Related papers: Data selection: at the interface of PDE-based inve…

The main contribution of this paper is to develop a hierarchical Bayesian formulation of PINNs for linear inverse problems, which is called BPINN-IP. The proposed methodology extends PINN to account for prior knowledge on the nature of the…

One of the grand challenges of Mathematics instruction is to provide students with problems that are both accessible and have a reasonably elegant solution. Instructors commonly resort to resources like course textbooks, online-learning…

In recent work it has been shown that determining a feedforward ReLU neural network to within high uniform accuracy from point samples suffers from the curse of dimensionality in terms of the number of samples needed. As a consequence,…

This paper is concerned with the development, analysis and numerical realization of a novel variational model for the regularization of inverse problems in imaging. The proposed model is inspired by the architecture of generative…

To quantify uncertainties in inverse problems of partial differential equations (PDEs), we formulate them into statistical inference problems using Bayes' formula. Recently, well-justified infinite-dimensional Bayesian analysis methods have…

Neural networks have emerged as effective tools for solving ill-posed inverse problems. In many scientific applications, however, observational training data are insufficient, and learned inverse operators must instead be trained on…

We explore a multiple-stage variant of the min-max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this…

This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…

We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…

In this work we analyze principle component analysis (PCA) as a deterministic input-output system. We show that the relative information loss induced by reducing the dimensionality of the data after performing the PCA is the same as in…

We consider the problem of learning a linear operator $\theta$ between two Hilbert spaces from empirical observations, which we interpret as least squares regression in infinite dimensions. We show that this goal can be reformulated as an…

The Bayesian approach to inverse problems provides a practical way to solve ill-posed problems by augmenting the observation model with prior information. Due to the measure-theoretic underpinnings, the approach has raised theoretical…

This paper focuses on a specific aspect of human visual discrimination from computationally generated solutions for CAAD ends. The bottleneck at work here concern informational ratios of discriminative rates over generative ones. The amount…

Information divergence that measures the difference between two nonnegative matrices or tensors has found its use in a variety of machine learning problems. Examples are Nonnegative Matrix/Tensor Factorization, Stochastic Neighbor…

When, in terms of the number of data points, the size of a dataset exceeds available computing resources, or when labeling is expensive, an attractive solution consists of selecting only some of the data points (subdata) for further…

We present a deep transformation model for probabilistic regression. Deep learning is known for outstandingly accurate predictions on complex data but in regression tasks, it is predominantly used to just predict a single number. This…

Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often…

Although deep neural networks have achieved super-human performance on many classification tasks, they often exhibit a worrying lack of robustness towards adversarially generated examples. Thus, considerable effort has been invested into…

We present a framework for recovering/approximating unknown time-dependent partial differential equation (PDE) using its solution data. Instead of identifying the terms in the underlying PDE, we seek to approximate the evolution operator of…

The linear ordering problem (LOP), which consists in ordering M objects from their pairwise comparisons, is commonly applied in many areas of research. While efforts have been made to devise efficient LOP algorithms, verification of whether…