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We introduce a new compositional framework for generalized variational inference, clarifying the different parts of a model, how they interact, and how they compose. We explain that both exact Bayesian inference and the loss functions…
An elaboration of Dempster's method of constructing belief functions suggests a broadly applicable strategy for constructing lower probabilities under a variety of evidentiary constraints.
We consider the problem of constructing Bayesian based confidence sets for linear functionals in the inverse Gaussian white noise model. We work with a scale of Gaussian priors indexed by a regularity hyper-parameter and apply the…
Deciding what to sense is a crucial task, made harder by dependencies and by a nonadditive utility function. We develop approximation algorithms for selecting an optimal set of measurements, under a dependency structure modeled by a…
Generative Bayesian Filtering (GBF) provides a powerful and flexible framework for performing posterior inference in complex nonlinear and non-Gaussian state-space models. Our approach extends Generative Bayesian Computation (GBC) to…
We consider the task of aggregating beliefs of severalexperts. We assume that these beliefs are represented as probabilitydistributions. We argue that the evaluation of any aggregationtechnique depends on the semantic context of this task.…
Consider a Gaussian memoryless multiple source with $m$ components with joint probability distribution known only to lie in a given class of distributions. A subset of $k \leq m$ components are sampled and compressed with the objective of…
In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a…
Belief function theory provides a flexible way to combine information provided by different sources. This combination is usually followed by a decision making which can be handled by a range of decision rules. Some rules help to choose the…
Generating synthetic datasets that accurately reflect real-world observational data is critical for evaluating causal estimators, but it remains a challenging task. Existing generative methods offer a solution by producing synthetic…
We propose a novel Bayesian model framework for discrete ordinal and count data based on conditional transformations of the responses. The conditional transformation function is estimated from the data in conjunction with an a priori chosen…
Harnessing the predictive capability of Markov process models requires propagating probability density functions (beliefs) through the model. For many existing models however, belief propagation is analytically infeasible, requiring…
A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is…
We propose a Bayesian nonparametric (BNP) approach to causal inference using observational data consisting of outcome, treatment, and a set of confounders. The conditional distribution of the outcome given treatment and confounders is…
We present a new approach for inference in Bayesian networks, which is mainly based on partial differentiation. According to this approach, one compiles a Bayesian network into a multivariate polynomial and then computes the partial…
Foundation models, and in particular large language models, can generate highly informative responses, prompting growing interest in using these ''synthetic'' outputs as data in empirical research and decision-making. This paper introduces…
Complex data usually results from the interaction of objects produced by different generating mechanisms. Here we introduce a universal, unsupervised and parameter-free model-oriented approach, based upon the seminal concept of algorithmic…
Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…
Basic principles of statistical inference are commonly violated in network data analysis. Under the current approach, it is often impossible to identify a model that accommodates known empirical behaviors, possesses crucial inferential…
Prediction is a central task of statistics and machine learning, yet many inferential settings provide only partial information, typically in the form of moment constraints or estimating equations. We develop a finite, fully Bayesian…