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Score-based models have achieved remarkable results in the generative modeling of many domains. By learning the gradient of smoothed data distribution, they can iteratively generate samples from complex distribution e.g. natural images.…
In our previous work, we introduced the rule-based Bayesian Regression, a methodology that leverages two concepts: (i) Bayesian inference, for the general framework and uncertainty quantification and (ii) rule-based systems for the…
Real-world data often exhibits sequential dependence, across diverse domains such as human behavior, medicine, finance, and climate modeling. Probabilistic methods capture the inherent uncertainty associated with prediction in these…
In a standard regression problem, we have a set of explanatory variables whose effect on some response vector is modeled. For wide binary data, such as genetic marker data, we often have two limitations. First, we have more parameters than…
Promising results have driven a recent surge of interest in continuous optimization methods for Bayesian network structure learning from observational data. However, there are theoretical limitations on the identifiability of underlying…
Bayesian models provide recursive inference naturally because they can formally reconcile new data and existing scientific information. However, popular use of Bayesian methods often avoids priors that are based on exact posterior…
Natural language processing has greatly benefited from the introduction of the attention mechanism. However, standard attention models are of limited interpretability for tasks that involve a series of inference steps. We describe an…
Recursive graph queries are increasingly popular for extracting information from interconnected data found in various domains such as social networks, life sciences, and business analytics. Graph data often come with schema information that…
Causal graphs (CGs) are compact representations of the knowledge of the data generating processes behind the data distributions. When a CG is available, e.g., from the domain knowledge, we can infer the conditional independence (CI)…
This paper is devoted to the estimation of a partial graphical model with a structural Bayesian penalization. Precisely, we are interested in the linear regression setting where the estimation is made through the direct links between…
For decades, researchers in fields, such as the natural and social sciences, have been verifying causal relationships and investigating hypotheses that are now well-established or understood as truth. These causal mechanisms are properties…
Modeling multivariate time series as temporal signals over a (possibly dynamic) graph is an effective representational framework that allows for developing models for time series analysis. In fact, discrete sequences of graphs can be…
We address the problem of learning graphical models which correspond to high dimensional autoregressive stationary stochastic processes. A graphical model describes the conditional dependence relations among the components of a stochastic…
Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make…
Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…
Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…
We derive a novel generative model from iterative Gaussian posterior inference. By treating the generated sample as an unknown variable, we can formulate the sampling process in the language of Bayesian probability. Our model uses a…
Tackling the problem of learning probabilistic classifiers from incomplete data in the context of Knowledge Graphs expressed in Description Logics, we describe an inductive approach based on learning simple belief networks. Specifically, we…
Graphs serve as generic tools to encode the underlying relational structure of data. Often this graph is not given, and so the task of inferring it from nodal observations becomes important. Traditional approaches formulate a convex inverse…
Priors are essential for reconstructing images from noisy and/or incomplete measurements. The choice of the prior determines both the quality and uncertainty of recovered images. We propose turning score-based diffusion models into…