相关论文: Stochastic and Private Nonconvex Outlier-Robust PC…

When synthesizing multi-source high-dimensional data, a key objective is to extract low-dimensional representations that effectively approximate the original features across different sources. Such representations facilitate the discovery…

Principal component analysis (PCA), along with its extensions to manifolds and outlier contaminated data, have been indispensable in computer vision and machine learning. In this work, we present a unifying formalism for PCA and its…

This paper investigates the phase retrieval problem, which aims to recover a signal from the magnitudes of its linear measurements. We develop statistically and computationally efficient algorithms for the situation when the measurements…

We propose a neural network for unsupervised anomaly detection with a novel robust subspace recovery layer (RSR layer). This layer seeks to extract the underlying subspace from a latent representation of the given data and removes outliers…

The Noisy-SGD algorithm is widely used for privately training machine learning models. Traditional privacy analyses of this algorithm assume that the internal state is publicly revealed, resulting in privacy loss bounds that increase…

In the paper, we study a class of useful minimax problems on Riemanian manifolds and propose a class of effective Riemanian gradient-based methods to solve these minimax problems. Specifically, we propose an effective Riemannian gradient…

We consider the problem of recovering an unknown signal $\pmb{x}_0\in \mathbb{R}^{n}$ from phaseless measurements. In this paper, we study the convex phase retrieval problem via PhaseLift from linear Gaussian measurements perturbed by…

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…

Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on…

This paper will serve as an introduction to the body of work on robust subspace recovery. Robust subspace recovery involves finding an underlying low-dimensional subspace in a dataset that is possibly corrupted with outliers. While this…

This paper presents a new approach to a robust Gaussian process (GP) regression. Most existing approaches replace an outlier-prone Gaussian likelihood with a non-Gaussian likelihood induced from a heavy tail distribution, such as the…

Block coordinate descent methods and stochastic subgradient methods have been extensively studied in optimization and machine learning. By combining randomized block sampling with stochastic subgradient methods based on dual averaging, we…

In this paper, we propose a new stochastic column-block gradient descent method for solving nonlinear systems of equations. It has a descent direction and holds an approximately optimal step size obtained through an optimization problem. We…

Differentially private synthetic data provide a powerful mechanism to enable data analysis while protecting sensitive information about individuals. However, when the data lie in a high-dimensional space, the accuracy of the synthetic data…

This study addresses some algorithms for solving structured unconstrained convex optimiza- tion problems using first-order information where the underlying function includes high-dimensional data. The primary aim is to develop an…

We provide the first study of the problem of finding differentially private (DP) second-order stationary points (SOSP) in stochastic (non-convex) minimax optimization. Existing literature either focuses only on first-order stationary points…

We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…

Linear regression is an important tool across many fields that work with sensitive human-sourced data. Significant prior work has focused on producing differentially private point estimates, which provide a privacy guarantee to individuals…

In this paper, we are concerned with differentially private {stochastic gradient descent (SGD)} algorithms in the setting of stochastic convex optimization (SCO). Most of the existing work requires the loss to be Lipschitz continuous and…

Optimization techniques are at the core of many scientific and engineering disciplines. The steepest descent methods play a foundational role in this area. In this paper we studied a generalized steepest descent method on Riemannian…