MIT press provides another excellent book in creative commons. I plan to buy it and I recommend you do. This book provides a broad introduction to algorithms for decision making under uncertainty. An agent is an entity that acts based on observations of its environment. The interaction between the agent and the environment follows an observe-act cycle or loop.

We consider the problem of modeling trajectories of drivers in a road network from the perspective of inverse reinforcement learning. As rational agents, drivers are trying to maximize some reward function unknown to an external observer as they make up their trajectories. We apply the concept of random utility from microeconomic theory to model the unknown reward function as a function of observable features plus an error term which represents features known only to the driver. We develop a parameterized generative model for the trajectories based on a random utility Markov decision process formulation of drivers decisions. We show that maximum entropy inverse reinforcement learning is a particular case of our proposed formulation when we assume a Gumbel density function for the unobserved reward error terms. We illustrate Bayesian inference on model parameters through a case study with real trajectory data from a large city obtained from sensors placed on sparsely distributed points on the street network.

In this paper, we show that coherent sets of gambles can be embedded into the algebraic structure of information algebra. This leads firstly, to a new perspective of the algebraic and logical structure of desirability and secondly, it connects desirability, hence imprecise probabilities, to other formalism in computer science sharing the same underlying structure. Both the domain-free and the labeled view of the information algebra of coherent sets of gambles are presented, considering general possibility spaces.

Bayesian structure learning allows inferring Bayesian network structure from data while reasoning about the epistemic uncertainty -- a key element towards enabling active causal discovery and designing interventions in real world systems. In this work, we propose a general, fully differentiable framework for Bayesian structure learning (DiBS) that operates in the continuous space of a latent probabilistic graph representation. Building on recent advances in variational inference, we use DiBS to devise an efficient method for approximating posteriors over structural models. Contrary to existing work, DiBS is agnostic to the form of the local conditional distributions and allows for joint posterior inference of both the graph structure and the conditional distribution parameters. This makes our method directly applicable to posterior inference of nonstandard Bayesian network models, e.g., with nonlinear dependencies encoded by neural networks. In evaluations on simulated and real-world data, DiBS significantly outperforms related approaches to joint posterior inference.

A test is adaptive when its sequence and number of questions is dynamically tuned on the basis of the estimated skills of the taker. Graphical models, such as Bayesian networks, are used for adaptive tests as they allow to model the uncertainty about the questions and the skills in an explainable fashion, especially when coping with multiple skills. A better elicitation of the uncertainty in the question/skills relations can be achieved by interval probabilities. This turns the model into a credal network, thus making more challenging the inferential complexity of the queries required to select questions. This is especially the case for the information theoretic quantities used as scores to drive the adaptive mechanism. We present an alternative family of scores, based on the mode of the posterior probabilities, and hence easier to explain. This makes considerably simpler the evaluation in the credal case, without significantly affecting the quality of the adaptive process. Numerical tests on synthetic and real-world data are used to support this claim.

After the tremendous advances of deep learning and other AI methods, more attention is flowing into other properties of modern approaches, such as interpretability, fairness, etc. combined in frameworks like Responsible AI. Two research directions, namely Explainable AI and Uncertainty Quantification are becoming more and more important, but have been so far never combined and jointly explored. In this paper, I show how both research areas provide potential for combination, why more research should be done in this direction and how this would lead to an increase in trustability in AI systems.

Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its computation is key to several probabilistic reasoning tasks. Given the #P-hardness of computing the partition function, several techniques have been proposed over the years with varying guarantees on the quality of estimates and their runtime behavior. This paper seeks to present a survey of 18 techniques and a rigorous empirical study of their behavior across an extensive set of benchmarks. Our empirical study draws up a surprising observation: exact techniques are as efficient as the approximate ones, and therefore, we conclude with an optimistic view of opportunities for the design of approximate techniques with enhanced scalability. Motivated by the observation of an order of magnitude difference between the Virtual Best Solver and the best performing tool, we envision an exciting line of research focused on the development of portfolio solvers.

Machine learning has achieved an important role in the automatic classification of variable stars, and several classifiers have been proposed over the last decade. These classifiers have achieved impressive performance in several astronomical catalogues. However, some scientific articles have also shown that the training data therein contain multiple sources of bias. Hence, the performance of those classifiers on objects not belonging to the training data is uncertain, potentially resulting in the selection of incorrect models. Besides, it gives rise to the deployment of misleading classifiers. An example of the latter is the creation of open-source labelled catalogues with biased predictions. In this paper, we develop a method based on an informative marginal likelihood to evaluate variable star classifiers. We collect deterministic rules that are based on physical descriptors of RR Lyrae stars, and then, to mitigate the biases, we introduce those rules into the marginal likelihood estimation. We perform experiments with a set of Bayesian Logistic Regressions, which are trained to classify RR Lyraes, and we found that our method outperforms traditional non-informative cross-validation strategies, even when penalized models are assessed. Our methodology provides a more rigorous alternative to assess machine learning models using astronomical knowledge. From this approach, applications to other classes of variable stars and algorithmic improvements can be developed.

We introduce a simple and scalable method for training Gaussian process (GP) models that exploits cross-validation and nearest neighbor truncation. To accommodate binary and multi-class classification we leverage P\`olya-Gamma auxiliary variables and variational inference. In an extensive empirical comparison with a number of alternative methods for scalable GP regression and classification, we find that our method offers fast training and excellent predictive performance. We argue that the good predictive performance can be traced to the non-parametric nature of the resulting predictive distributions as well as to the cross-validation loss, which provides robustness against model mis-specification.

In some cases we will need an array with more than two axes. In the general case, an array of numbers arranged on a regular grid with a variable number of axes is known as a tensor. Tensors and Multidimensional arrays are different types of object, the first is a type of function, the second is a data structure suitable for representing a tensor in a coordinate system. A scalar is just a single number, in contrast to most of the other objects studied in linear algebra, which are usually arrays of multiple numbers. In terms of tensor -- A tensor that contains only one number is called a Scalar(or scalar tensor, or 0-dimensional tensor, or 0D tensor).