Related papers: Expected information gain estimation via density a…

Inverse analysis, such as model calibration, often suffers from a lack of informative data in complex real-world scenarios. The standard remedy, designing new experimental setups, is often costly and time-consuming, while readily available…

Bayesian optimal design is considered for experiments where the response distribution depends on the solution to a system of non-linear ordinary differential equations. The motivation is an experiment to estimate parameters in the equations…

Mutual information (MI) is a fundamental quantity in information theory and machine learning. However, direct estimation of MI is intractable, even if the true joint probability density for the variables of interest is known, as it involves…

A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…

This paper presents a general asymptotic theory of sequential Bayesian estimation giving results for the strongest, almost sure convergence. We show that under certain smoothness conditions on the probability model, the greedy information…

Simultaneous analysis of gene expression data and genetic variants is highly of interest, especially when the number of gene expressions and genetic variants are both greater than the sample size. Association of both causal genes and…

Machine learning systems operate under the assumption that training and test data are sampled from a fixed probability distribution. However, this assumptions is rarely verified in practice, as the conditions upon which data was acquired…

Conventional Bayesian optimal experimental design seeks to maximize the expected information gain (EIG) on model parameters. However, the end goal of the experiment often is not to learn the model parameters, but to predict downstream…

The generation of decision-theoretic Bayesian optimal designs is complicated by the significant computational challenge of minimising an analytically intractable expected loss function over a, potentially, high-dimensional design space. A…

Design of experiments has traditionally relied on the frequentist hypothesis testing framework where the optimal size of the experiment is specified as the minimum sample size that guarantees a required level of power. Sample size…

The intrinsic dimensionality of an inverse problem is affected by prior information, the accuracy and number of observations, and the smoothing properties of the forward operator. From a Bayesian perspective, changes from the prior to the…

In this paper, we propose an information geometry (IG) framework to solve the standard linear regression problem. The proposed framework is an extension of the one for computing the mean of complex multivariate Gaussian distribution. By…

We design efficient distance approximation algorithms for several classes of structured high-dimensional distributions. Specifically, we show algorithms for the following problems: - Given sample access to two Bayesian networks $P_1$ and…

Although Bayesian density estimation using discrete mixtures has good performance in modest dimensions, there is a lack of statistical and computational scalability to high-dimensional multivariate cases. To combat the curse of…

Motivated by the presence of deep connections among dynamical equations, experimental data, physical systems, and statistical modeling, we report on a series of findings uncovered by the Authors and collaborators during the last decade…

We propose a method for estimating the posterior distribution of a standard geostatistical model. After choosing the model formulation and specifying a prior, we use normal mixture densities to approximate the posterior distribution. The…

By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…

Bayesian optimal experimental design (OED) seeks to conduct the most informative experiment under budget constraints to update the prior knowledge of a system to its posterior from the experimental data in a Bayesian framework. Such…

Efficient signal representation is essential for the functioning of living and artificial systems operating under resource constraints. A widely recognized framework for deriving such representations is the information bottleneck method,…

Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…