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The computational burden of probabilistic inference remains a hurdle for applying probabilistic programming languages to practical problems of interest. In this work, we provide a semantic and algorithmic foundation for efficient exact…

This paper considers a distributionally robust chance constraint model with a general ambiguity set. We show that a sample based approximation of this model converges under suitable sufficient conditions. We also show that upper and lower…

Mixtures of experts probabilistically divide the input space into regions, where the assumptions of each expert, or conditional model, need only hold locally. Combined with Gaussian process (GP) experts, this results in a powerful and…

In the following article we consider approximate Bayesian parameter inference for observation driven time series models. Such statistical models appear in a wide variety of applications, including econometrics and applied mathematics. This…

Bayesian networks (BNs) are probabilistic graphical models for describing complex joint probability distributions. The main problem for BNs is inference: Determine the probability of an event given observed evidence. Since exact inference…

Individual treatment effects are not point-identified from data. The Probability of Necessity and Sufficiency (PNS) circumvents this limitation by characterizing individual-level causality through intersection bounds derived from combined…

Computational mechanics, an approach to structural complexity, defines a process's causal states and gives a procedure for finding them. We show that the causal-state representation--an $\epsilon$-machine--is the minimal one consistent with…

The concept of Probability of Causation (PC) is critically important in legal contexts and can help in many other domains. While it has been around since 1986, current operationalizations can obtain only the minimum and maximum values of…

Approximate Bayesian Computation (ABC) enables parameter inference for complex physical systems in cases where the true likelihood function is unknown, unavailable, or computationally too expensive. It relies on the forward simulation of…

Bayesian Neural Networks (BNNs) offer a principled and natural framework for proper uncertainty quantification in the context of deep learning. They address the typical challenges associated with conventional deep learning methods, such as…

The Conditional Neural Process (CNP) family of models offer a promising direction to tackle few-shot problems by achieving better scalability and competitive predictive performance. However, the current CNP models only capture the overall…

We improve recently published results about resources of Restricted Boltzmann Machines (RBM) and Deep Belief Networks (DBN) required to make them Universal Approximators. We show that any distribution p on the set of binary vectors of…

Bayesian inference methods are useful in infectious diseases modeling due to their capability to propagate uncertainty, manage sparse data, incorporate latent structures, and address high-dimensional parameter spaces. However, parameter…

We present a new method to propagate lower bounds on conditional probability distributions in conventional Bayesian networks. Our method guarantees to provide outer approximations of the exact lower bounds. A key advantage is that we can…

Theoretical approaches to binary-state models on complex networks are generally restricted to infinite size systems, where a set of non-linear deterministic equations is assumed to characterize its dynamics and stationary properties. We…

Annotating the right data for training deep neural networks is an important challenge. Active learning using uncertainty estimates from Bayesian Neural Networks (BNNs) could provide an effective solution to this. Despite being theoretically…

Stochastic spreading models defined on complex network topologies are used to mimic the diffusion of diseases, information, and opinions in real-world systems. Existing theoretical approaches to the characterization of the models in terms…

Since exact probabilistic inference is intractable in general for large multiply connected belief nets, approximate methods are required. A promising approach is to use heuristic search among hypotheses (instantiations of the network) to…

Deep neural networks (NNs) are known for their high-prediction performances. However, NNs are prone to yield unreliable predictions when encountering completely new situations without indicating their uncertainty. Bayesian variants of NNs…

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…