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The abundance of models of complex networks and the current insufficient validation standards make it difficult to judge which models are strongly supported by data and which are not. We focus here on likelihood maximization methods for…

Bayesian networks provide a method of representing conditional independence between random variables and computing the probability distributions associated with these random variables. In this paper, we extend Bayesian network structures to…

This paper explores algorithms for processing probabilistic and deterministic information when the former is represented as a belief network and the latter as a set of boolean clauses. The motivating tasks are 1. evaluating beliefs networks…

While Bayesian neural networks (BNNs) hold the promise of being flexible, well-calibrated statistical models, inference often requires approximations whose consequences are poorly understood. We study the quality of common variational…

Deep directed generative models have attracted much attention recently due to their expressive representation power and the ability of ancestral sampling. One major difficulty of learning directed models with many latent variables is the…

In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…

We present new algorithms for inference in credal networks --- directed acyclic graphs associated with sets of probabilities. Credal networks are here interpreted as encoding strong independence relations among variables. We first present a…

A Bayesian belief network models a joint distribution with an directed acyclic graph representing dependencies among variables and network parameters characterizing conditional distributions. The parameters are viewed as random variables to…

In recent years the belief network has been used increasingly to model systems in Al that must perform uncertain inference. The development of efficient algorithms for probabilistic inference in belief networks has been a focus of much…

The No Unmeasured Confounding Assumption is widely used to identify causal effects in observational studies. Recent work on proximal inference has provided alternative identification results that succeed even in the presence of unobserved…

The belief propagation (BP) algorithm is widely applied to perform approximate inference on arbitrary graphical models, in part due to its excellent empirical properties and performance. However, little is known theoretically about when…

To learn (statistical) dependencies among random variables requires exponentially large sample size in the number of observed random variables if any arbitrary joint probability distribution can occur. We consider the case that sparse data…

In this paper we consider the inference rules of System P in the framework of coherent imprecise probabilistic assessments. Exploiting our algorithms, we propagate the lower and upper probability bounds associated with the conditional…

Large-margin classifiers are popular methods for classification. We derive the asymptotic expression for the generalization error of a family of large-margin classifiers in the limit of both sample size $n$ and dimension $p$ going to…

We study product regular conditional probabilities under measures of two coordinates with respect to the second coordinate that are weakly continuous on the support of the marginal of the second coordinate. Assuming that there exists a…

Variational inference provides a powerful tool for approximate probabilistic in- ference on complex, structured models. Typical variational inference methods, however, require to use inference networks with computationally tractable proba-…

Inference algorithms for arbitrary belief networks are impractical for large, complex belief networks. Inference algorithms for specialized classes of belief networks have been shown to be more efficient. In this paper, we present a…

Likelihood-free inference refers to inference when a likelihood function cannot be explicitly evaluated, which is often the case for models based on simulators. Most of the literature is based on sample-based `Approximate Bayesian…

Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…

When the historical data are limited, the conditional probabilities associated with the nodes of Bayesian networks are uncertain and can be empirically estimated. Second order estimation methods provide a framework for both estimating the…