Related papers: A Neural Bayesian Estimator for Conditional Probab…

A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated…

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…

We show an alternative way of representing a Bayesian belief network by sensitivities and probability distributions. This representation is equivalent to the traditional representation by conditional probabilities, but makes dependencies…

We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…

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…

Stochastic processes defined on integer valued state spaces are popular within the physical and biological sciences. These models are necessary for capturing the dynamics of small systems where the individual nature of the populations…

Maximum likelihood estimation is effective for identifying dynamical systems, but applying it to large networks becomes computationally prohibitive. This paper introduces a maximum likelihood estimation method that enables identification of…

We establish statistical properties of random-weighting methods in LASSO regression under different regularization parameters $\lambda_n$ and suitable regularity conditions. The random-weighting methods in view concern repeated optimization…

System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…

Bayesian neural networks with latent variables are scalable and flexible probabilistic models: They account for uncertainty in the estimation of the network weights and, by making use of latent variables, can capture complex noise patterns…

Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory.…

Bayesian network is a complete model for the variables and their relationships, it can be used to answer probabilistic queries about them. A Bayesian network can thus be considered a mechanism for automatically applying Bayes' theorem to…

In this paper, a Neural network is derived from first principles, assuming only that each layer begins with a linear dimension-reducing transformation. The approach appeals to the principle of Maximum Entropy (MaxEnt) to find the posterior…

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

Bayesian optimization (BO) is a sample-efficient method and has been widely used for optimizing expensive black-box functions. Recently, there has been a considerable interest in BO literature in optimizing functions that are affected by…

We present a new family of exchangeable stochastic processes, the Functional Neural Processes (FNPs). FNPs model distributions over functions by learning a graph of dependencies on top of latent representations of the points in the given…

We study active structure learning of Bayesian networks in an observational setting, in which there are external limitations on the number of variable values that can be observed from the same sample. Random samples are drawn from the joint…

Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…

Normalizing Flows (NFs) are able to model complicated distributions p(y) with strong inter-dimensional correlations and high multimodality by transforming a simple base density p(z) through an invertible neural network under the change of…

Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…