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Stochastic versions of recursive integrated climate-economy assessment models are essential for studying and quantifying policy decisions under uncertainty. However, as the number of stochastic shocks increases, solving these models as dynamic programming problems using deterministic grid methods becomes computationally infeasible, and simulation-based methods are needed. The least-squares Monte Carlo (LSMC) method has become popular for solving optimal stochastic control problems in quantitative finance. In this paper, we extend the application of the LSMC method to stochastic climate-economy models. We exemplify this approach using a stochastic version of the DICE model with all five main uncertainties discussed in the literature. To address the complexity and high dimensionality of these models, we incorporate deep neural network approximations in place of standard regression techniques within the LSMC framework. Our results demonstrate that the deep LSMC method can be used to efficiently derive optimal policies for climate-economy models in the presence of uncertainty., Comment: 27 pages with 2 tables and 8 figures

Functional Isolation Forest (FIF) is a recent state-of-the-art Anomaly Detection (AD) algorithm designed for functional data. It relies on a tree partition procedure where an abnormality score is computed by projecting each curve observation on a drawn dictionary through a linear inner product. Such linear inner product and the dictionary are a priori choices that highly influence the algorithm's performances and might lead to unreliable results, particularly with complex datasets. This work addresses these challenges by introducing \textit{Signature Isolation Forest}, a novel AD algorithm class leveraging the rough path theory's signature transform. Our objective is to remove the constraints imposed by FIF through the proposition of two algorithms which specifically target the linearity of the FIF inner product and the choice of the dictionary. We provide several numerical experiments, including a real-world applications benchmark showing the relevance of our methods.

We have devised a data-driven framework for uncovering hidden control strategies used by an evolutionary system described by an evolutionary probability distribution. This innovative framework enables deciphering of the concealed mechanisms that contribute to the progression or mitigation of such situations as the spread of COVID-19. Novel algorithms are used to estimate the optimal control in tandem with the parameters for evolution in general dynamical systems, thereby extending the concept of model predictive control. This is a significant departure from conventional control methods, which require knowledge of the system to manipulate its evolution and of the controller's strategy or parameters. We used a generalized additive model, supplemented by extensive statistical testing, to identify a set of predictor covariates closely linked to the control. Using real-world COVID-19 data, we successfully delineated the descriptive behaviors of the COVID-19 epidemics in five prefectures in Japan and nine countries. We compared these nine countries and grouped them on the basis of shared profiles, providing valuable insights into their pandemic responses. Our findings underscore the potential of our framework as a powerful tool for understanding and managing complex evolutionary processes., Comment: 18 pages

We propose a new framework that generalizes the parameters of neural network models to $C^*$-algebra-valued ones. $C^*$-algebra is a generalization of the space of complex numbers. A typical example is the space of continuous functions on a compact space. This generalization enables us to combine multiple models continuously and use tools for functions such as regression and integration. Consequently, we can learn features of data efficiently and adapt the models to problems continuously. We apply our framework to practical problems such as density estimation and few-shot learning and show that our framework enables us to learn features of data even with a limited number of samples. Our new framework highlights the potential possibility of applying the theory of $C^*$-algebra to general neural network models., Comment: Accepted at ICML 2022

The classical DICE model is a widely accepted integrated assessment model for the joint modeling of economic and climate systems, where all model state variables evolve over time deterministically. We reformulate and solve the DICE model as an optimal control dynamic programming problem with six state variables (related to the carbon concentration, temperature, and economic capital) evolving over time deterministically and affected by two controls (carbon emission mitigation rate and consumption). We then extend the model by adding a discrete stochastic shock variable to model the economy in the stressed and normal regimes as a jump process caused by events such as the COVID-19 pandemic. These shocks reduce the world gross output leading to a reduction in both the world net output and carbon emission. The extended model is solved under several scenarios as an optimal stochastic control problem, assuming that the shock events occur randomly on average once every 100 years and last for 5 years. The results show that, if the world gross output recovers in full after each event, the impact of the COVID-19 events on the temperature and carbon concentration will be immaterial even in the case of a conservative 10\% drop in the annual gross output over a 5-year period. The impact becomes noticeable, although still extremely small (long-term temperature drops by $0.1^\circ \mathrm{C}$), in a presence of persistent shocks of a 5\% output drop propagating to the subsequent time periods through the recursively reduced productivity. If the deterministic DICE model policy is applied in a presence of stochastic shocks (i.e. when this policy is suboptimal), then the drop in temperature is larger (approximately $0.25^\circ \mathrm{C}$), that is, the lower economic activities owing to shocks imply that more ambitious mitigation targets are now feasible at lower costs.

The COVID-19 pandemic, which began in December 2019, progressed in a complicated manner and thus caused problems worldwide. Seeking clues to the reasons for the complicated progression is necessary but challenging in the fight against the pandemic. We sought clues by investigating the relationship between reactions on social media and the COVID-19 epidemic in Japan. Twitter was selected as the social media platform for study because it has a large user base in Japan and because it quickly propagates short topic-focused messages ("tweets"). Analysis using Japanese Twitter data suggests that reactions on social media and the progression of the COVID-19 pandemic may have a close relationship. Experiments to evaluate the potential of using tweets to support the prediction of how an epidemic will progress demonstrated the value of using epidemic-related social media data. Our findings provide insights into the relationship between user reactions on social media, particularly Twitter, and epidemic progression, which can be used to fight pandemics., Comment: 14 pages, 4 figures

A practical algorithm has been developed for closeness analysis of sequential data that combines closeness testing with algorithms based on the Markov chain tester. It was applied to reported sequential data for COVID-19 to analyze the evolution of COVID-19 during a certain time period (week, month, etc.).

In the era of open data, Poisson and other count regression models are increasingly important. Still, conventional Poisson regression has remaining issues in terms of identifiability and computational efficiency. Especially, due to an identification problem, Poisson regression can be unstable for small samples with many zeros. Provided this, we develop a closed-form inference for an over-dispersed Poisson regression including Poisson additive mixed models. The approach is derived via mode-based log-Gaussian approximation. The resulting method is fast, practical, and free from the identification problem. Monte Carlo experiments demonstrate that the estimation error of the proposed method is a considerably smaller estimation error than the closed-form alternatives and as small as the usual Poisson regressions. For counts with many zeros, our approximation has better estimation accuracy than conventional Poisson regression. We obtained similar results in the case of Poisson additive mixed modeling considering spatial or group effects. The developed method was applied for analyzing COVID-19 data in Japan. This result suggests that influences of pedestrian density, age, and other factors on the number of cases change over periods.

As with the advancement of geographical information systems, non-Gaussian spatial data sets are getting larger and more diverse. This study develops a general framework for fast and flexible non-Gaussian regression, especially for spatial/spatiotemporal modeling. The developed model, termed the compositionally-warped additive mixed model (CAMM), combines an additive mixed model (AMM) and the compositionally-warped Gaussian process to model a wide variety of non-Gaussian continuous data including spatial and other effects. A specific advantage of the proposed CAMM is that it requires no explicit assumption of data distribution unlike existing AMMs. Monte Carlo experiments show the estimation accuracy and computational efficiency of CAMM for modeling non-Gaussian data including fat-tailed and/or skewed distributions. Finally, the model is applied to crime data to examine the empirical performance of the regression analysis and prediction. The result shows that CAMM provides intuitively reasonable coefficient estimates and outperforms AMM in terms of prediction accuracy. CAMM is verified to be a fast and flexible model that potentially covers a wide variety of non-Gaussian data modeling. The proposed approach is implemented in an R package spmoran.

The statistical quantification of temperature processes for the analysis of urban heat island (UHI) effects and local heat-waves is an increasingly important application domain in smart city dynamic modelling. This leads to the increased importance of real-time heatwave risk management on a fine-grained spatial resolution. This study attempts to analyze and develop new methods for modelling the spatio-temporal behavior of ground temperatures. The developed models consider higher-order stochastic spatial properties such as skewness and kurtosis, which are key components for understanding and describing local temperature fluctuations and UHI's. The developed models are applied to the greater Tokyo metropolitan area for a detailed real-world data case study. The analysis also demonstrates how to statistically incorporate a variety of real data sets. This includes remotely sensed imagery and a variety of ground-based monitoring site data to build models linking city and urban covariates to air temperature. The air temperature models are then used to capture high-resolution spatial emulator outputs for ground surface temperature modelling. The main class of processes studied includes the Tukey g-and-h processes for capturing spatial and temporal aspects of heat processes in urban environments.

Real-time urban climate monitoring provides useful information that can be utilized to help monitor and adapt to extreme events, including urban heatwaves. Typical approaches to the monitoring of climate data include weather station monitoring and remote sensing. However, climate monitoring stations are very often distributed spatially in a sparse manner, and consequently, this has a significant impact on the ability to reveal exposure risks due to extreme climates at an intra-urban scale. Additionally, traditional remote sensing data sources are typically not received and analyzed in real-time which is often required for adaptive urban management of climate extremes, such as sudden heatwaves. Fortunately, recent social media, such as Twitter, furnishes real-time and high-resolution spatial information that might be useful for climate condition estimation. The objective of this study is utilizing geo-tagged tweets (participatory sensing data) for urban temperature analysis. We first detect tweets relating hotness (hot-tweets). Then, we study relationships between monitored temperatures and hot-tweets via a statistical model framework based on copula modelling methods. We demonstrate that there are strong relationships between "hot-tweets" and temperatures recorded at an intra-urban scale. Subsequently, we then investigate the application of "hot-tweets" informing spatio-temporal Gaussian process interpolation of temperatures as an application example of "hot-tweets". We utilize a combination of spatially sparse weather monitoring sensor data and spatially and temporally dense lower quality twitter data. Here, a spatial best linear unbiased estimation technique is applied. The result suggests that tweets provide some useful auxiliary information for urban climate assessment. Lastly, effectiveness of tweets toward a real-time urban risk management is discussed based on the results.

We propose in this paper a new family of kernels to handle times series, notably speech data, within the framework of kernel methods which includes popular algorithms such as the Support Vector Machine. These kernels elaborate on the well known Dynamic Time Warping (DTW) family of distances by considering the same set of elementary operations, namely substitutions and repetitions of tokens, to map a sequence onto another. Associating to each of these operations a given score, DTW algorithms use dynamic programming techniques to compute an optimal sequence of operations with high overall score. In this paper we consider instead the score spanned by all possible alignments, take a smoothed version of their maximum and derive a kernel out of this formulation. We prove that this kernel is positive definite under favorable conditions and show how it can be tuned effectively for practical applications as we report encouraging results on a speech recognition task.