Related papers: Vector-Valued Least-Squares Regression under Outpu…

Finite linear least squares is one of the core problems of numerical linear algebra, with countless applications across science and engineering. Consequently, there is a rich and ongoing literature on algorithms for solving linear least…

In this dissertation, we focus on several important problems in structured prediction. In structured prediction, the label has a rich intrinsic substructure, and the loss varies with respect to the predicted label and the true label pair.…

Fr\'echet regression has emerged as a promising approach for regression analysis involving non-Euclidean response variables. However, its practical applicability has been hindered by its reliance on ideal scenarios with abundant and…

Stochastic gradient methods for machine learning and optimization problems are usually analyzed assuming data points are sampled \emph{with} replacement. In practice, however, sampling \emph{without} replacement is very common, easier to…

We study the problem of estimating a low-rank positive semidefinite (PSD) matrix from a set of rank-one measurements using sensing vectors composed of i.i.d. standard Gaussian entries, which are possibly corrupted by arbitrary outliers.…

We propose a sparse and low-rank tensor regression model to relate a univariate outcome to a feature tensor, in which each unit-rank tensor from the CP decomposition of the coefficient tensor is assumed to be sparse. This structure is both…

The low-rank stochastic semidefinite optimization has attracted rising attention due to its wide range of applications. The nonconvex reformulation based on the low-rank factorization, significantly improves the computational efficiency but…

The reduced-rank vector autoregressive (VAR) model can be interpreted as a supervised factor model, where two factor modelings are simultaneously applied to response and predictor spaces. This article introduces a new model, called vector…

We study the inverse problem of parameter identification in non-coercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map by using the first-order and…

We study consistency properties of machine learning methods based on minimizing convex surrogates. We extend the recent framework of Osokin et al. (2017) for the quantitative analysis of consistency properties to the case of inconsistent…

Real life data often includes information from different channels. For example, in computer vision, we can describe an image using different image features, such as pixel intensity, color, HOG, GIST feature, SIFT features, etc.. These…

We consider the problem of robustly predicting as well as the best linear combination of $d$ given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. For…

Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible. Unfortunately, existing methods for matrix completion are heuristics that, while highly…

We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient…

The problem of fitting experimental data to a given model function $f(t; p_1,p_2,\dots,p_N)$ is conventionally solved numerically by methods such as that of Levenberg-Marquardt, which are based on approximating the Chi-squared measure of…

We present a new machine learning approach to estimate personalized treatment effects in the classical potential outcomes framework with binary outcomes. To overcome the problem that both treatment and control outcomes for the same unit are…

Parameter-efficient training based on low-rank optimization has become a highly successful tool for fine-tuning large deep learning models. However, these methods often fail for low-rank pre-training, where simultaneously maintaining…

Sparse reduced-rank regression is an important tool to uncover meaningful dependence structure between large numbers of predictors and responses in many big data applications such as genome-wide association studies and social media…

Vector Quantization (VQ) is an appealing model compression method to obtain a tiny model with less accuracy loss. While methods to obtain better codebooks and codes under fixed clustering dimensionality have been extensively studied,…

In this work we address the subspace recovery problem. Given a set of data samples (vectors) approximately drawn from a union of multiple subspaces, our goal is to segment the samples into their respective subspaces and correct the possible…