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This paper introduces a novel stochastic model for credit spreads. The stochastic approach leverages the diffusion of default intensities via a CIR++ model and is formulated within a risk-neutral probability space. Our research primarily addresses two gaps in the literature. The first is the lack of credit spread models founded on a stochastic basis that enables continuous modeling, as many existing models rely on factorial assumptions. The second is the limited availability of models that directly yield a term structure of credit spreads. An intermediate result of our model is the provision of a term structure for the prices of defaultable bonds. We present the model alongside an innovative, practical, and conservative calibration approach that minimizes the error between historical and theoretical volatilities of default intensities. We demonstrate the robustness of both the model and its calibration process by comparing its behavior to historical credit spread values. Our findings indicate that the model not only produces realistic credit spread term structure curves but also exhibits consistent diffusion over time. Additionally, the model accurately fits the initial term structure of implied survival probabilities and provides an analytical expression for the credit spread of any given maturity at any future time.

This study presents a dynamic Bayesian network framework that facilitates intuitive gradual edge changes. We use two conditional dynamics to model the edge addition and deletion, and edge selection separately. Unlike previous research that uses a mixture network approach, which restricts the number of possible edge changes, or structural priors to induce gradual changes, which can lead to unclear network evolution, our model induces more frequent and intuitive edge change dynamics. We employ Markov chain Monte Carlo (MCMC) sampling to estimate the model structures and parameters and demonstrate the model's effectiveness in a portfolio selection application.

Functional data analysis (FDA) and ensemble learning can be powerful tools for analyzing complex environmental time series. Recent literature has highlighted the key role of diversity in enhancing accuracy and reducing variance in ensemble methods.This paper introduces Randomized Spline Trees (RST), a novel algorithm that bridges these two approaches by incorporating randomized functional representations into the Random Forest framework. RST generates diverse functional representations of input data using randomized B-spline parameters, creating an ensemble of decision trees trained on these varied representations. We provide a theoretical analysis of how this functional diversity contributes to reducing generalization error and present empirical evaluations on six environmental time series classification tasks from the UCR Time Series Archive. Results show that RST variants outperform standard Random Forests and Gradient Boosting on most datasets, improving classification accuracy by up to 14\%. The success of RST demonstrates the potential of adaptive functional representations in capturing complex temporal patterns in environmental data. This work contributes to the growing field of machine learning techniques focused on functional data and opens new avenues for research in environmental time series analysis., Comment: 20 pages

Random delays between the occurrence of accident events and the corresponding reporting times of insurance claims is a standard feature of insurance data. The time lag between the reporting and the processing of a claim depends on whether the claim can be processed without delay as it arrives or whether it remains unprocessed for some time because of temporarily insufficient processing capacity that is shared between all incoming claims. We aim to explain and analyze the nature of processing delays and build-up of backlogs. We show how to select processing capacity optimally in order to minimize claims costs, taking delay-adjusted costs and fixed costs for claims settlement capacity into account. Theoretical results are combined with a large-scale numerical study that demonstrates practical usefulness of our proposal.

The demand for innovation in product design necessitates a prolific ideation phase. Conversational AI (CAI) systems that use Large Language Models (LLMs) such as GPT (Generative Pre-trained Transformer) have been shown to be fruitful in augmenting human creativity, providing numerous novel and diverse ideas. Despite the success in ideation quantity, the qualitative assessment of these ideas remains challenging and traditionally reliant on expert human evaluation. This method suffers from limitations such as human judgment errors, bias, and oversight. Addressing this gap, our study introduces a comprehensive mathematical framework for automated analysis to objectively evaluate the plethora of ideas generated by CAI systems and/or humans. This framework is particularly advantageous for novice designers who lack experience in selecting promising ideas. By converting the ideas into higher dimensional vectors and quantitatively measuring the diversity between them using tools such as UMAP, DBSCAN and PCA, the proposed method provides a reliable and objective way of selecting the most promising ideas, thereby enhancing the efficiency of the ideation phase., Comment: 20 pages, 12 figures, 5 tables

Global trade is shaped by a complex mix of factors beyond supply and demand, including tangible variables like transport costs and tariffs, as well as less quantifiable influences such as political and economic relations. Traditionally, economists model trade using gravity models, which rely on explicit covariates but often struggle to capture these subtler drivers of trade. In this work, we employ optimal transport and a deep neural network to learn a time-dependent cost function from data, without imposing a specific functional form. This approach consistently outperforms traditional gravity models in accuracy while providing natural uncertainty quantification. Applying our framework to global food and agricultural trade, we show that the global South suffered disproportionately from the war in Ukraine's impact on wheat markets. We also analyze the effects of free-trade agreements and trade disputes with China, as well as Brexit's impact on British trade with Europe, uncovering hidden patterns that trade volumes alone cannot reveal.

We develop variational search distributions (VSD), a method for finding and generating discrete, combinatorial designs of a rare desired class in a batch sequential manner with a fixed experimental budget. We formalize the requirements and desiderata for active generation and formulate a solution via variational inference. In particular, VSD uses off-the-shelf gradient based optimization routines, can learn powerful generative models for designs, and can take advantage of scalable predictive models. We derive asymptotic convergence rates for learning the true conditional generative distribution of designs with certain configurations of our method. After illustrating the generative model on images, we empirically demonstrate that VSD can outperform existing baseline methods on a set of real sequence-design problems in various biological systems., Comment: 36 pages with supplementary material included

This article gives an integrative review of research using projective methods in the consumer research domain. We give a general historical overview of the use of projective methods, both in psychology and in consumer research applications, and discuss the reliability and validity aspects and measurement for projective techniques. We review the literature on projective techniques in the areas of marketing, hospitality & tourism, and consumer & food science, with a mixed methods research focus on the interplay of qualitative and quantitative techniques. We review the use of several quantitative techniques used for structuring and analyzing projective data and run an empirical reanalysis of previously gathered data. We give recommendations for improved rigor and for potential future work involving mixed methods in projective techniques.

It is important for official statistics production to apply ML with statistical rigor, as it presents both opportunities and challenges. Although machine learning has enjoyed rapid technological advances in recent years, its application does not possess the methodological robustness necessary to produce high quality statistical results. In order to account for all sources of error in machine learning models, the Total Machine Learning Error (TMLE) is presented as a framework analogous to the Total Survey Error Model used in survey methodology. As a means of ensuring that ML models are both internally valid as well as externally valid, the TMLE model addresses issues such as representativeness and measurement errors. There are several case studies presented, illustrating the importance of applying more rigor to the application of machine learning in official statistics., Comment: 29 pages, 4 figures, 1 table. To appear in the proceedings of the conference on Foundations and Advances of Machine Learning in Official Statistics, which was held in Wiesbaden, from 3rd to 5th April, 2024

This article considers a problem arising from a two-player game based on the classical secretary problem. First, Player 1 selects one object from a sequence as in the secretary problem. All of the other objects are then presented to Player 2 in the same order as in the original sequence. The goal of both players is to select the best object. The optimal response of Player 2 is adapted to the optimal strategy in the secretary problem. This means that when Player 2 observes an object that is the best seen so far, it can be inferred whether Player 1 selected one of the earlier objects in the original sequence. However, Player 2 cannot compare the current object with the one selected by Player 1. Hence, this game defines an auxiliary problem in which Player 2 has incomplete information on the relative rank of an object. It is shown that the optimal strategy of Player 2 is based on both the number of objects to have appeared and the probability that the current object is better than the object chosen by Player 1 (if Player 1 chose an earlier object in the sequence). However, this probability is dependent on the previously observed objects. A lower bound on the optimal expected reward in the auxiliary problem is defined by limiting the memory of Player 2. An upper bound is derived by giving Player 2 additional information at appropriate times. The methods used illustrate approaches that can be used to approximate the optimal reward in a stopping problem when there is incomplete information on the ranks of objects and/or the optimal strategy is history dependent, as in the Robbins' problem, Comment: 52 pages

In this paper we present computational experiments with the Markov Chain Monte Carlo Matrix Inversion ($(\text{MC})^2\text{MI}$) on several accelerator architectures and investigate their impact on performance and scalability of the method. The method is used as a preconditioner and for solving the corresponding system of linear equations iterative methods, such as generalized minimal residuals (GMRES) or bi-conjugate gradient (stabilized) (BICGstab), are used. Numerical experiments are carried out to highlight the benefits and deficiencies of both approaches and to assess their overall usefulness in light of scalability of the method., Comment: 10 pages, 8 figures, 2 pages IEEE artifact information, accepted to the 9th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems

In this paper, we propose an approach for an application of Bayesian optimization using Sequential Monte Carlo (SMC) and concepts from the statistical physics of classical systems. Our method leverages the power of modern machine learning libraries such as NumPyro and JAX, allowing us to perform Bayesian optimization on multiple platforms, including CPUs, GPUs, TPUs, and in parallel. Our approach enables a low entry level for exploration of the methods while maintaining high performance. We present a promising direction for developing more efficient and effective techniques for a wide range of optimization problems in diverse fields., Comment: 8 pages, 7 figures, accepted to the International Conference on Computer Science 2023

The predominant method for computing confidence intervals (CI) in few-shot learning (FSL) is based on sampling the tasks with replacement, i.e.\ allowing the same samples to appear in multiple tasks. This makes the CI misleading in that it takes into account the randomness of the sampler but not the data itself. To quantify the extent of this problem, we conduct a comparative analysis between CIs computed with and without replacement. These reveal a notable underestimation by the predominant method. This observation calls for a reevaluation of how we interpret confidence intervals and the resulting conclusions in FSL comparative studies. Our research demonstrates that the use of paired tests can partially address this issue. Additionally, we explore methods to further reduce the (size of the) CI by strategically sampling tasks of a specific size. We also introduce a new optimized benchmark, which can be accessed at https://github.com/RafLaf/FSL-benchmark-again

Recently, many self-supervised learning methods for image reconstruction have been proposed that can learn from noisy data alone, bypassing the need for ground-truth references. Most existing methods cluster around two classes: i) Noise2Self and similar cross-validation methods that require very mild knowledge about the noise distribution, and ii) Stein's Unbiased Risk Estimator (SURE) and similar approaches that assume full knowledge of the distribution. The first class of methods is often suboptimal compared to supervised learning, and the second class tends to be impractical, as the noise level is often unknown in real-world applications. In this paper, we provide a theoretical framework that characterizes this expressivity-robustness trade-off and propose a new approach based on SURE, but unlike the standard SURE, does not require knowledge about the noise level. Throughout a series of experiments, we show that the proposed estimator outperforms other existing self-supervised methods on various imaging inverse problems

When entering French university, the students' foreign language level is assessed through a placement test. In this work, we model the placement test results using binary latent block models which allow to simultaneously form homogeneous groups of students and of items. However, a major difficulty in latent block models is to select correctly the number of groups of rows and the number of groups of columns. The first purpose of this paper is to tune the number of initializations needed to limit the initial values problem in the estimation algorithm in order to propose a model selection procedure in the placement test context. Computational studies based on simulated data sets and on two placement test data sets are investigated. The second purpose is to investigate the robustness of the proposed model selection procedure in terms of stability of the students groups when the number of students varies., Comment: 23 pages, 6 figures, 8 tables, soumission

The article focuses on the urgent issue of femicide in Veracruz, Mexico, and the development of the MFM_FEM_VER_CP_2024 model, a mathematical framework designed to predict femicide risk using fuzzy logic. This model addresses the complexity and uncertainty inherent in gender based violence by formalizing risk factors such as coercive control, dehumanization, and the cycle of violence. These factors are mathematically modeled through membership functions that assess the degree of risk associated with various conditions, including personal relationships and specific acts of violence. The study enhances the original model by incorporating new rules and refining existing membership functions, which significantly improve the model predictive accuracy., Comment: 24 pages, 2 tables, 3 figures

Our focus is on simulating the dynamics of non-interacting particles, which, under certain assumptions, can be formally described by the Dean-Kawasaki equation. The Dean-Kawasaki equation can be solved numerically using standard finite volume methods. However, the numerical approximation implicitly requires a sufficiently large number of particles to ensure the positivity of the solution and accurate approximation of the stochastic flux. To address this challenge, we extend hybrid algorithms for particle systems to scenarios where the density is low. The aim is to create a hybrid algorithm that switches from a finite volume discretization to a particle-based method when the particle density falls below a certain threshold. We develop criteria for determining this threshold by comparing higher-order statistics obtained from the finite volume method with particle simulations. We then demonstrate the use of the resulting criteria for dynamic adaptation in both two- and three-dimensional spatial settings.

In the era of Big Data, scalable and accurate clustering algorithms for high-dimensional data are essential. We present new Bayesian Distance Clustering (BDC) models and inference algorithms with improved scalability while maintaining the predictive accuracy of modern Bayesian non-parametric models. Unlike traditional methods, BDC models the distance between observations rather than the observations directly, offering a compromise between the scalability of distance-based methods and the enhanced predictive power and probabilistic interpretation of model-based methods. However, existing BDC models still rely on performing inference on the partition model to group observations into clusters. The support of this partition model grows exponentially with the dataset's size, complicating posterior space exploration and leading to many costly likelihood evaluations. Inspired by K-medoids, we propose using tessellations in discrete space to simplify inference by focusing the learning task on finding the best tessellation centers, or "medoids." Additionally, we extend our models to effectively handle multi-view data, such as data comprised of clusters that evolve across time, enhancing their applicability to complex datasets. The real data application in numismatics demonstrates the efficacy of our approach., Comment: 45 pages, 11 figures, 7 tables

We introduce a sound and complete equational theory capturing equivalence of discrete probabilistic programs, that is, programs extended with primitives for Bernoulli distributions and conditioning, to model distributions over finite sets of events. To do so, we translate these programs into a graphical syntax of probabilistic circuits, formalised as string diagrams, the two-dimensional syntax of symmetric monoidal categories. We then prove a first completeness result for the equational theory of the conditioning-free fragment of our syntax. Finally, we extend this result to a complete equational theory for the entire language. Note these developments are also of interest for the development of probability theory in Markov categories: our first result gives a presentation by generators and equations of the category of Markov kernels, restricted to objects that are powers of the two-elements set., Comment: 41 pages

This paper introduces a novel supervised classification strategy that integrates functional data analysis (FDA) with tree-based methods, addressing the challenges of high-dimensional data and enhancing the classification performance of existing functional classifiers. Specifically, we propose augmented versions of functional classification trees and functional random forests, incorporating a new tool for assessing the importance of functional principal components. This tool provides an ad-hoc method for determining unbiased permutation feature importance in functional data, particularly when dealing with correlated features derived from successive derivatives. Our study demonstrates that these additional features can significantly enhance the predictive power of functional classifiers. Experimental evaluations on both real-world and simulated datasets showcase the effectiveness of the proposed methodology, yielding promising results compared to existing methods., Comment: 33 pages

A graphon is a limiting object used to describe the behaviour of large networks through a function that captures the probability of edge formation between nodes. Although the merits of graphons to describe large and unlabelled networks are clear, they traditionally are used for describing only binary edge information, which limits their utility for more complex relational data. Decorated graphons were introduced to extend the graphon framework by incorporating richer relationships, such as edge weights and types. This specificity in modelling connections provides more granular insight into network dynamics. Yet, there are no existing inference techniques for decorated graphons. We develop such an estimation method, extending existing techniques from traditional graphon estimation to accommodate these richer interactions. We derive the rate of convergence for our method and show that it is consistent with traditional non-parametric theory when the decoration space is finite. Simulations confirm that these theoretical rates are achieved in practice. Our method, tested on synthetic and empirical data, effectively captures additional edge information, resulting in improved network models. This advancement extends the scope of graphon estimation to encompass more complex networks, such as multiplex networks and attributed graphs, thereby increasing our understanding of their underlying structures.

The advent of big data has raised significant challenges in analysing high-dimensional datasets across various domains such as medicine, ecology, and economics. Functional Data Analysis (FDA) has proven to be a robust framework for addressing these challenges, enabling the transformation of high-dimensional data into functional forms that capture intricate temporal and spatial patterns. However, despite advancements in functional classification methods and very high performance demonstrated by combining FDA and ensemble methods, a critical gap persists in the literature concerning the transparency and interpretability of black-box models, e.g. Functional Random Forests (FRF). In response to this need, this paper introduces a novel suite of explainability tools to illuminate the inner mechanisms of FRF. We propose using Functional Partial Dependence Plots (FPDPs), Functional Principal Component (FPC) Probability Heatmaps, various model-specific and model-agnostic FPCs' importance metrics, and the FPC Internal-External Importance and Explained Variance Bubble Plot. These tools collectively enhance the transparency of FRF models by providing a detailed analysis of how individual FPCs contribute to model predictions. By applying these methods to an ECG dataset, we demonstrate the effectiveness of these tools in revealing critical patterns and improving the explainability of FRF., Comment: 33 pages

Fluctuations are inherent to biological systems, arising from the stochastic nature of molecular interactions, and influence various aspects of system behavior, stability, and robustness. These fluctuations can be categorized as intrinsic, stemming from the system's inherent structure and dynamics, and extrinsic, arising from external factors, such as temperature variations. Understanding the interplay between these fluctuations is crucial for obtaining a comprehensive understanding of biological phenomena. However, studying these effects poses significant computational challenges. In this study, we used an underexplored methodology to analyze the effect of extrinsic fluctuations in stochastic systems using ordinary differential equations instead of solving the Master Equation with stochastic parameters. By incorporating temperature fluctuations into reaction rates, we explored the impact of extrinsic factors on system dynamics. We constructed a master equation and calculated the equations for the dynamics of the first two moments, offering computational efficiency compared with directly solving the chemical master equation. We applied this approach to analyze a biological oscillator, focusing on the p53 model and its response to temperature-induced extrinsic fluctuations. Our findings underscore the impact of extrinsic fluctuations on the nature of oscillations in biological systems, with alterations in oscillatory behavior depending on the characteristics of extrinsic fluctuations. We observed an increased oscillation amplitude and frequency of the p53 concentration cycle. This study provides valuable insights into the effects of extrinsic fluctuations on biological oscillations and highlights the importance of considering them in more complex systems to prevent unwanted scenarios related to health issues., Comment: 21 pages, 9 figures

In this study, we analyzed urn models by solving the discrete-time master equation using an expansion in moments. This approach is a viable alternative to conventional methods, such as system-size expansion, allowing for the determination of analytical expressions for the mean and variance in an exact form and thus valid for any system size. In particular, this approach was used to study Bernoulli-Laplace and Ehrenfest urns, for which analytic expressions describing their evolution were found. This approach and the results will contribute to a more comprehensive understanding of stochastic systems and statistical physics for small-sized systems, where the thermodynamic limit cannot be assumed., Comment: 6 pages, 5 figures

In a class of heterogeneous random networks, where each node dynamics is a random dynamical system, interacting with neighbor nodes via a random coupling function, we characterize the hub behavior as the mean-field, subject to statistically controlled fluctuations. In particular, we prove that the fluctuations are small over exponentially long time scales and obtain Berry-Esseen estimates for the fluctuation statistics at any fixed time. Our results provide a mathematical explanation for several numerical observations, including the scaling relation between system size and frequency of large fluctuations, as well as system size induced desynchronization. To our best knowledge, these are the first characterizations of mean-field fluctuations on networks with a degree distribution that follows a power-law, a common feature for many realistic systems., Comment: 40 pages, 7 figures

We identify certain gaps in the literature on the approximability of stationary random variables using the Autoregressive Moving Average (ARMA) model. To quantify approximability, we propose that an ARMA model be viewed as an approximation of a stationary random variable. We map these stationary random variables to Hardy space functions, and formulate a new function approximation problem that corresponds to random variable approximation, and thus to ARMA. Based on this Hardy space formulation we identify a class of stationary processes where approximation guarantees are feasible. We also identify an idealized stationary random process for which we conjecture that a good ARMA approximation is not possible. Next, we provide a constructive proof that Pad\'e approximations do not always correspond to the best ARMA approximation. Finally, we note that the spectral methods adopted in this paper can be seen as a generalization of unit root methods for stationary processes even when an ARMA model is not defined., Comment: 10 pages, 3 figures

Poverty is a serious issue that harms humanity progression. The simplest solution is to use one-shirt-size policy to alleviate it. Nevertheless, each region has its unique issues, which require a unique solution to solve them. In the aspect of spatial analysis, neighbor regions can provide useful information to analyze issues of a given region. In this work, we proposed inferred boundaries of regions of Thailand that can explain better the poverty dynamics, instead of the usual government administrative regions. The proposed regions maximize a trade-off between poverty-related features and geographical coherence. We use a spatial analysis together with Moran's cluster algorithms and Bayesian hierarchical regression models, with the potential of assist the implementation of the right policy to alleviate the poverty phenomenon. We found that all variables considered show a positive spatial autocorrelation. The results of analysis illustrate that 1) Northern, Northeastern Thailand, and in less extend Northcentral Thailand are the regions that require more attention in the aspect of poverty issues, 2) Northcentral, Northeastern, Northern and Southern Thailand present dramatically low levels of education, income and amount of savings contrasted with large cities such as Bangkok-Pattaya and Central Thailand, and 3) Bangkok-Pattaya is the only region whose average years of education is above 12 years, which corresponds (approx.) with a complete senior high school., Comment: Codes to reproduce our results are available in https://github.com/IrvingGomez/SpatialPovertyFactors

The Hawkes process is a popular point process model for event sequences that exhibit temporal clustering. The intensity process of a Hawkes process consists of two components, the baseline intensity and the accumulated excitation effect due to past events, with the latter specified via an excitation kernel. The classical Hawkes process assumes a constant baseline intensity and an exponential excitation kernel. This results in an intensity process that is Markovian, a fact that has been used extensively to establish the strong consistency and asymtpotic normality of maximum likelihood estimators or similar. However, these assumptions can be overly restrictive and unrealistic for modelling the many applications which require the baseline intensity to vary with time and the excitation kernel to have non-exponential decay. However, asymptotic properties of maximum likelihood inference for the parameters specifying the baseline intensity and the self-exciting decay under this setup are substantially more difficult since the resulting intensity process is non-Markovian. To overcome this challenge, we develop an approximation procedure to show the intensity process is asymptotically ergodic in a suitably defined sense. This allows for the identification of an ergodic limit to the likelihood function and its derivatives, as required for obtaining large sample inference under minimal regularity conditions., Comment: 41 pages, 3 figures

We use Fourier analysis to access risk in financial products. With it we analyze price changes of e.g. stocks. Via Fourier analysis we scrutinize quantitatively whether the frequency of change is higher than a change in (conserved) company value would allow. If it is the case, it would be a clear indicator of speculation and with it risk. The entire methods or better its application is fairly new. However, there were severe flaws in previous attempts; making the results (not the method) doubtful. We corrected all these mistakes by e.g. using Fourier transformation instead of discrete Fourier analysis. Our analysis is reliable in the entire frequency band, even for fre-quency of 1/1d or higher if the prices are noted accordingly. For the stocks scrutinized we found that the price of stocks changes disproportionally within one week which clearly indicates spec-ulation. It would be an interesting extension to apply the method to crypto currencies as these currencies have no conserved value which makes normal considerations of volatility difficult., Comment: 14 pages, 11 figures

The kendallknight package introduces an efficient implementation of Kendall's correlation coefficient computation, significantly improving the processing time for large datasets without sacrificing accuracy. The kendallknight package, following Knight (1966) and posterior literature, reduces the computational complexity resulting in drastic reductions in computation time, transforming operations that would take minutes or hours into milliseconds or minutes, while maintaining precision and correctly handling edge cases and errors. The package is particularly advantageous in econometric and statistical contexts where rapid and accurate calculation of Kendall's correlation coefficient is desirable. Benchmarks demonstrate substantial performance gains over the base R implementation, especially for large datasets., Comment: 9 pages with references, 2 tables, 2 figures

This paper presents the LiU-ICE fault diagnosis benchmark. The purpose of the benchmark is to support fault diagnosis research by providing data and a model of an industrially relevant system. Data has been collected from an internal combustion engine test bench operated in both nominal and faulty modes. A state-of-the-art model of the air path through an internal combustion engine with unknown parameters is provided. This benchmark has previously been used in a competition at the 12th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes (Safe Process) 2024, Ferrara, Italy., Comment: 4 pages, 7 figures

Bayesian priors are investigated for detecting targets of known spectral signature (but unknown strength) in cluttered backgrounds. A specific problem is the construction (or ``sculpting'') of a Bayesian prior that uniformly outperforms its non-Bayesian counterpart, the nominally sub-optimal but widely used Generalized Likelihood Ratio Test (GLRT)., Comment: 11 pages, 7 figures

Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian literature is well-developed and there are no substantial differences in the model selection consistency results available from the two schools. For the more challenging generalized linear models (GLMs), however, Bayesian model selection consistency results are lacking in several ways. In this paper, we construct a Bayesian posterior distribution using an appropriate data-dependent prior and develop its asymptotic concentration properties using new theoretical techniques. In particular, we leverage Spokoiny's powerful non-asymptotic theory to obtain sharp quadratic approximations of the GLM's log-likelihood function, which leads to tight bounds on the errors associated with the model-specific maximum likelihood estimators and the Laplace approximation of our Bayesian marginal likelihood. In turn, these improved bounds lead to significantly stronger, near-optimal Bayesian model selection consistency results, e.g., far weaker beta-min conditions, compared to those available in the existing literature. In particular, our results are applicable to the Poisson regression model, in which the score function is not sub-Gaussian., Comment: submitted

Time series forecasting is an important task in many fields ranging from supply chain management to weather forecasting. Recently, Transformer neural network architectures have shown promising results in forecasting on common time series benchmark datasets. However, application to supply chain demand forecasting, which can have challenging characteristics such as sparsity and cross-series effects, has been limited. In this work, we explore the application of Transformer-based models to supply chain demand forecasting. In particular, we develop a new Transformer-based forecasting approach using a shared, multi-task per-time series network with an initial component applying attention across time series, to capture interactions and help address sparsity. We provide a case study applying our approach to successfully improve demand prediction for a medical device manufacturing company. To further validate our approach, we also apply it to public demand forecasting datasets as well and demonstrate competitive to superior performance compared to a variety of baseline and state-of-the-art forecast methods across the private and public datasets.

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. We demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion-reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.

We introduce the Robustness of Hierarchically Organized Time Series (RHiOTS) framework, designed to assess the robustness of hierarchical time series forecasting models and algorithms on real-world datasets. Hierarchical time series, where lower-level forecasts must sum to upper-level ones, are prevalent in various contexts, such as retail sales across countries. Current empirical evaluations of forecasting methods are often limited to a small set of benchmark datasets, offering a narrow view of algorithm behavior. RHiOTS addresses this gap by systematically altering existing datasets and modifying the characteristics of individual series and their interrelations. It uses a set of parameterizable transformations to simulate those changes in the data distribution. Additionally, RHiOTS incorporates an innovative visualization component, turning complex, multidimensional robustness evaluation results into intuitive, easily interpretable visuals. This approach allows an in-depth analysis of algorithm and model behavior under diverse conditions. We illustrate the use of RHiOTS by analyzing the predictive performance of several algorithms. Our findings show that traditional statistical methods are more robust than state-of-the-art deep learning algorithms, except when the transformation effect is highly disruptive. Furthermore, we found no significant differences in the robustness of the algorithms when applying specific reconciliation methods, such as MinT. RHiOTS provides researchers with a comprehensive tool for understanding the nuanced behavior of forecasting algorithms, offering a more reliable basis for selecting the most appropriate method for a given problem., Comment: Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD '24), August 25--29, 2024, Barcelona, Spain

We proposed the tensor-input tree (TT) method for scalar-on-tensor and tensor-on-tensor regression problems. We first address scalar-on-tensor problem by proposing scalar-output regression tree models whose input variable are tensors (i.e., multi-way arrays). We devised and implemented fast randomized and deterministic algorithms for efficient fitting of scalar-on-tensor trees, making TT competitive against tensor-input GP models. Based on scalar-on-tensor tree models, we extend our method to tensor-on-tensor problems using additive tree ensemble approaches. Theoretical justification and extensive experiments on real and synthetic datasets are provided to illustrate the performance of TT., Comment: 36 pages, 9 Figures

This document presents a compilation of results related to the theory of stochastic processes, with a specific focus on Markov processes, regenerative processes, renewal processes, and stationary processes. The relevance of these topics lies in the ability to identify regeneration points and the necessary conditions to ensure the stationarity of the process. The study begins with a review of Markov chains and continues with the analysis of processes that satisfy the strong Markov property. Subsequently, it delves into renewal processes, regenerative processes, and finally, stationary regenerative processes, highlighting the results presented by Thorisson [22]. This work is not intended to be exhaustive but aims to provide a solid foundation for further deepening the knowledge of these processes, given their broad range of applications in cryptography [16], queueing theory [15], and Monte Carlo methods [23]. Additionally, the importance of Poisson-type processes is emphasized due to their numerous applications (see [8])., Comment: 21 pages, in Spanish language

While the tracking of multiple extended targets demands for sophisticated algorithms to handle the high complexity inherent to the task, it also requires low runtime for online execution in real-world scenarios. In this work, we derive a batch update for the recently introduced elliptical-target tracker called MEM-EKF*. The MEM-EKF* is based on the same likelihood as the well-established random matrix approach but is derived from the multiplicative error model (MEM) and uses an extended Kalman filter (EKF) to update the target state sequentially, i.e., measurement-by-measurement. Our batch variant updates the target state in a single step based on straightforward sums over all measurements and the MEM-specific pseudo-measurements. This drastically reduces the scaling constant for typical implementations and indeed we find a speedup of roughly 100x in our numerical experiments. At the same time, the estimation error which we measure using the Gaussian Wasserstein distance stays significantly below that of the random matrix approach in coordinated turn scenarios while being comparable otherwise., Comment: This is the accepted version (not the IEEEpublished version). copyright 20XX IEEE

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an It\^o equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a projection on a reduced-order vector basis related to the training dataset, using the diffusion maps (DMAPS) basis constructed with a time-independent isotropic kernel. In this paper, we propose a new ISDE projection vector basis built from a transient anisotropic kernel, providing an alternative to the DMAPS basis to improve statistical surrogates for stochastic manifolds with heterogeneous data. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. For larger times, the differences between the two bases are characterized by the angle of their spanned vector subspaces. The optimal instant yielding the optimal transient basis is determined using an estimation of mutual information from Information Theory, which is normalized by the entropy estimation to account for the effects of the number of realizations used in the estimations. Consequently, this new vector basis better represents statistical dependencies in the learned probability measure for any dimension. Three applications with varying levels of statistical complexity and data heterogeneity validate the proposed theory, showing that the transient anisotropic kernel improves the learned probability measure., Comment: 44 pages, 14 figures

In this paper, we propose a new distribution over the unit interval which can be characterized as a ratio of the type $Z=Y/(X+Y)$ where $X$ and $Y$ are two correlated Birnbaum-Saunders random variables. The density of $Z$ may be unimodal or bimodal. Simple expressions for the cumulative distribution function, moment-generating function and moments are obtained. Moreover, the stress-strength probability between $X$ and $Y$ is calculated explicitly in the symmetric case, that is, when the respective scale parameters are equal. Two applications of the ratio distribution are discussed., Comment: 22 pages; 10 figures

Electricity storage is crucial for a successful transition towards carbon-neutral energy production. Despite considerable research and a number of promising future alternatives such as hydrogen, battery storages currently remain the first choice. However, costs remain high and it remains to be shown whether an investment can be profitable. This article addresses this question by modelling a battery storage operating in the German power market. We consider two periods with very distinct price dynamics, namely a calm year (2020) and a turbulent year (2023). It shows that even for low battery costs a 2020 style price environment does not allow for profitable battery operation, whereas current market conditions allow for positive payoffs., Comment: Preprint submitted to IEEE I and CPS Asia Conference 2024

Maintenance decisions range from the simple detection of faults to ultimately predicting future failures and solving the problem. These traditionally human decisions are nowadays increasingly supported by data and the ultimate aim is to make them autonomous. This paper explores the challenges encountered in data driven maintenance, and proposes to consider four aspects in a maturity framework: data / decision maturity, the translation from the real world to data, the computability of decisions (using models) and the causality in the obtained relations. After a discussion of the theoretical concepts involved, the exploration continues by considering a practical fault detection and identification problem. Two approaches, i.e. experience based and model based, are compared and discussed in terms of the four aspects in the maturity framework. It is observed that both approaches yield the same decisions, but still differ in the assignment of causality. This confirms that a maturity assessment not only concerns the type of decision, but should also include the other proposed aspects., Comment: in Proceedings of the 8th European Conference of the Prognostics and Health Management Society 2024

In this study, the combined use of structural equation modeling (SEM) and Bayesian network modeling (BNM) in causal inference analysis is revisited. The perspective highlights the debate between proponents of using BNM as either an exploratory phase or even as the sole phase in the definition of structural models, and those advocating for SEM as the superior alternative for exploratory analysis. The individual strengths and limitations of SEM and BNM are recognized, but this exploration evaluates the contention between utilizing SEM's robust structural inference capabilities and the dynamic probabilistic modeling offered by BNM. A case study of the work of, \citet{balaguer_2022} in a structural model for personal positive youth development (\textit{PYD}) as a function of positive parenting (\textit{PP}) and perception of the climate and functioning of the school (\textit{CFS}) is presented. The paper at last presents a clear stance on the analytical primacy of SEM in exploratory causal analysis, while acknowledging the potential of BNM in subsequent phases., Comment: 38 pages, 9 figures, 2 tables

We define *fDistances*, which generalize Euclidean distances, squared distances, and log distances. The least squares loss function to fit fDistances to dissimilarity data is *fStress*. We give formulas and R/C code to compute partial derivatives of orders one to four of fStress, relying heavily on the use of Fa\`a di Bruno's chain rule formula for higher derivatives., Comment: 27 pages, R code, C code

Modifications of the smacof algorithm for multidimensional scaling are proposed that provide a convergent majorization algorithm for Kruskal's stress formula two., Comment: 16 pages, 4 figures, R code

This study introduces novel superior scoring rules called Penalized Brier Score (PBS) and Penalized Logarithmic Loss (PLL) to improve model evaluation for probabilistic classification. Traditional scoring rules like Brier Score and Logarithmic Loss sometimes assign better scores to misclassifications in comparison with correct classifications. This discrepancy from the actual preference for rewarding correct classifications can lead to suboptimal model selection. By integrating penalties for misclassifications, PBS and PLL modify traditional proper scoring rules to consistently assign better scores to correct predictions. Formal proofs demonstrate that PBS and PLL satisfy strictly proper scoring rule properties while also preferentially rewarding accurate classifications. Experiments showcase the benefits of using PBS and PLL for model selection, model checkpointing, and early stopping. PBS exhibits a higher negative correlation with the F1 score compared to the Brier Score during training. Thus, PBS more effectively identifies optimal checkpoints and early stopping points, leading to improved F1 scores. Comparative analysis verifies models selected by PBS and PLL achieve superior F1 scores. Therefore, PBS and PLL address the gap between uncertainty quantification and accuracy maximization by encapsulating both proper scoring principles and explicit preference for true classifications. The proposed metrics can enhance model evaluation and selection for reliable probabilistic classification., Comment: 21 Pages, 3 Figures, 3 Tables

Mixed Poisson distributions provide a flexible approach to the analysis of count data with overdispersion, zero inflation, or heavy tails. Since the Poisson mean must be nonnegative, the mixing distribution is typically assumed to have nonnegative support. We show this assumption is unnecessary and real-valued mixing distributions are also possible. Informally, the mixing distribution merely needs to have a light (subexponential) left tail and a small amount of probability mass on negative values. We provide several concrete examples, including the mixed Poisson-extreme stable family, where the mixing distribution has a power law tail.

Smart-city services are typically developed as closed systems within each city's vertical, communicating and interacting with cloud services while remaining isolated within each provider's domain. With the emergence of 5G private domains and the introduction of new M2M services focusing on autonomous systems, there is a shift from the cloud-based approach to a distributed edge computing paradigm, in a \textit{continuum} orchestration. However, an essential component is missing. Current orchestration tools, designed for cloud-based deployments, lack robust workload isolation, fail to meet timing constraints, and are not tailored to the resource-constrained nature of edge devices. Therefore, new orchestration methods are needed to support MEC environments. The work presented in this paper addresses this gap. Based on the real needs of a smart-city testbed - the Aveiro Living Lab-, we developed a set of orchestration components to facilitate the seamless orchestration of both cloud and edge-based services, encompassing both critical and non-critical services. This work extends the current Kubernetes orchestration platform to include a novel location-specific resource definition, a custom scheduler to accommodate real-time and legacy services, continuous service monitoring to detect sub-optimal states, and a refined load balancing mechanism that prioritizes the fastest response times.

The full-dimensional (metric, Euclidean, least squares) multidimensional scaling stress loss function is combined with a quadratic external penalty function term. The trajectory of minimizers of stress for increasing values of the penalty parameter is then used to find (tentative) global minima for low-dimensional multidimensional scaling. This is illustrated with several one-dimensional and two-dimensional examples., Comment: 39 pages