Probabilistic time-series models become popular in the forecasting field as they help to make optimal decisions under uncertainty. Despite the growing interest, a lack of thorough analysis hinders choosing what is worth applying for the desired task. In this paper, we analyze the performance of three prominent probabilistic time-series models for sales forecasting. To remove the role of random chance in architecture's performance, we make two experimental principles; 1) Large-scale dataset with various cross-validation sets. 2) A standardized training and hyperparameter selection. The experimental results show that a simple Multi-layer Perceptron and Linear Regression outperform the probabilistic models on RMSE without any feature engineering. Overall, the probabilistic models fail to achieve better performance on point estimation, such as RMSE and MAPE, than comparably simple baselines. We analyze and discuss the performances of probabilistic time-series models.

A new fuzzy method is developed using triangular/trapezoidal fuzzy numbers for evaluating a group's mean performance, when qualitative grades instead of numerical scores are used for assessing its members' individual performance. Also, a new technique is developed for solving Linear Programming problems with fuzzy coefficients and everyday life applications are presented to illustrate our results.

Researchers have proposed a wide variety of model explanation approaches, but it remains unclear how most methods are related or when one method is preferable to another. We establish a new class of methods, removal-based explanations, that are based on the principle of simulating feature removal to quantify each feature's influence. These methods vary in several respects, so we develop a framework that characterizes each method along three dimensions: 1) how the method removes features, 2) what model behavior the method explains, and 3) how the method summarizes each feature's influence. Our framework unifies 25 existing methods, including several of the most widely used approaches (SHAP, LIME, Meaningful Perturbations, permutation tests). This new class of explanation methods has rich connections that we examine using tools that have been largely overlooked by the explainability literature. To anchor removal-based explanations in cognitive psychology, we show that feature removal is a simple application of subtractive counterfactual reasoning. Ideas from cooperative game theory shed light on the relationships and trade-offs among different methods, and we derive conditions under which all removal-based explanations have information-theoretic interpretations. Through this analysis, we develop a unified framework that helps practitioners better understand model explanation tools, and that offers a strong theoretical foundation upon which future explainability research can build.

We introduce factorize sum split product networks (FSPNs), a new class of probabilistic graphical models (PGMs). FSPNs are designed to overcome the drawbacks of existing PGMs in terms of estimation accuracy and inference efficiency. Specifically, Bayesian networks (BNs) have low inference speed and performance of tree structured sum product networks(SPNs) significantly degrades in presence of highly correlated variables. FSPNs absorb their advantages by adaptively modeling the joint distribution of variables according to their dependence degree, so that one can simultaneously attain the two desirable goals: high estimation accuracy and fast inference speed. We present efficient probability inference and structure learning algorithms for FSPNs, along with a theoretical analysis and extensive evaluation evidence. Our experimental results on synthetic and benchmark datasets indicate the superiority of FSPN over other PGMs.

We present an approach to data fusion that combines the interpretability of structured probabilistic graphical models with the flexibility of neural networks. The proposed method, lightweight data fusion (LDF), emphasizes posterior analysis over latent variables using two types of information: primary data, which are well-characterized but with limited availability, and auxiliary data, readily available but lacking a well-characterized statistical relationship to the latent quantity of interest. The lack of a forward model for the auxiliary data precludes the use of standard data fusion approaches, while the inability to acquire latent variable observations severely limits direct application of most supervised learning methods. LDF addresses these issues by utilizing neural networks as conjugate mappings of the auxiliary data: nonlinear transformations into sufficient statistics with respect to the latent variables. This facilitates efficient inference by preserving the conjugacy properties of the primary data and leads to compact representations of the latent variable posterior distributions. We demonstrate the LDF methodology on two challenging inference problems: (1) learning electrification rates in Rwanda from satellite imagery, high-level grid infrastructure, and other sources; and (2) inferring county-level homicide rates in the USA by integrating socio-economic data using a mixture model of multiple conjugate mappings.

Bayesian inference is a major problem in statistics that is also encountered in many machine learning methods. For example, Gaussian mixture models, for classification, or Latent Dirichlet Allocation, for topic modelling, are both graphical models requiring to solve such a problem when fitting the data. Meanwhile, it can be noticed that Bayesian inference problems can sometimes be very difficult to solve depending on the model settings (assumptions, dimensionality, …). In large problems, exact solutions require, indeed, heavy computations that often become intractable and some approximation techniques have to be used to overcome this issue and build fast and scalable systems. In this post we will discuss the two main methods that can be used to tackle the Bayesian inference problem: Markov Chain Monte Carlo (MCMC), that is a sampling based approach, and Variational Inference (VI), that is an approximation based approach.

Structure learning algorithms that learn the graph of a Bayesian network from observational data often do so by assuming the data correctly reflect the true distribution of the variables. However, this assumption does not hold in the presence of measurement error, which can lead to spurious edges. This is one of the reasons why the synthetic performance of these algorithms often overestimates real-world performance. This paper describes an algorithm that can be added as an additional learning phase at the end of any structure learning algorithm, and serves as a correction learning phase that removes potential false positive edges. The results show that the proposed correction algorithm successfully improves the graphical score of four well-established structure learning algorithms spanning different classes of learning in the presence of measurement error.

This paper presents how the hybrid combination of behavior trees and the neuroscientific principle of active inference can be used for action planning and execution for reactive robot behaviors in dynamic environments. We show how complex robotic tasks can be formulated as a free-energy minimisation problem, and how state estimation and symbolic decision making are handled within the same framework. The general behavior is specified offline through behavior trees, where the leaf nodes represent desired states, not actions as in classical behavior trees. The decision of which action to execute to reach a state is left to the online active inference routine, in order to resolve unexpected contingencies. This hybrid combination improves the robustness of plans specified through behavior trees, while allowing to cope with the curse of dimensionality in active inference. The properties of the proposed algorithm are analysed in terms of robustness and convergence, and the theoretical results are validated using a mobile manipulator in a retail environment.

Background: The methods with which prediction models are usually developed mean that neither the parameters nor the predictions should be interpreted causally. For many applications this is perfectly acceptable. However, when prediction models are used to support decision making, there is often a need for predicting outcomes under hypothetical interventions. Aims: We aimed to identify and compare published methods for developing and validating prediction models that enable risk estimation of outcomes under hypothetical interventions, utilizing causal inference. We aimed to identify the main methodological approaches, their underlying assumptions, targeted estimands, and possible sources of bias. Finally, we aimed to highlight unresolved methodological challenges. Methods: We systematically reviewed literature published by December 2019, considering papers in the health domain that used causal considerations to enable prediction models to be used to evaluate predictions under hypothetical interventions. We included both methodology development studies and applied studies. Results: We identified 4919 papers through database searches and a further 115 papers through manual searches. Of these, 87 papers were retained for full text screening, of which 12 were selected for inclusion. We found papers from both the statistical and the machine learning literature. Most of the identified methods for causal inference from observational data were based on marginal structural models and g-estimation.

Deep reinforcement learning has achieved impressive successes yet often requires a very large amount of interaction data. This result is perhaps unsurprising, as using complicated function approximation often requires more data to fit, and early theoretical results on linear Markov decision processes provide regret bounds that scale with the dimension of the linear approximation. Ideally, we would like to automatically identify the minimal dimension of the approximation that is sufficient to encode an optimal policy. Towards this end, we consider the problem of model selection in RL with function approximation, given a set of candidate RL algorithms with known regret guarantees. The learner's goal is to adapt to the complexity of the optimal algorithm without knowing it \textit{a priori}. We present a meta-algorithm that successively rejects increasingly complex models using a simple statistical test. Given at least one candidate that satisfies realizability, we prove the meta-algorithm adapts to the optimal complexity with $\tilde{O}(L^{5/6} T^{2/3})$ regret compared to the optimal candidate's $\tilde{O}(\sqrt T)$ regret, where $T$ is the number of episodes and $L$ is the number of algorithms. The dimension and horizon dependencies remain optimal with respect to the best candidate, and our meta-algorithmic approach is flexible to incorporate multiple candidate algorithms and models. Finally, we show that the meta-algorithm automatically admits significantly improved instance-dependent regret bounds that depend on the gaps between the maximal values attainable by the candidates.