Related papers: A Correlation-induced Finite Difference Estimator

Conformal predictors are an important class of algorithms that allow predictions to be made with a user-defined confidence level. They are able to do this by outputting prediction sets, rather than simple point predictions. The conformal…

In this article, we present a simple technique for boosting the order of accuracy of finite difference schemes for time dependent partial differential equations by optimally selecting the time step used to advance the numerical solution and…

Stepped-wedge designs are increasingly used in randomized experiments to accommodate logistical and ethical constraints by staggering treatment roll-out over time. Despite their popularity, existing analytical methods largely rely on…

This work investigates finite differences and the use of interpolation models to obtain approximations to the first and second derivatives of a function. Here, it is shown that if a particular set of points is used in the interpolation…

In sparse estimation, such as fused lasso and convex clustering, we apply either the proximal gradient method or the alternating direction method of multipliers (ADMM) to solve the problem. It takes time to include matrix division in the…

We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…

This paper considers the problem of design-based inference for the average treatment effect in finely stratified experiments. Here, by "design-based'' we mean that the only source of uncertainty stems from the randomness in treatment…

Correlation filters are special classifiers designed for shift-invariant object recognition, which are robust to pattern distortions. The recent literature shows that combining a set of sub-filters trained based on a single or a small group…

This study develops a numerical scheme for path-dependent FBSDEs and PDEs. We introduce a Picard iteration method for solving path-dependent FBSDEs, prove its convergence to the true solution, and establish its rate of convergence. A key…

This paper studies the performative prediction problem where a learner aims to minimize the expected loss with a decision-dependent data distribution. Such setting is motivated when outcomes can be affected by the prediction model, e.g., in…

Conformal prediction provides a distribution-free framework for uncertainty quantification via prediction sets with exact finite-sample coverage. In low dimensions these sets are easy to interpret, but in high-dimensional or structured…

This study introduces a novel forecasting strategy that leverages the power of fractional differencing (FD) to capture both short- and long-term dependencies in time series data. Unlike traditional integer differencing methods, FD preserves…

First-order methods for stochastic optimization have undeniable relevance, in part due to their pivotal role in machine learning. Variance reduction for these algorithms has become an important research topic. In contrast to common…

We consider the problem of efficient statistical inference for comparing two regression curves estimated from two samples of dependent measurements. Based on a representation of the best pair of linear unbiased estimators in continuous time…

This paper introduces a novel error estimator for the Proper Generalized Decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: It builds on concentration inequalities of Gaussian maps and an…

For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…

When maximum likelihood estimation is infeasible, one often turns to score matching, contrastive divergence, or minimum probability flow to obtain tractable parameter estimates. We provide a unifying perspective of these techniques as…

Stochastic gradient descent (SGD) or stochastic approximation has been widely used in model training and stochastic optimization. While there is a huge literature on analyzing its convergence, inference on the obtained solutions from SGD…

In this paper, we introduce a fast row-stochastic decentralized algorithm, referred to as FRSD, to solve consensus optimization problems over directed communication graphs. The proposed algorithm only utilizes row-stochastic weights,…

Multi-fidelity Monte Carlo (MFMC) is a variance reduction method that leverages a multi-fidelity ensemble of models of varying cost and accuracy levels. Constructing an MFMC estimator with optimal variance requires knowledge of the…