Active inference (AI) is a persuasive theoretical framework from computational neuroscience that seeks to describe action and perception as inference-based computation. However, this framework has yet to provide practical sensorimotor control algorithms that are competitive with alternative approaches. In this work, we frame active inference through the lens of control as inference (CaI), a body of work that presents trajectory optimization as inference. From the wider view of `probabilistic numerics', CaI offers principled, numerically robust optimal control solvers that provide uncertainty quantification, and can scale to nonlinear problems with approximate inference. We show that AI may be framed as partially-observed CaI when the cost function is defined specifically in the observation states.

This book is devoted to the problem of sequential probability forecasting, that is, predicting the probabilities of the next outcome of a growing sequence of observations given the past. This problem is considered in a very general setting that unifies commonly used probabilistic and non-probabilistic settings, trying to make as few as possible assumptions on the mechanism generating the observations. A common form that arises in various formulations of this problem is that of mixture predictors, which are formed as a combination of a finite or infinite set of other predictors attempting to combine their predictive powers. The main subject of this book are such mixture predictors, and the main results demonstrate the universality of this method in a very general probabilistic setting, but also show some of its limitations. While the problems considered are motivated by practical applications, involving, for example, financial, biological or behavioural data, this motivation is left implicit and all the results exposed are theoretical. The book targets graduate students and researchers interested in the problem of sequential prediction, and, more generally, in theoretical analysis of problems in machine learning and non-parametric statistics, as well as mathematical and philosophical foundations of these fields. The material in this volume is presented in a way that presumes familiarity with basic concepts of probability and statistics, up to and including probability distributions over spaces of infinite sequences. Familiarity with the literature on learning or stochastic processes is not required.

We give methods for Bayesian inference of directed acyclic graphs, DAGs, and the induced causal effects from passively observed complete data. Our methods build on a recent Markov chain Monte Carlo scheme for learning Bayesian networks, which enables efficient approximate sampling from the graph posterior, provided that each node is assigned a small number K of candidate parents. We present algorithmic tricks to significantly reduce the space and time requirements of the method, making it feasible to use substantially larger values of K. Furthermore, we investigate the problem of selecting the candidate parents per node so as to maximize the covered posterior mass. Finally, we combine our sampling method with a novel Bayesian approach for estimating causal effects in linear Gaussian DAG models. Numerical experiments demonstrate the performance of our methods in detecting ancestor-descendant relations, and in effect estimation our Bayesian method is shown to outperform existing approaches.

Reinforcement learning methods for traffic signal control has gained increasing interests recently and achieved better performances compared with traditional transportation methods. However, reinforcement learning based methods usually requires heavy training data and computational resources which largely limit its application in real-world traffic signal control. This makes meta-learning, which enables data-efficient and fast-adaptation training by leveraging the knowledge of previous learning experiences, catches attentions in traffic signal control. In this paper, we propose a novel value-based Bayesian meta-reinforcement learning framework BM-DQN to robustly speed up the learning process in new scenarios by utilizing well-trained prior knowledge learned from existing scenarios. This framework based on our proposed fast-adaptation variation to Gradient-EM Bayesian Meta-learning and the fast update advantage of DQN, which allows fast adaptation to new scenarios with continual learning ability and robustness to uncertainty. The experiments on 2D navigation and traffic signal control show that our proposed framework adapts more quickly and robustly in new scenarios than previous methods, and specifically, much better continual learning ability in heterogeneous scenarios.

General fuzzy min-max neural network (GFMMNN) is one of the efficient neuro-fuzzy systems for data classification. However, one of the downsides of its original learning algorithms is the inability to handle and learn from the mixed-attribute data. While categorical features encoding methods can be used with the GFMMNN learning algorithms, they exhibit a lot of shortcomings. Other approaches proposed in the literature are not suitable for on-line learning as they require entire training data available in the learning phase. With the rapid change in the volume and velocity of streaming data in many application areas, it is increasingly required that the constructed models can learn and adapt to the continuous data changes in real-time without the need for their full retraining or access to the historical data. This paper proposes an extended online learning algorithm for the GFMMNN. The proposed method can handle the datasets with both continuous and categorical features. The extensive experiments confirmed superior and stable classification performance of the proposed approach in comparison to other relevant learning algorithms for the GFMM model.

This paper exploits extended Bayesian networks for uncertainty reasoning on Petri nets, where firing of transitions is probabilistic. In particular, Bayesian networks are used as symbolic representations of probability distributions, modelling the observer's knowledge about the tokens in the net. The observer can study the net by monitoring successful and failed steps. An update mechanism for Bayesian nets is enabled by relaxing some of their restrictions, leading to modular Bayesian nets that can conveniently be represented and modified. As for every symbolic representation, the question is how to derive information - in this case marginal probability distributions - from a modular Bayesian net. We show how to do this by generalizing the known method of variable elimination. The approach is illustrated by examples about the spreading of diseases (SIR model) and information diffusion in social networks. We have implemented our approach and provide runtime results.

Online Social Networks (OSNs) provide a platform for users to share their thoughts and opinions with their community of friends or to the general public. In order to keep the platform safe for all users, as well as to keep it compliant with local laws, OSNs typically create a set of community standards organized into policy groups, and use Machine Learning (ML) models to identify and remove content that violates any of the policies. However, out of the billions of content that is uploaded on a daily basis only a small fraction is so unambiguously violating that it can be removed by the automated models. Prevalence estimation is the task of estimating the fraction of violating content in the residual items by sending a small sample of these items to human labelers to get ground truth labels. This task is exceedingly hard because even though we can easily get the ML scores or features for all of the billions of items we can only get ground truth labels on a few thousands of these items due to practical considerations. Indeed the prevalence can be so low that even after a judicious choice of items to be labeled there can be many days in which not even a single item is labeled violating. A pragmatic choice for such low prevalence, $10^{-4}$ to $10^{-5}$, regimes is to report the upper bound, or $97.5\%$ confidence interval, prevalence (UBP) that takes the uncertainties of the sampling and labeling processes into account and gives a smoothed estimate. In this work we present two novel techniques Bucketed-Beta-Binomial and a Bucketed-Gaussian Process for this UBP task and demonstrate on real and simulated data that it has much better coverage than the commonly used bootstrapping technique.

In this article, I will show how missing values can lead to biased estimates by working through a common dataset in 4 scenarios where the missing value mechanism differs. The content in this article is based on Chapter 15 in [1]. The code to reproduce the results in this article can be found in this notebook. I assume the reader is familiar with building generalized linear models (GLMs) and using directed acyclic graphs (DAGs) to illustrate causality. Suppose we want to study the effect of student diligence and homework quality. Let's imagine that we were somehow able to assign a real number to measure a student's diligence and that homework quality is measured on a 10-point scale, 0 to 10.

We analyze the $\ell_1$ and $\ell_\infty$ convergence rates of k nearest neighbor density estimation method. Our analysis includes two different cases depending on whether the support set is bounded or not. In the first case, the probability density function has a bounded support and is bounded away from zero. We show that kNN density estimation is minimax optimal under both $\ell_1$ and $\ell_\infty$ criteria, if the support set is known. If the support set is unknown, then the convergence rate of $\ell_1$ error is not affected, while $\ell_\infty$ error does not converge. In the second case, the probability density function can approach zero and is smooth everywhere. Moreover, the Hessian is assumed to decay with the density values. For this case, our result shows that the $\ell_\infty$ error of kNN density estimation is nearly minimax optimal. The $\ell_1$ error does not reach the minimax lower bound, but is better than kernel density estimation.

The emergence of Big Data raises the question of how to model economic relations when there is a large number of possible explanatory variables. We revisit the issue by comparing the possibility of using dense or sparse models in a Bayesian approach, allowing for variable selection and shrinkage. More specifically, we discuss the results reached by Giannone, Lenza, and Primiceri (2020) through a "Spike-and-Slab" prior, which suggest an "illusion of sparsity" in economic data, as no clear patterns of sparsity could be detected. We make a further revision of the posterior distributions of the model, and propose three experiments to evaluate the robustness of the adopted prior distribution. We find that the pattern of sparsity is sensitive to the prior distribution of the regression coefficients, and present evidence that the model indirectly induces variable selection and shrinkage, which suggests that the "illusion of sparsity" could be, itself, an illusion. Code is available on github.com/bfava/IllusionOfIllusion.