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This paper introduces a novel parameter estimation method for the probability tables of Bayesian network classifiers (BNCs), using hierarchical Dirichlet processes (HDPs). The main result of this paper is to show that improved parameter…

We define a measure for the complexity of Boolean functions related to their implementation in neural networks, and in particular close related to the generalization ability that could be obtained through the learning process. The measure…

Neural networks (NN) have achieved state-of-the-art performance in various applications. Unfortunately in applications where training data is insufficient, they are often prone to overfitting. One effective way to alleviate this problem is…

A major problem for the learning of Bayesian networks (BNs) is the exponential number of parameters needed for conditional probability tables. Recent research reduces this complexity by modeling local structure in the probability tables. We…

This paper describes a new library for learning Bayesian networks from data containing discrete and continuous variables (mixed data). In addition to the classical learning methods on discretized data, this library proposes its algorithm…

Neural networks are becoming increasingly prevalent in software, and it is therefore important to be able to verify their behavior. Because verifying the correctness of neural networks is extremely challenging, it is common to focus on the…

We introduce a novel combination of Bayesian Models (BMs) and Neural Networks (NNs) for making predictions with a minimum expected risk. Our approach combines the best of both worlds, the data efficiency and interpretability of a BM with…

In this paper, we introduce BNN-DP, an efficient algorithmic framework for analysis of adversarial robustness of Bayesian Neural Networks (BNNs). Given a compact set of input points $T\subset \mathbb{R}^n$, BNN-DP computes lower and upper…

We show at a physics level of rigor that Bayesian inference with a fully connected neural network and a shaped nonlinearity of the form $\phi(t) = t + \psi t^3/L$ is (perturbatively) solvable in the regime where the number of training…

Bayesian methods, distributionally robust optimization methods, and regularization methods are three pillars of trustworthy machine learning combating distributional uncertainty, e.g., the uncertainty of an empirical distribution compared…

In recent years, researchers in decision analysis and artificial intelligence (Al) have used Bayesian belief networks to build models of expert opinion. Using standard methods drawn from the theory of computational complexity, workers in…

We introduce two algorithms for computing tight guarantees on the probabilistic robustness of Bayesian Neural Networks (BNNs). Computing robustness guarantees for BNNs is a significantly more challenging task than verifying the robustness…

We provide a new characterization of the Dirichlet distribution. This characterization implies that under assumptions made by several previous authors for learning belief networks, a Dirichlet prior on the parameters is inevitable.

In Bayesian Network Structure Learning (BNSL), one is given a variable set and parent scores for each variable and aims to compute a DAG, called Bayesian network, that maximizes the sum of parent scores, possibly under some structural…

Belief updating in Bayes nets, a well known computationally hard problem, has recently been approximated by several deterministic algorithms, and by various randomized approximation algorithms. Deterministic algorithms usually provide…

The paper introduces mixed networks, a new framework for expressing and reasoning with probabilistic and deterministic information. The framework combines belief networks with constraint networks, defining the semantics and graphical…

State-of-the-art neural network-based methods for learning summary statistics have delivered promising results for simulation-based likelihood-free parameter inference. Existing approaches require density estimation as a post-processing…

Bayesian neural networks (BNNs) have been long considered an ideal, yet unscalable solution for improving the robustness and the predictive uncertainty of deep neural networks. While they could capture more accurately the posterior…

Belief propagation (BP) is a message-passing heuristic for statistical inference in graphical models such as Bayesian networks and Markov random fields. BP is used to compute marginal distributions or maximum likelihood assignments and has…

This paper introduces a computational framework for reasoning in Bayesian belief networks that derives significant advantages from focused inference and relevance reasoning. This framework is based on d -separation and other simple and…