Related papers: Optimal use of time dependent probability density …

Data augmentation is an effective technique to improve the generalization of deep neural networks. However, previous data augmentation methods usually treat the augmented samples equally without considering their individual impacts on the…

Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models…

In many scientific applications, the target probability distribution cannot be evaluated in closed form or sampled from directly. Instead, it can often be decomposed into multiple components, some of which are accessible only through…

Sampling complex free energy surfaces is one of the main challenges of modern atomistic simulation methods. The presence of kinetic bottlenecks in such surfaces often renders a direct approach useless. A popular strategy is to identify a…

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…

The theory of spectral filtering is a remarkable tool to understand the statistical properties of learning with kernels. For least squares, it allows to derive various regularization schemes that yield faster convergence rates of the excess…

In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a…

We design a new iterative algorithm, called REINFORCE-OPT, for solving a general type of optimization problems. This algorithm parameterizes the solution search rule and iteratively updates the parameter using a reinforcement learning (RL)…

Robust Bayesian inference using density power divergence (DPD) has emerged as a promising approach for handling outliers in statistical estimation. Although the DPD-based posterior offers theoretical guarantees of robustness, its practical…

Uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electric grids. Among various approaches for decision making in uncertain environments,…

The improved method of intermittent data analysis is proposed. It exploits, in addition to the standard density moments, the information on the bin-bin correlations, observed in the data and expressed in terms of the density correlators.…

Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, which are a necessity due to the ill-posedness of inverse problems. Tikhonov-type regularization methods are very popular in…

We develop a tractable and flexible approach for incorporating side information into dynamic optimization under uncertainty. The proposed framework uses predictive machine learning methods (such as $k$-nearest neighbors, kernel regression,…

We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…

Conditional stability estimates allow us to characterize the degree of ill-posedness of many inverse problems, but without further assumptions they are not sufficient for the stable solution in the presence of data perturbations. We here…

In this work, we investigate the inverse problem of recovering a potential coefficient in an elliptic partial differential equation from the observations at deterministic sampling points in the domain subject to random noise. We employ a…

In this work, we explore the use of operator splitting algorithms for solving regularized structural topology optimization problems. The context is the classical structural design problems (e.g., compliance minimization and compliant…

We study weighted Tikhonov regularization for large-scale linear discrete ill-posed problems with random noise. Under a polynomial upper-bound assumption on the generalized eigenvalues of the discrete forward operator, we derive stochastic…

Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…

We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an…