相关论文: Score estimation in the monotone single index mode…

We construct a semi-Lagrangian scheme for first-order, time-dependent, and non-local Mean Field Games. The convergence of the scheme to a weak solution of the system is analyzed by exploiting a key monotonicity property. To solve the…

We consider the basic problem of learning Single-Index Models with respect to the square loss under the Gaussian distribution in the presence of adversarial label noise. Our main contribution is the first computationally efficient algorithm…

Given a matrix $\mathbf{A}\in\mathbb{R}^{n\times d}$ and a vector $b \in\mathbb{R}^{d}$, we show how to compute an $\epsilon$-approximate solution to the regression problem $ \min_{x\in\mathbb{R}^{d}}\frac{1}{2} \|\mathbf{A} x - b\|_{2}^{2}…

The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov…

Score matching estimators have gained widespread attention in recent years partly because they are free from calculating the integral of normalizing constant, thereby addressing the computational challenges in maximum likelihood estimation…

We consider the problem of nonparametric regression when the covariate is $d$-dimensional, where $d \geq 1$. In this paper we introduce and study two nonparametric least squares estimators (LSEs) in this setting---the entirely monotonic LSE…

We study the problem of parameter estimation for reflected stochastic processes driven by a standard Brownian motion. The estimator is obtained using nonlinear least squares method based on discretely observed processes. Under some certain…

In this article, we study a partially linear single-index model for longitudinal data under a general framework which includes both the sparse and dense longitudinal data cases. A semiparametric estimation method based on a combination of…

Gradient-based dimension reduction decreases the cost of Bayesian inference and probabilistic modeling by identifying maximally informative (and informed) low-dimensional projections of the data and parameters, allowing high-dimensional…

Given an undirected and connected graph $G$ on $T$ vertices, suppose each vertex $t$ has a latent signal $x_t \in \mathbb{R}^n$ associated to it. Given partial linear measurements of the signals, for a potentially small subset of the…

We want to reconstruct a signal based on inhomogeneous data (the amount of data can vary strongly), using the model of regression with a random design. Our aim is to understand the consequences of inhomogeneity on the accuracy of estimation…

We consider the problem of fitting a relationship (e.g. a potential scientific law) to data involving multiple variables. Ordinary (least squares) regression is not suitable for this because the estimated relationship will differ according…

We propose a novel score-based particle method for solving the Landau equation in plasmas, that seamlessly integrates learning with structure-preserving particle methods [arXiv:1910.03080]. Building upon the Lagrangian viewpoint of the…

This paper introduces a novel framework for estimation and inference in penalized M-estimators applied to robust high-dimensional linear regression models. Traditional methods for high-dimensional statistical inference, which predominantly…

A least product relative error criterion is proposed for multiplicative regression models. It is invariant under scale transformation of the outcome and covariates. In addition, the objective function is smooth and convex, resulting in a…

We study methods for aggregating pairwise comparison data in order to estimate outcome probabilities for future comparisons among a collection of n items. Working within a flexible framework that imposes only a form of strong stochastic…

It was recently shown [7, 9] that "properly built" linear and polyhedral estimates nearly attain minimax accuracy bounds in the problem of recovery of unknown signal from noisy observations of linear images of the signal when the signal set…

Imputation is an attractive tool for dealing with the widespread issue of missing values. Consequently, studying and developing imputation methods has been an active field of research over the last decade. Faced with an imputation task and…

We investigate the calibration of estimations to increase performance with an optimal monotone transform on the estimator outputs. We start by studying the traditional square error setting with its weighted variant and show that the optimal…

In this paper, we study the equality constrained nonlinear least squares problem, where the Jacobian matrices of the objective function and constraints are unavailable or expensive to compute. We approximate the Jacobian matrices via…