We focus on the problem of modeling deterministic equations over continuous variables in discrete Bayesian networks. This is typically achieved by a discretization of both input and output variables and a degenerate quantification of the corresponding conditional probability tables. This approach, based on classical probabilities, cannot properly model the information loss induced by the discretization. We show that a reliable modeling of such epistemic uncertainty can be instead achieved by credal sets, i.e., convex sets of probability mass functions. This transforms the original Bayesian network in a credal network, possibly returning interval-valued inferences, that are robust with respect to the information loss induced by the discretisation. Algorithmic strategies for an optimal choice of the discretisation bins are also provided.

In this paper, we present a Bayesian approach for finite mixture models based on three-parameter bivariate Beta distributions. The estimation of the parameters is based on the Monte Carlo simulation technique of Gibbs sampling mixed with a Metropolis-Hastings step. The performance of our Bayesian algorithm is verified by several synthetic datasets and in the end, the feasibility of the proposed method is demonstrated by experimenting on some real datasets in which, the results are compared with those obtained by implementing the same approach using Gaussian mixture model.

Bayesian networks (BNs) encode conditional independence to avoid combinatorial explosion on the number of variables, but are subject to exponential growth of space and inference time on the number of causes per effect variable. Among space-efficient local models, we focus on the Non-Impeding Noisy-AND Tree (NIN-AND Tree or NAT) models due to their multiple merits, and on NAT-modeled BNs where each multi-parent variable family may be encoded as a NAT-model. Although BN inference is generally exponential on treewidth, inference is tractable with NAT-modeled BNs of high treewidth and low density. In this work, we present the first study to learn NAT-modeled BNs from data. We apply the MDL principle to learning NAT-modeled BNs by developing a corresponding scoring function, and we couple it with heuristic structure search.

Bayesian inference is crucial to challenging scenarios that involve complex probabilistic models, which are usually intractable. In this work, we develop an expectation propagation approach to learn finite mixture models of EDCMs. The EDCM (Elkan 2006) is an exponential-family approximation to the widely used Dirichlet Compound Multinomial distribution and has been shown to offer excellent modeling capabilities in the case of sparse count data. Expectation propagation is a deterministic approach that provides accurate approximations to the full posterior and allows to include prior beliefs in the model as opposed to the maximum-likelihood method, which provides point estimates only. We evaluate the efficiency of our framework on several datasets for sentiment analysis and shape recognition.

Structure learning is a fundamental and challenging issue in dealing with Bayesian networks. In this paper we introduce a two-step clustering-based strategy, which can automatically generate prior information from data in order to further improve the accuracy and time efficiency of state-of-the-art algorithms in Bayesian network structure learning. Our clustering-based strategy is composed of two steps. In the first step, we divide the potential nodes into several groups via clustering analysis and apply Bayesian network structure learning to obtain some pre-existing arcs within each cluster. In the second step, with all the within-cluster arcs being well preserved, we learn the between-cluster structure of the given network. Experimental results on benchmark data sets show that a wide range of structure learning algorithms benefit from the proposed clustering-based strategy in terms of both accuracy and efficiency.

In this paper we address the task of extracting risk events and probabilities from free text, focusing in particular on the biomedical domain. While our initial motivation is to enable the determination of the parameters of a Bayesian belief network, our approach is not specific to that use case. We are the first to investigate this task as a sequence tagging problem where we label spans of text as events A or B that are then used to construct probability statements of the form P(A B) x. We show that our approach significantly outperforms an entity extraction baseline on a new annotated medical risk event corpus. We also explore semi-supervised methods that lead to modest improvement, encouraging further work in this direction.

Smart decision making at the tactical level is important for Artificial Intelligence (AI) agents to perform well in the domain of real-time strategy (RTS) games. Winning battles is crucial in RTS games, and while humans can decide when and how to attack based on their experience, it is challenging for AI agents to estimate combat outcomes accurately. A few existing models address this problem in the game of StarCraft but present many restrictions, such as not modeling injured units, supporting only a small number of unit types, or being able to predict the winner of a fight but not the remaining army. Prediction using simulations is a popular method, but generally slow and requires extensive coding to model the game engine accurately. This paper introduces a model based on Lanchester's attrition laws which addresses the mentioned limitations while being faster than running simulations. Unit strength values are learned using maximum likelihood estimation from past recorded battles. We present experiments that use a StarCraft simulator for generating battles for both training and testing, and show that the model is capable of making accurate predictions. Furthermore, we implemented our method in a StarCraft bot that uses either this or traditional simulations to decide when to attack or to retreat. We present tournament results (against top bots from 2014 AIIDE competition) comparing the performances of the two versions, and show increased winning percentages for our method.

PGMax is an open-source Python package for easy specification of discrete Probabilistic Graphical Models (PGMs) as factor graphs, and automatic derivation of efficient and scalable loopy belief propagation (LBP) implementation in JAX. It supports general factor graphs, and can effectively leverage modern accelerators like GPUs for inference. Compared with existing alternatives, PGMax obtains higher-quality inference results with orders-of-magnitude inference speedups. PGMax additionally interacts seamlessly with the rapidly growing JAX ecosystem, opening up exciting new possibilities. Our source code, examples and documentation are available at https://github.com/vicariousinc/PGMax.

Bayesian methods hold significant promise for improving the uncertainty quantification ability and robustness of deep neural network models. Recent research has seen the investigation of a number of approximate Bayesian inference methods for deep neural networks, building on both the variational Bayesian and Markov chain Monte Carlo (MCMC) frameworks. A fundamental issue with MCMC methods is that the improvements they enable are obtained at the expense of increased computation time and model storage costs. In this paper, we investigate the potential of sparse network structures to flexibly trade-off model storage costs and inference run time against predictive performance and uncertainty quantification ability. We use stochastic gradient MCMC methods as the core Bayesian inference method and consider a variety of approaches for selecting sparse network structures. Surprisingly, our results show that certain classes of randomly selected substructures can perform as well as substructures derived from state-of-the-art iterative pruning methods while drastically reducing model training times.

Multi-model ensemble analysis integrates information from multiple climate models into a unified projection. However, existing integration approaches based on model averaging can dilute fine-scale spatial information and incur bias from rescaling low-resolution climate models. We propose a statistical approach, called NN-GPR, using Gaussian process regression (GPR) with an infinitely wide deep neural network based covariance function. NN-GPR requires no assumptions about the relationships between models, no interpolation to a common grid, no stationarity assumptions, and automatically downscales as part of its prediction algorithm. Model experiments show that NN-GPR can be highly skillful at surface temperature and precipitation forecasting by preserving geospatial signals at multiple scales and capturing inter-annual variability. Our projections particularly show improved accuracy and uncertainty quantification skill in regions of high variability, which allows us to cheaply assess tail behavior at a 0.44$^\circ$/50 km spatial resolution without a regional climate model (RCM). Evaluations on reanalysis data and SSP245 forced climate models show that NN-GPR produces similar, overall climatologies to the model ensemble while better capturing fine scale spatial patterns. Finally, we compare NN-GPR's regional predictions against two RCMs and show that NN-GPR can rival the performance of RCMs using only global model data as input.