponte. Em segundo lugar, examinamos o comportamento da convergência do algoritmo de descida do gradiente estocástico em redes neurais de duas camadas no limite de alta dimensão. Com base nas abordagens clássicas da física estatística e estendendo-as para uma ampla faixa de taxa de aprendizado, escalas de tempo e tamanho da camada oculta, construímos um diagrama de fase descrevendo os vários cenários de aprendizado que surgem no limite de alta dimensionalidade. Também discutimos a relação entre a taxa de aprendizado e o tamanho da camada oculta, o que tem sido crucial nas recentes teorias de campo médio. Em terceiro lugar, estudamos os erros de generalização Bayes-ótimo e empírico do perceptron multi-classe no cenário professor-aluno. Caracterizamos uma transição de fase de primeira ordem na performance Bayes-ótimo para professores com acoplamentos Rademacher e observamos que, para professores com acoplamentos gaussianos, a minimização de entropia cruzada com regularização pode resultar em desempenho próximo ao Bayes-ótimo.

O risco de crédito é a incerteza envolvendo a capacidade de uma firma de honrar seus compromissos financeiros e suas dívidas. Apesar da relevância deste tipo de risco, apenas recentemente as instituições financeiras passaram a se preocupar em testar modelos mais rigorosos e sofisticados para a correta apuração do risco de crédito que provem de desenvolvimento do tema de modelagem do risco de default, essa dissertação propõe um modelo para quantificar este risco em um nível agregado. A abordagem utilizada e baseada no modelo de Merton [1974] para o apreçamento de títulos corporativos e utiliza técnicas de otimização de forma a estimar o risco de um portfólio composto por debêntures. Como resultado, encontra-se uma medida de risco mais conservadora que o value at risk (VaR), usando um modelo simples e de baixo custo computacional. Neste trabalho, também e resolvido o problema de alocação ótima para a carteira de debêntures citada. Credit risk is the uncertainty surrounding a firm\'s ability to accomplish its financial obligations. Despite the historical relevance of this kind of risk, only recently the financial institutions are more concerned about implementing sophisticated systems in an attempt to model correctly the credit risk arising from their business lines. In order to collaborate with the recent development of credit risk modeling, this dissertation proposes a methodology to quantify default risk in a cross-section of corporate bonds. The approach is based both on the Merton\'s corporate bond pricing model [1974] and on optimization techniques in order to calculate the risk of a portfolio composed by corporate bonds. As a result, we find a risk measure that is more conservative than value at risk (VaR), using a simple and low-cost model. In this work, we also solve the problem of optimal portfolio allocation under default risk.

O objetivo desta dissertação é apresentar um modelo de inferência não linear para alocação de carteira baseado em redes neurais multicamada. A primeira parte do modelo concentra-se na predição dos retornos dos ativos. As redes neurais utilizam os preços de mercado observados para extrair informações sobre as expectativas dos participantes do mercado ou sobre a distribuição implícita dos retornos ou o mecanismo de apreçamento do mercado, tornando um poderoso modelo de predição dos retornos. Com base nos retornos esperados, a alocação das proporções de investimentos é feita por um algoritmo de otimização com controle de risco implícito. Para implementação do modelo é utilizada uma carteira contendo ações negociadas na Bolsa de Valores de São Paulo e os resultados são comparados com o tradicional modelo de média-variância elaborado por Markowitz (1952) This work proposes a non-linear inference model for optimal asset allocation based on multilayer neural networks . The first part focuses on the expected assets returns prediction model. Based on the historical market prices, the neural networks extract valuable information about the participant\'s expectation or the implicit returns distributions or even the market pricing mechanism, becoming a powerful prediction model. An optimization algorithm makes the investment proportional allocations with implicit risk control based on the expected returns. The model is implemented using a portfolio made by stocks traded at the São Paulo Stock Exchange and the results are compared against the tradicional mean-variance model written by Markowitz (1952)

Mensurar risco operacional é um grande desafio para as instituições financeiras hoje. À medida que a data de publicação do Novo Acordo de Capital da Basiléia se aproxima, a modelagem de risco operacional está se tornando cada vez mais importante para as instituições financeiras e órgãos reguladores. Os bancos e as empresas financeiras estão em busca de metodologias adequadas para mensuração e proteção contra as perdas de risco operacional. Neste estudo nós implementamos o Método de Distribuição de Perdas como base para mensuração do risco operacional. Adicionalmente à abordagem clássica, nós introduzimos um modelo de distribuição de perdas com recuperações como uma extensão ao modelo padrão. Os resultados obtidos neste estudo foram bastantes motivadores e abrem caminho para futuras pesquisas Measuring operacional risk is a major challenge in running financial institutions. As the publication date of the New Basel Capital Accord sets closer, modeling operacional risk is becoming increasingly important for financial institutions and regulators. Banks and financial institutions are looking for adequate methodologies to measure and protect against losses from operacional risk. In this work we implement a Loss Distribution Approach (LDA) as plataform for measuring operacional risk. In addition to the classical model, we introduce a loss distribution model with recoveries as an extension to standard model. The results achieved in this work are promissing and motivate future research

Neste trabalho avaliamos a habilidade de um modelo conexionista no reconhecimento de possíveis padrões apresentados em séries financeiras. Através da abordagem de um problema de divisão em classes, utilizamos uma rede multicamada do tipo Êeed-6orward tendo como algoritmo de aprendizado back-propagation otimizado pelo método gradiente conjugado escalonado. Tomando como entrada os retornos diários das séries de lbovespa, Telemar PN e Petrobrás PN em períodos semanais, diversas topologias coram treinadas, variando pelo número de unidades ocultas e o número de iterações no critério de parada, gerando como saída ordens de compra e venda dadas pela previsão do movimento do preço do ativo para a semana seguinte. As arquiteturas treinadas foram avaliadas com base na taxa de classificação e lucratividade, e os resultados obtidos confirmaram a validação do modelo proposto. This work presents the performance valuation of a conexionist model for the pattern recognition of financial series. We adopted the approach of classification problem for a back-propagation feed-forward multi-layer network optimized by the scaled conjugated gradient method, applied to the lbovespa, Telemar PN and Petrobrás PN daily retums series, grouped in weekly periods, as input. Several topologies were trained with different number of hidden units and iterations, which was the stop criterion. The output was the buy or self predicted order of the specinic asset for next week. We evaluated the trained architectures based on the classification and pronitability values. The results provided the validation of the proposed modal.

In supervised learning, we often have access to a limited sample, in size or quality (e.g., lack of labels), of the population/distribution of interest, for which we want to create predictive models. However, it is possible that we have less limited access to data sampled from another population, more or less similar to the one of interest. Training models using only data from the population of interest may be impossible or result in sub-optimal models, so it would be interesting to use data from the other population in order to get better results or make training possible. In these situations, as the distributions of interest and the one that we can sample with few restrictions are different, we say that there is dataset shift. In dataset shift situations, employing domain adaptation techniques when training supervised models is essential for theoretical guarantees of good results in the population of interest. The two kinds of dataset shift we will discuss about in this work are covariate shift and concept drift/shift. The main objectives of this work are: (i) to review the main concepts and methods related to covariate shift and covariate shift adaptation; (ii) propose contributions to the covariate shift adaptation literature, connecting concepts present in modern literature; (iii) propose the decomposition of the dataset shift into covariate shift and expected concept drift/shift as a new approach to better understand situations in which we deal with dataset shift. No aprendizado supervisionado, muitas vezes temos acesso a uma amostra limitada, em tamanho ou qualidade (e.g., falta de rotulos), de dados da populacao/distribuicao de interesse, para a qual queremos criar modelos preditivos. No entanto, e possivel que tenhamos acesso pouco limitado a dados amostrados de outra populacao, mais ou menos parecida com a de interesse. Treinar modelos utilizando somente dados da populacao de interesse pode ser impossivel ou resultar em modelos sub-otimos, entao seria interessante utilizar os dados provenientes da outra populacao a fim de obter melhores resultados ou tornar o treinamento possivel. Nessas situacoes, como as distribuicoes de interesse e aquela que podemos amostrar com poucas restricoes sao diferentes, dizemos que ha dataset shift. Em situacoes de dataset shift, empregar tecnicas de adaptacao de dominio ao treinar modelos supervisionados e essencial para garantias teoricas de bons resultados na populacao de interesse. Os dois tipos de dataset shift que discutiremos neste trabalho sao covariate shift e concept drift/shift. Os objetivos principais deste trabalho sao: (i) revisar principais conceitos e metodos relacionados ao covariate shift e covariate shift adaptation; (ii) propor contribuicoes para a literatura de covariate shift adaptation, conectando conceitos presentes em discussoes atuais; (iii) propor a decomposicao do dataset Shift em covariate shift e concept drift/shift esperado como uma nova abordagem para melhor entendimento de situacoes em que lidamos com dataset shift.

The essence of Machine Learning modelling may be summarized as: to unravel the implicit pattern in the data by having access to only a finite number of samples. The theory which studies this process is rich, and two quantities are of particular importance: the performance errors inside and outside the sample. The error inside the sample is called the training error, and is calculated over the set used to optimize the models parameters. The outside error is the average error amongst all samples, and may be understood as the true error. Although the final objective is to construct a model with low true error, we only have access to the training error, which is an empirical estimation. Thus, in order to deduce the general pattern in the data, is necessary that both are similar.The distance between those errors is called the generalization gap, and much of the theory is dedicated to study its properties and upper bounds, so that we may understand under what circumstances it is controlled. The gap is a measure of the models ability to properly induce the global pattern, and is a major topic in all applied instances of Machine Learning.The classical view of statistics correlates the generalization property with the model capacity to fit patterns in the data. The reasoning behind this is that, being capable of fitting many configurations, the model is prone to read noise in the sample, and thus perform poorly in general. However, the definition of a models complexity is loose, and while it usually translates to the number of parameters, there is one hypothesis space which seemingly escapes this intuition. That is the case of Neural Networks. Using Neural Networks with many layers (Deep learning) is proving to be the best modelling paradigm for many benchmark problems, and many of the advances in the industry are due to their success. However, this seemingly goes against what classical Statistical Learning theory states about generalization and complexity, since Deep networks are capable offitting many patterns. Indeed, there has been experiments showing that networks may fit even random labels.This apparent paradox is an open question in the field and the main topic of this work.After a introduction and overview of the classical understanding of generalization, we introduce the work of [20], which is the central to our contributions. In it a new approach named Analytical Learning is proposed, aiming to complement the classical one, hopefully bringingsome insights about the apparent contradiction emerged from Deep Learning. Instead of analyzing probabilistic bounds, in this paper the generalization gap is studied in a context where the predictor and the dataset are fixed. By doing so, we prevent the pessimistic cases, and a tighter bound is hopefully achieved. Additionally, it provides a more real scenario, since in practice usually the data is given. The main result of [20] bounds the gap involving a term related to the data and another related to the loss function\'s Hardy-Kruase Variation. Our main contribution revolves around tracing similarities between this variation term with the stability concept studied in the classical approach of generalization, making parallels with what may be understood in the Analytical case as information.The main idea is that the loss function variation decreases if the partial derivatives of the predictor, according to the instance space, are close to the oracles. The derivatives in this sense may be understood as how much information the function is reading, since it measures the impact of a certain dimension in a local prediction. Thus, if the predictor reads information similarly to the oracle, then we guarantee a low gap. With this, we argue that the partial derivatives of the predictor are the main measure of regularization in the analytical sense. One of the advantages of this is simplicity: rewriting the SGD (Stochastic Gradient Descent) optimization step in the function space, we have an easy way to investigate the evolution of the models complexity during training.Furthermore, we use this interpretation to develop on relative recent papers trying to tackle the generalization paradox in deep learning, [28] and [37]. In the former we make an extensive analysis. while in the latter we make a more brief qualitative approach, showing how our interpretation relates with their result. In [28], the complexity of networks is studied through the lens of Fourier Theory. There is shown that the space of ReLU (Rectifier Linear Unit) networks has a high spectral decay:during optimization, the increments in the k-th harmonic caused by the weights updates decreases with at least k^2. This means that high frequencies magnitudes in this space are naturally damped during training, suggesting an inherent regularization property. However,at no moment in [28] the generalization gap is mentioned, and so it is not clear if the spectral decay is enough to guarantee a good estimation of the true error. Motivated by this, we show a bound using the Hardy-Krause Variation on splines which decreases with the degree, justifying the special properties of ReLU activation functions.In [37] the main theorem shows that if the architecture of the network follows a funnel pattern (when the number of neurons in the network decreases as we go deeper), then increasing the number of layers actually reduces the generalization gap, thus supporting the deep learning approach. This happens because the funnel like architecture forces a nontrivial kernel in the linear transformations, which translates into a loss of information. This implies that as the number of layers increases, the information shared between the final layerand the dataset decreases, making the prediction less data dependant and thus regularized.This result relates closely to our interpretation of information in the analytical sense.Having a non trivial kernel means that in some cases the prediction is constant with respect to disruptions in certain dimensions. This means that the overall variation (in the sense ofderivatives) will be smaller, which according to Analytical Learning translates to a smaller generalization gap. A essência do Aprendizado de Máquina pode ser resumida como: revelar padrões implícitos nos dados tendo em posse apenas uma amostra finita. A Teoria que estuda essa questão é vasta, e duas quantidades são de particular importância: os erros do modelo dentro e fora da amostra. O primeiro é chamado de erro de treinamento, e mede a performance dentro do conjunto usado para otimizar. O segundo é a média do erro em todas as amostras, e pode ser compreendido como o erro real. Apesar do verdadeiro indicador de performance ser o erro real, podemos calcular apenas a performance dentro da amostra, que é uma estimativa empírica. Portanto, para deduzir o padrão geral, é necessário que tais erros sejam similares. A distância entre estes erros é chamada de generalization gap, e grande parte da teoria se dedica a estudar as suas propriedades e limites superiores. Ele é uma medida da habilidade do modelo de induzir corretamente o comportamento global, e é um tópico central em todas as aplicações de Aprendizagem de Máquina. A visão clássica da Estatística correlaciona a propriedade de generalização com a capacidade do modelo de ajustar os dados. A ideia é de que, se o modelo é capaz de performar em diversas configurações, então ele será sensível a ruídos presentes, e então performará mal fora da amostra. Entretanto, a definição de complexidade de um modelo é vaga, e apesar de muitas vezes ser caracterizado pelo número de parâmetros, existe um espaço de hipóteses que aparentemente escapa essa intuição. É o caso das redes neurais profundas. Fazer uso de redes com muitas camadas (aprendizado profundo) está provando ser um dos melhores paradigmas de modelagem em diversos problemas de referência, e os avanços da indústria se devem em grande parte ao seu grande sucesso. Entretanto, isso aparentemente contradiz o que a teoria de Aprendizado Estatístico nos fala sobre complexidade e generalização, já que redes profundas são capazes de ajustar diversos padrões. De fato, existem experimentos que mostram que elas podem ajustar até variáveis respostas aleatórias. Esse possível paradoxo é uma questão em aberto na área e é o principal tópico neste estudo. Após uma introdução e revisão sobre a teoria clássica de generalização, nós introduzir o trabalho de [20], que é central para as nossas contribuições. Nele é proposta uma nova abordagem chamada de Analytical Learning com o intuito de complementar o entendimento clássico, almejando trazer uma nova visão sobre essa aparente contradição revelada pelo aprendizado profundo. Neste artigo, ao invés de analisar limites de natureza probabilística, o generalization gap é estudado em um contexto onde o preditor e o conjunto de dados é fixo. Assim, desconsideramos os casos pessimistas, e uma majoração mais precisa poderia ser alcançada. Além disso, essa proposta considera um cenário mais real, pois na prática a amostra é dada. O principal resultado de [20] é uma majoração que envolve um termo relacionado aos dados, e um outro relacionado à Variação de Hardy-Krause da função perda. Nossa principal contribuição envolve traçar similaridades entre esse termo de variação com a noção de estabilidade estudada na abordagem estatística da generalização, fazendo paralelos com o que pode ser entendido no caso Analítico como informação. A ideia principal é que a variação da função perda decresce se as derivadas parciais do preditor são próximas das do oráculo. Dessa forma, as derivadas nesse sentido podem ser compreendidas como a quantidade de informação que está sendo usada, já que ela mede o impacto de uma certa dimensão na predição local. Portanto, se o preditor lê a informação da mesma forma que a função que gerou os dados, então podemos garantir uma aproximação do erro de treinamento com o erro real. Com isso, argumentamos que a derivada parcial é a principal forma de medir a regularização de um modelo no sentido analítico. Uma das vantagens dessa abordagem é simplicidade: reescrevendo o passo de otimização do DGE (descida pelo gradiente estocástico) no espaço das funções, adquirimos uma forma simples de investigar a evolução da complexidade do modelo durante o treinamento. Ademais, usamos essa interpretação para elaborar em recentes artigos abordando o problema da generalização em aprendizado profundo, [28] e [37]. No primeiro fazemos uma análise extensiva, enquanto no segundo fazemos uma análise qualitativa mais abreviada, mostrando como nossa interpretação se relaciona com os resultados neles presentes. Em [28], a complexidade das redes neurais é estudada sob a lente da Teoria de Fourier. Nele é mostrado que o espaço de redes ReLU (Rectifier Linear Unit) apresenta um decaimento espectral particularmente intenso: durante a otimização, os incrementos no k-ésimo harmônico decorrente da atualização dos pesos decresce com pelo menos k². Isso significa que as magnitudes de frequências mais altas são naturalmente amortecidas durante o treinamento, sugerindo uma propriedade regularizadora intrínseca no espaço. Apesar disso, em momento algum [28] menciona o generalization gap, e portanto não é claro se o decaimento espectral é suficiente para garantir que o erro de treinamento seja uma boa estimativa do erro real. Motivados por isso, mostramos um limite superior usando a Variação de Hardy-Krause em splines que decresce com o grau, justificando as propriedades especiais da função de ligação ReLU. O principal teorema em [37] mostra que, para arquiteturas com um formato de funil (quando o número de neurônios decresce à medida que nos aprofundamos na rede), aumentar o número de camadas implica em uma redução no generalization gap, fundamentando portanto o aprendizado profundo nesses casos. Isso ocorre pois uma arquitetura com tal formato força núcleos não triviais nas transformações lineares, o que implica em uma perda de informação. Ou seja, ao aumentar o número de camadas, a quantidade de informação nos dados usada pelo preditor diminui, tornando a predição menos dependente da amostra, e portanto regularizada. Esse resultado se relaciona muito com a nossa interpretação de informação no sentido analítico. Ter um núcleo não trivial na arquitetura significa que em alguns casos a predição vai permanecer inalterada com relação à mudanças em certas dimensões. Isso implica que a variação geral (no sentido de derivadas) será menor, o que de acordo com a teoria do Aprendizado Analítico, acarreta em uma melhor estimativa do erro real.

In this work we present an agent based model for community for- mation on societies from the dynamics for opinion exchange and dis- trust between agents. The development framework relies on Proba- bility Theory, Machine Learning and MaxEnt principles, from which we derive a new form of Entropic Dynamics for Information Process- ing Systems, in particular for simple Neural Networks, the Entropic Learning Dynamics. The resulting theory and model for agents interactions are an- alyzed in a few scenarios, chosen due to their intuitive nature and connection with possible real scenarios. We started the analysis with the properties of systems with 2 agents interacting under different trust and opinion initial conditions, and showed that the dynamics is not trivial nor leads to results with absurd interpretations. Then, we analyzed the properties of societies with many agents, varying the distribution of opinions and distrust, as well as the subjects they could discuss, and found different situations leading to consensus, polarization and even frustrated state like a spin glass. Finally, we applied the model to study the behavior of judges due the availability of data regarding the influence of political party ideology in the voting patterns of judges in the U.S Court of Appeals. In this application, although just a caricature aiming just to provide a quantitative tool for experts in the field, we tried to mimic the typical situations a panel of three judges would be submitted, attributing to agents representing judges a common knowledge of the Law, a Party bias, a Personality and exposing them to different distrust scenarios. The only scenario capable of reproducing the available data had to consider similar contributions of the Law, Party bias and Personality, as well as having Courteous and Certain judges, who extended the courtesy of attributing low distrust to agents of the opposing political party. Neste trabalho apresentamos um modelo para a formação de comu- nidades em sociedades a partir da dinâmica de trocas de opinião e de- sconfiança entre agentes. A teoria é desnvolvida com base na Teoria de Probabilidades, Aprendizado de Máquina no princípio de Máx- ima Entropia (MaxEnt), dos quais deduzimos uma nova forma de Dinâmica Entrópica para Sistemas de Processamento de Informação, em particular para Redes Neurais simples, a Dinâmica Entrópica de Aprendizado. A teoria e o modelo para a interação de agentes foram analisa- dos em alguns cenários, escolhidos pela natureza intuitiva e de pos- sível associação com circunstâncias reais. Começamos com a análise de sistemas com 2 agentes interagindo em diferentes condições de opinião e desconfiança iniciais, mostrando que a dinâmica deduzina não apresenta apenas fases triviais e não leva a interpretações ab- surdas. Em seguida, analisamos as propriedades de sociedades com muitos agentes, variando a distribuição de opiniões e desconfianças iniciais, bem como os assuntos que poderiam ser discutidos pelos agentes, mostrando que diferentes condições levam a consenso, po- larização ou até mesmo a uma fase frustrada como um video de spin. Finalizamos com uma aplicação do modelo para o comporta- mento dos juízes, dada a disponibilidade de dados a respeito da influência ideológico-partidária nos padrões de decisão judicial da Corte de Apelações dos EUA. Nesta aplicação, apesar de se apresen- tar como uma caricatura com o objetivo de dispor uma ferramenta quantitativa para especialistas na área, tentamos imitar as situações típicas às quais um colégio judicial composto por três juízes estaria submetido, atribuindo aos agentes representantes dos juízes um con- hecimento da Lei, um viés do Partido, uma Personalidade e os ex- pondo a diferentes cenários de desconfiança. O único cenárioi capaz de reproduzir o padrão empírico de votações requer que os juízes se- jam representados por agentes que atribuem pesos similares à Lei, ao viés Paridário e à Pesonalidade, bem como que extendam a Cortesia Certeira de confiar em juízes com vieses políticos opostos.

A concepção e operação de estratégias de compra e venda de ações por mecanismos de inteligência artificial ganharam escala na última década visando resultados acima da média do mercado para seus usuários, em geral, hedge funds, investidores institucionais e grandes bancos de investimentos. O aprendizado de máquina se tornou o arcabouço central no desenvolvimento desses processos, em função de sua extraordinária capacidade de revelação de padrões escondidos em um universo obscuro de dados, que até então apenas dificultava o processo de tomada de decisão tradicional, realizado pelos agentes do mercado de capitais. Em particular, este trabalho visa compreender se no mercado acionário brasileiro é possível tomar decisões consistentes, em um processo diário de seleção de ações, com auxílio de redes neurais recorrentes do tipo Long Short-Term Memory (LSTM), que em determinados níveis de profundidade e conectividade são conhecidas como deep learning. Os modelos baseados na arquitetura LSTM são propícios para a extração de informações relevantes de longas sequências de dados, portanto, são naturalmente aplicáveis ao problema de previsão do retorno futuro de ações a partir de séries temporais financeiras históricas, como os preços diários das próprias ações, os índices gerais de mercado, a cotação do dólar, entre outras. Assim, foi proposta uma metodologia que utiliza redes neurais LSTM, em conjunto com tais séries temporais, como modelos preditivos para apoiar a tomada de decisão no mercado acionário brasileiro. Com isso, diversos experimentos foram realizados para encontrar a melhor arquitetura e verificar seu potencial econômico, compreendendo as ações constituintes do Índice Bovespa (Ibovespa) no período entre 2007 e 2018. Em linha com as evidências apontadas em estudos prévios, os modelos apresentaram ótimos resultados, mesmo em configurações relativamente simples. Grandes estruturas LSTM tiveram performance ligeiramente inferior às arquiteturas menores. Além disso, observou-se que o conjunto de informações complementares aos preços das ações melhoraram o aprendizado e a acurácia dos modelos, sobretudo os índices de mercado e a taxa de câmbio. Em termos econômicos, o retorno médio anual bruto de uma carteira que simula compras diárias de 10 ações atingiu a marca de 22,3%. Esse resultado supera em mais de 100% o retorno médio das ações constituintes do Ibovespa, no mesmo período. Sobretudo, a curva de rentabilidade dessa carteira foi consistentemente maior que a curva referente ao Ibovespa. As evidências encontradas sugerem, portanto, que a metodologia proposta é capaz de revelar fortes variáveis preditivas e proporcionar ganhos de capital relevantes, através da aplicação das redes neurais LSTM no mercado brasileiro. The design and operation of stock buying and selling strategies by artificial intelligence mechanisms has gained scale over the past decade aiming at above-average market outcomes for its users, generally hedge funds, institutional investors and large investment banks. Machine learning has become the central framework in the development of these processes, due to its extraordinary ability to reveal patterns hidden in a dark universe of data, which until then only hindered the traditional decision-making process undertaken by market players. In particular, this work aims to understand if in the Brazilian stock market it is possible to make consistent decisions, in a daily stock selection process, with the aid of some type of recurrent neural networks called Long Short-Term Memory (LSTM), which at certain depth levels and connectivity are known as deep learning. Models based on the LSTM architecture are lucky to extracting relevant information from long data strings, so they are naturally applicable to the problem of predicting future stock returns from historical financial time series, such as daily stock prices, the general market indexes, the dollar quotation, among others. Thus, a methodology was proposed that uses LSTM neural networks, together with such time series, as predictive models to support decision making in the Brazilian stock market. Several experiments were performed to find the best architecture and verify its economic potential, including the actions that composed the Bovespa Index (Ibovespa) in years between 2007 and 2018. In line with the evidences pointed out in previous studies, the models presented excellent results, even in relatively simple configurations. Large LSTM structures performed slightly lower than smaller architectures. In addition, it was observed that the complementary set of stock price information improved the learning and accuracy of the models, especially the market indexes and the exchanges rates. In economic terms, the average annual return on a portfolio that simulates daily purchases of 10 shares reached 22.3% annually, excluding fees and taxes. This result exceeds by more than 100% the average return of Ibovespa\'s constituent shares in the same period. Withal, the portfolio yield curve was consistently higher than the Ibovespa curve. Therefore, there is positive evidence on the temporal consistency of the proposed methodology, on its ability to reveal strong predictive variables, and thereafter potential application of LSTM neural networks in the Brazilian market.

While most statistical learning methods are designed to work with data stored in a single table, many large datasets are stored in relational database systems. Probabilistic Relational Models (PRM) extend Bayesian networks by introducing relations and individuals, thus making it possible to represent information in a relational database. However, learning a PRM from relational data is a more complex task than learning a Bayesian Network from \"flat\" data. The main difficulties that arise while learning a PRM are establishing what are the legal dependency structures, searching for possible structures, and scoring them. This thesis focuses on the development of a novel approach to learn the structure of a PRM, describes a package in the R language to support the learning framework, and applies it to a real, large scale scenario of a city named Atibaia, in the state of São Paulo, Brazil. The research is based on a database combining three different tables, each representing one class in the domain of study. The first table contains 27 attributes from 110,816 citizens of Atibaia. The second table contains 9 attributes from 20,162 companies located in the city. And finally, the third table has 8 attributes from 327 census sectors (small territorial units that comprise the city of Atibaia). The proposed framework is applied to learn a PRM structure and parameters from the database. The model is used to verify if the Social Class of a person can be explained by the location where they live, their neighbors, and the companies nearby. Preliminary experiments have been conducted and a paper published in the 2017 Symposium on Knowledge Discovery, Mining and Learning (KDMiLe). The algorithm performance was further evaluated by extensive experimentation, and a broader study using Serasa Experian data was conducted. Finally, the package in the R language that supports our method was refined along with proper documentation and a tutorial. Embora a maioria dos métodos de aprendizado estatístico tenha sido desenvolvida para se trabalhar com dados armazenados em uma única tabela, muitas bases de dados estão armazenadas em bancos de dados relacionais. Modelos Probabilísticos Relacionai (PRM) estendem Redes Bayesianas introduzindo relações e indivíduos, tornando possível a representação de informação em uma base de dados relacional. Entretanto, aprender um PRM através de dados relacionais é uma tarefa mais complexa que aprender uma Rede Bayesiana de uma única tabela. As maiores dificuldades que se impõe enquanto se aprende um PRM são estabelecer quais são as estruturas de dependência legais, procurar por possíveis estruturas, e avalia-las. Esta tese foca em desenvolver um novo método de aprendizado de estruturas de PRM, descrever um pacote na linguagem R que suporte este método e aplica-lo a um cenário real e de grande escala, a cidade de Atibaia, no estado de São Paulo, Brasil. Esta pesquisa está baseada em uma base de dados combinando três tabelas distintas, cada uma representando uma classe no domínio de estudo. A primeira tabela contém 27 atributos de 110.816 habitantes de Atibaia, e a segunda tabela contém 9 atributos de 20.162 empresas da cidade. Por fim, a terceira tabela possui 8 atributos para 327 setores censitários (pequenas unidades territoriais que formam a cidade de Atibaia). A proposta é aplicada para aprender-se a estrutura de um PRM e seus parâmetros através desta base de dados. O modelo foi utilizado para verificar se a classe social de uma pessoa pode ser explicada pelo local onde ela vive, seus vizinhos e as companhias próximas. Experimentos preliminares foram conduzidos e um artigo foi publicado no Symposium on Knowledge Discovery, Mining and Learning (KDMiLe). O desempenho do algoritmo foi reavaliada através de extensiva experimentação, e um estudo mais amplo foi conduzido com os dados da Serasa Experian. Por fim, o pacote em R que suporta o método proposto foi refinado, e documentação e tutorial apropriado foram descritos.

Neste trabalho, Compressed Sensing é introduzido do ponto de vista da Física Estatística. Após uma introdução sucinta onde os conceitos básicos da teoria são apresentados, incluindo condições necessárias para as medições e métodos básicos de reconstrução do sinal, a performance típica do esquema Bayesiano de reconstrução é analisada através de um cálculo de réplicas exposto em detalhe pedagógico. Em seguida, a principal contribuição original do trabalho é introduzida --- o algoritmo Bayesiano de Compressed Sensing Online faz uso de uma aproximação de campo médio para simplificar cálculos e reduzir os requisitos de memória e computação, enquanto mantém a acurácia de reconstrução do esquema offline na presença de ruído aditivo. A última parte deste trabalho contém duas extensões do algoritmo online que permitem reconstrução otimizada do sinal no cenário mais realista onde conhecimento perfeito da distribuição geradora não está disponível. In this work, Compressed Sensing is introduced from a Statistical Physics point of view. Following a succinct introduction where the basic concepts of the framework are presented, including necessary measurement conditions and basic signal reconstruction methods, the typical performance of the Bayesian reconstruction scheme is analyzed through a replica calculation shown in pedagogical detail. Thereafter, the main original contribution of this work is introduced --- the Bayesian Online Compressed Sensing algorithm makes use of a mean-field approximation to simplify calculations and reduce memory and computation requirements, while maintaining the asymptotic reconstruction accuracy of the offline scheme in the presence of additive noise. The last part of this work are two extensions of the online algorithm that allow for optimized signal reconstruction in the more realistic scenarios where perfect knowledge of the generating distribution is unavailable.

No contexto dos sistemas complexos, o presente trabalho investiga 3 estratégias de precificação:(1)desnatação,(2) penetração e (3)aprendizado, na difusão de carros elétricos em diferentes contextos.Por meio da modelagem baseada em agentes com 100.000 entidades autônomas, o primeiro modelo testa três situações relacionados à demanda energética:(1)desabastecimento,(2)estabilidade e (3)crescimento moderado da demanda.A forte escassez de energia estimulou a rápida migração dos agentes aos carros elétricos. As três estratégias de precificação exibiram resultados similares em termos de faturamento e % na participação do mercado, no entanto a estratégia de penetração foi capaz de capturar uma parcela maior do mercado em menor tempo.No segundo modelo,3 diferentes comportamentos sociais são aplicadas aos agentes: (1)conservador,(2)racional e (3) social,em diferentes proporções afim de avaliar a influência da composição social na dinâmica difusora.No que concerne ao faturamento e % na participação do mercado, o segundo modelo detectou diferenças estatisticamente significativas para cada estratégia de precificação.Em sociedades proeminentemente conservadoras, as três estratégias não apresentaram indícios de diferença significativa no tocante relação ao faturamento,% na participação final do mercado e taxa de adoção média.Sociedades compostas majoritariamente por agentes racionais, apresentaram a mais rápida convergência aos carros elétricos,sendo este, o veículo mais caro.Isto se deve à percepção positiva do custo/benefício ao longo prazo.O maior faturamento é proveniente das sociedades compostas preponderantemente por agentes com atitudes sociais dado à compra e troca mais recorrente entre diferentes veículos no decorrer das interações.A estratégia de desnatação demonstrou maior versatilidade ao exibir performance superior com maior regularidade no que tange em faturamento em todas as composições sociais testadas.A estratégia de penetração exibiu índices maiores em taxa de adoção e faturamento em redes compostas integralmente por agentes com comportamentos sociais iguais,mas não foi possível detectar este padrão em redes parciais. Por fim, a estratégia de aprendizado apresentou o menor faturamento em todos os cenários, no entanto, sua taxa de adoção similar à estratégia de penetração, pode ser a estratégia de precificação mais crível e eficiente para empresas iniciantes In the context of complex systems,the following research investigated 3 pricing strategies:(1)skimming,(2)penetration and (3)learning, at electric car diffusion in several different scenarios. Through the agent-based modelling with 100.000 autonomous entities, the first model tested 3 situations related to energy demand:(1)severe shortage,(2)stability and (3)moderate growing of demand. The strong shortage of energy forced an fast-paced migration of agents towards the electric cars. The 3 strategies showed up similar results in terms revenues and market share, however the penetration strategy was able to capture a large part of the market faster than others. At the second model, 3 different social behaviors were implemented in each agent:(1)conservative,(2)rational and (3)social,in different proportions in order to assess social composition and its influence in the innovation diffusion process. Revenue and market share as concerned,the second model detected significant statistic difference for each pricing strategy. For societies predominantly conservative, all strategies did not show significant differences evidences regarding to revenue,market share and average adoption rate. Societies comprised mostly of rational agents presented the quickest convergence to electric cars, which it is the most expensive car. This is because a positive perception of benefits over cost in the long term.The largest revenue were derived from societies primarily composed of agents with social behaviors due to recurrent purchase and exchange between different vehicles over the interactions. Skimming strategy demonstrated greater versatility by displaying superior performance more regularly in terms of revenue in every social composition simulated. Penetration strategy exhibited highest rates of adoption and revenue in social networks composed entirely of agents with same social behavior, but it was not possible to detect such pattern at partial social networks. Finally, the learning strategy reported the lowest revenues at every scenario, none the less, its rate of adoption was equivalent to penetrations strategy rates, this strategy could be the most feasible and efficient to startups and small companies

O estudo de sistemas complexos nos ajuda a entender como regras locais simples podem gerar padrões agregados complexos e muitas vezes inesperados. Quando as regras são bem definidas e os padrões observáveis, o sistema pode ser modelado e seus resultados comparados. Um dos maiores desafios para a modelagem de sistemas complexos é definir a regra de interação responsável pelo comportamento complexo. Em dinâmica de opiniões, padrão complexo e inesperado pode ser o súbito consenso ou até mesmo a polarização, e objetivo, então, se torna verificar em que circunstâncias podemos observar pessoas concordarem ou descordarem. Embora haja uma série de modelos de dinâmica de opiniões para descrever como as pessoas interagem, cada um define a regra de formação da opinião de forma ad hoc. O modelo CODA (Continuous opinions and Discret Actions) propõe uma fundamentação teórica para os modelos de dinâmica de opiniões baseada em teoria de probabilidade. Suas aplicações se estendem desde estudos sobre inovação à epistemologia. Nesta dissertação, aprofundamos os estudos de epistemologia que envolvem o CODA, investigando principalmente o efeito da confiança no processo de confirmação cientifica. Nossas simulações corroboram investigações sociológicas e históricas sobre o papel fundamental da confiança no processo de aquisição e geração do conhecimento The study of complex systems helps us understand how simple local rules can generate complex and often unexpected aggregate patterns. When the rules are well defined and patterns observed, the system can be modeled and its results compared. One of the major challenges for modeling complex systems is to define a rule of interaction responsible for complex behavior. In opinion dynamics, complex and unexpected pattern may be the sudden consensus or even a polarization, so the aim it is to verify under what circumstances we can observe agreement or disagreement. Although there are a number of models of opinion dynamics to describe how people should interact with each other, each one defines an ad hoc opinion formation rule. The model of opinion dynamics CODA (Continuous Opinions and Discret Actions) proposes a theoretical framework for the models of opinion dynamics, based on probability theory. Their applications range from studies on innovation to epistemology. In this dissertation, we deepen the studies of epistemology that involve the CODA, investigating mainly the effect of the trust in the process of scientific confirmation. Our simulations corroborates sociological and historical researches on the role of trust in the process of acquisition and generation of knowledge

A desigualdade material hereditária teria surgido no registro arqueológico pela primeira vez por volta de 6.500 A.C. na região da Mesopotâmia, tendo posteriormente emergido de maneira independente em diferentes localidades e contextos, dentro de um intervalo de tempo relativamente curto. Muitas teorias foram propostas para explicar os fenômenos, porém sua compreensão permanece em aberto. Buscou-se, aqui, abordar a questão sob a perspectiva dos Sistemas Adaptativos Complexos, construindo um Modelo Baseado em Agentes que teve como base teórica a literatura que trata da questão, focada nos últimos vinte anos do debate, aprofundada em dois estudos de caso: a Mesopotâmia e a Costa Noroeste da América do Norte. Dos nove parâmetros testados oito apresentaram relação direta com a assimetria material dos indivíduos podendo colaborar com a emergência da desigualdade material hereditária, de forma que fomos levados a considerar a igualdade material e a cooperação presente entre os caçadores e coletores como propriedades decorrentes de uma estrutura social de criticalidade auto-organizada The hereditary material inequality would have emerged for the first time in the archaeological record around 6.500 BC in Mesopotamia, emerging after it repeatedly and independently in different localities and contexts, in a small time period. Many theories have been proposed but the complete understanding of the issue remains open to debate. Thus, we have proposed here an approach of the phenomenon under the Complex Adaptive Systems perspective, through which an agent-based model have been built. Constitutes the background of the model the working papers and text books written in the last two decades, which were later checked agains two case studies: Mesopotamia and Northwest Coast, in North America. Among the nine parameters tested in the model eight presented direct relation to the material asymmetry of individuals, potentially participating of the precesses involved in the emergence of material inequality. This results leads us to consider the possibility of the egalitarian and cooperative social structures of huntergatherers to be one of self-organized criticality

In this thesis, we explore the potential of employing Statistical Mechanics techniques to study economic systems, showing how such an approach could greatly contribute by allowing the study of very complex systems, exhibiting rich behavior such as phase transitions, criticality and glassy phases, which are not found in the usual economic models. We exemplify this potential via three specific problems: (i) a Statistical Mechanics framework for dealing with irrational consumers, in which the rationality is set by a parameter akin to a temperature which controls deviations from the maximum of his utility function. We show that an irrational consumer increases the economic activity while decreasing his own utility; (ii) an analysis using Information Theory of real world Input-Output matrices, showing that the aggregation methods used to build them most likely underestimated the dependency of the production chain on a few crucial sectors, having important consequences for the analysis of these data; (iii) a zero intelligence model in which agents with a power law distributed initial wealth randomly trade goods of different prices. We show that this initial inequality generates a higher inequality in free cash, reducing the overall liquidity in the economy and slowing down the number of trades. We discuss the insights obtained with these three problems, along with their relevance for the larger picture in Economics. Nesta tese, exploramos o potencial de ser usar técnicas de Mecânica Estatística para o estudo de sistemas econômicos, mostrando como tal abordagem pode contribuir significativamente ao permitir o estudo de sistemas complexos que exibem comportamentos ricos como transições de fase, criticalidade e fases vítreas, não encontradas normalmente em modelos econômicos tradicionais. Exemplificamos este potencial através de três problemas específicos: (i) um framework de Mecânica Estatística para lidar com consumidores irracionais, no qual a racionalidade é controlada pela temperatura do sistema, que define o tamanho dos desvios do estado de máxima utilidade. Mostramos que um consumidor irracional aumenta a atividade econômica ao mesmo tempo que diminui seu próprio bem estar; (ii) uma anáise usando Teoria da Informação de matrizes Input-Output de economias reais, mostrando que os métodos de agregação utilizados para construí-las provavelmente subestima a dependência das cadeias de produção em certos setores cruciais, com consequências importantes para a analíse destes dados; (iii) um modelo em que agentes com uma riqueza inicial distributida como lei de potências trocam aleatoriamente objetos com preços distintos. Mostramos que esta desigualdade inicial gera uma desigualdade ainda maior em dinheiro livre, reduzindo a liquidez total na economia e diminuindo a quantidade de trocas. Discutimos as consequências dos resultados destes três problemas, bem como sua relevância na perspectiva geral em Economia.

This thesis is divided into two parts. In the first part, we show how problems of statistical inference and combinatorial optimization may be approached within a unified framework that employs tools from fields as diverse as machine learning, statistical physics and information theory, allowing us to i) design algorithms to solve the problems, ii) analyze the performance of these algorithms both empirically and analytically, and iii) to compare the results obtained with the optimal achievable ones. In the second part, we use this framework to study two specific problems, one of inference (compressed sensing) and the other of optimization (information hiding). In both cases, we review current approaches, identify their flaws, and propose new schemes to address these flaws, building on the use of message-passing algorithms, variational inference techniques, and spin glass models from statistical physics. Esta tese está dividida em duas partes. Na primeira delas, mostramos como problemas de inferência estatística e de otimização combinatória podem ser abordados sob um framework unificado que usa ferramentas de áreas tão diversas quanto o aprendizado de máquina, a física estatística e a teoria de informação, permitindo que i) projetemos algoritmos para resolver os problemas, ii) analisemos a performance destes algoritmos tanto empiricamente como analiticamente, e iii) comparemos os resultados obtidos com os limites teóricos. Na segunda parte, este framework é usado no estudo de dois problemas específicos, um de inferência (compressed sensing) e outro de otimização (ocultação de dados). Em ambos os casos, revisamos abordagens recentes, identificamos suas falhas, e propomos novos esquemas que visam corrigir estas falhas, baseando-nos sobretudo em algoritmos de troca de mensagens, técnicas de inferência variacional, e modelos de vidro de spin da física estatística.