Related papers: A Hybrid Algorithm to Compute Marginal and Joint B…

We consider probabilistic inference in general hybrid networks, which include continuous and discrete variables in an arbitrary topology. We reexamine the question of variable discretization in a hybrid network aiming at minimizing the…

We present new algorithms for learning Bayesian networks from data with missing values using a data augmentation approach. An exact Bayesian network learning algorithm is obtained by recasting the problem into a standard Bayesian network…

Discovery of an accurate causal Bayesian network structure from observational data can be useful in many areas of science. Often the discoveries are made under uncertainty, which can be expressed as probabilities. To guide the use of such…

We propose a novel Bayesian approach to the problem of variable selection in multiple linear regression models. In particular, we present a hierarchical setting which allows for direct specification of a-priori beliefs about the number of…

We consider a Bayesian method for learning the Bayesian network structure from complete data. Recently, Koivisto and Sood (2004) presented an algorithm that for any single edge computes its marginal posterior probability in O(n 2^n) time,…

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…

The interpretation of numerical methods, such as finite difference methods for differential equations, as point estimators suggests that formal uncertainty quantification can also be performed in this context. Competing statistical…

Analyzing multilayer networks is central to understanding complex relational measurements collected across multiple conditions or over time. A pivotal task in this setting is to quantify uncertainty in community structure while…

Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a…

Noisy-OR Bayesian Networks (BNs) are a family of probabilistic graphical models which express rich statistical dependencies in binary data. Variational inference (VI) has been the main method proposed to learn noisy-OR BNs with complex…

We study the problem of learning the best Bayesian network structure with respect to a decomposable score such as BDe, BIC or AIC. This problem is known to be NP-hard, which means that solving it becomes quickly infeasible as the number of…

Bayesian inference is an important technique throughout statistics. The essence of Beyesian inference is to derive the posterior belief updated from prior belief by the learned information, which is a set of differentially private answers…

A new variant of Newton's method for empirical risk minimization is studied, where at each iteration of the optimization algorithm, the gradient and Hessian of the objective function are replaced by robust estimators taken from existing…

Deep learning has been used to improve photoacoustic (PA) image reconstruction. One major challenge is that errors cannot be quantified to validate predictions when ground truth is unknown. Validation is key to quantitative applications,…

We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…

Incomplete data are a common feature in many domains, from clinical trials to industrial applications. Bayesian networks (BNs) are often used in these domains because of their graphical and causal interpretations. BN parameter learning from…

Despite the recent successes of probabilistic programming languages (PPLs) in AI applications, PPLs offer only limited support for random variables whose distributions combine discrete and continuous elements. We develop the notion of…

Real-world problems often require reasoning about hybrid beliefs, over both discrete and continuous random variables. Yet, such a setting has hardly been investigated in the context of planning. Moreover, existing online Partially…

This paper focuses on probability updates in multiply-connected belief networks. Pearl has designed the method of conditioning, which enables us to apply his algorithm for belief updates in singly-connected networks to multiply-connected…

We present a novel hybrid algorithm for Bayesian network structure learning, called Hybrid HPC (H2PC). It first reconstructs the skeleton of a Bayesian network and then performs a Bayesian-scoring greedy hill-climbing search to orient the…