Related papers: Statistical Query Lower Bounds for Tensor PCA

The problem of principle component analysis (PCA) is traditionally solved by spectral or algebraic methods. We show how computing the leading principal component could be reduced to solving a \textit{small} number of well-conditioned {\it…

A central question in high-dimensional statistics is to understand statistical--computational gaps: regimes in which recovering a hidden signal is information-theoretically possible but conjectured to be computationally intractable. The…

A key bottleneck in quantum machine learning is the computational cost of repeated quantum circuit evaluations during the inference phase. To address this, we present a framework for constructing fast, cheap, provably accurate classical…

Singular value decomposition (SVD) based principal component analysis (PCA) breaks down in the high-dimensional and limited sample size regime below a certain critical eigen-SNR that depends on the dimensionality of the system and the…

In this paper, we study the estimation of a rank-one spiked tensor in the presence of heavy tailed noise. Our results highlight some of the fundamental similarities and differences in the tradeoff between statistical and computational…

We consider the task of privately obtaining prediction error guarantees in ordinary least-squares regression problems with Gaussian covariates (with unknown covariance structure). We provide the first sample-optimal polynomial time…

We provide a computationally and statistically efficient estimator for the classical problem of truncated linear regression, where the dependent variable $y = w^T x + \epsilon$ and its corresponding vector of covariates $x \in R^k$ are only…

Suppose we observe data of the form $Y_i = D_i (S_i + \varepsilon_i) \in \mathbb{R}^p$ or $Y_i = D_i S_i + \varepsilon_i \in \mathbb{R}^p$, $i=1,\ldots,n$, where $D_i \in \mathbb{R}^{p\times p}$ are known diagonal matrices, $\varepsilon_i$…

The widespread use of multisensor technology and the emergence of big data sets have brought the necessity to develop more versatile tools to represent higher-order data with multiple aspects and high dimensionality. Data in the form of…

A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…

Given a random $n \times n$ symmetric matrix $\boldsymbol W$ drawn from the Gaussian orthogonal ensemble (GOE), we consider the problem of certifying an upper bound on the maximum value of the quadratic form $\boldsymbol x^\top \boldsymbol…

Traditional statistical analysis requires that the analysis process and data are independent. By contrast, the new field of adaptive data analysis hopes to understand and provide algorithms and accuracy guarantees for research as it is…

Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…

The field of fine-grained complexity aims at proving conditional lower bounds on the time complexity of computational problems. One of the most popular assumptions, Strong Exponential Time Hypothesis (SETH), implies that SAT cannot be…

We study the problem of high-dimensional robust linear regression where a learner is given access to $n$ samples from the generative model $Y = \langle X,w^* \rangle + \epsilon$ (with $X \in \mathbb{R}^d$ and $\epsilon$ independent), in…

In recent years, sparse principal component analysis has emerged as an extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a…

We study the question of closeness testing for two discrete distributions. More precisely, given samples from two distributions $p$ and $q$ over an $n$-element set, we wish to distinguish whether $p=q$ versus $p$ is at least $\eps$-far from…

We establish tight inapproximability bounds for max-LINSAT, the problem of maximizing the number of satisfied linear constraints over the finite field $\mathbb{F}_q$, where each constraint accepts $r$ values. Specifically, we prove by a…

We consider the well-studied problem of learning intersections of halfspaces under the Gaussian distribution in the challenging \emph{agnostic learning} model. Recent work of Diakonikolas et al. (2021) shows that any Statistical Query (SQ)…

The symmetric binary perceptron ($\mathrm{SBP}_{\kappa}$) problem with parameter $\kappa : \mathbb{R}_{\geq1} \to [0,1]$ is an average-case search problem defined as follows: given a random Gaussian matrix $\mathbf{A} \sim…