Related papers: Bayesian optimal experimental design with Wasserst…
We define the information threshold as the point of maximum curvature in the prior vs. posterior Bayesian curve, both of which are described as a function of the true positive and negative rates of the classification system in question. The…
We introduce a novel geometric framework for optimal experimental design (OED). Traditional OED approaches, such as those based on mutual information, rely explicitly on probability densities, leading to restrictive invariance properties.…
Most computational approaches to Bayesian experimental design require making posterior calculations repeatedly for a large number of potential designs and/or simulated datasets. This can be expensive and prohibit scaling up these methods to…
In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We…
We propose a novel Wasserstein method with a distillation mechanism, yielding joint learning of word embeddings and topics. The proposed method is based on the fact that the Euclidean distance between word embeddings may be employed as the…
History-dependent constitutive models serve as macroscopic closures for the aggregated effects of micromechanics. Their parameters are typically learned from experimental data. With a limited experimental budget, eliciting the full range of…
A model-based optimal experiment design (OED) of nonlinear systems is studied. OED represents a methodology for optimizing the geometry of the parametric joint-confidence regions (CRs), which are obtained in an a posteriori analysis of the…
We consider finite-dimensional Bayesian linear inverse problems with Gaussian priors and additive Gaussian noise models. The goal of this note is to present a simple derivation of the well-known fact that solving the Bayesian D-optimal…
Inferring the causal structure of a system typically requires interventional data, rather than just observational data. Since interventional experiments can be costly, it is preferable to select interventions that yield the maximum amount…
As a natural approach to modeling system safety conditions, chance constraint (CC) seeks to satisfy a set of uncertain inequalities individually or jointly with high probability. Although a joint CC offers stronger reliability certificate,…
The design of informatively rich input signals is essential for accurate system identification, yet classical Fisher-information-based methods are inherently local and often inadequate in the presence of significant model uncertainty and…
Clustering is an important exploratory data analysis technique to group objects based on their similarity. The widely used $K$-means clustering method relies on some notion of distance to partition data into a fewer number of groups. In the…
We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…
In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel. Recently, other distances…
We investigate the problem of estimating the causal effect of a treatment on individual subjects from observational data, this is a central problem in various application domains, including healthcare, social sciences, and online…
We propose a methodology for intercomparing climate models and evaluating their performance against benchmarks based on the use of the Wasserstein distance (WD). This distance provides a rigorous way to measure quantitatively the difference…
Split conformal prediction provides finite-sample marginal coverage under exchangeability, but this guarantee averages over the random calibration sample. We study instead the law of the calibration-conditional coverage induced by a…
We study Bayesian estimation of finite mixture models in a general setup where the number of components is unknown and allowed to grow with the sample size. An assumption on growing number of components is a natural one as the degree of…
Nowadays stochastic computer simulations with both numeral and distribution inputs are widely used to mimic complex systems which contain a great deal of uncertainty. This paper studies the design and analysis issues of such computer…
We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of…