相关论文: Phase transitions for support recovery under local…

We study the low-rank phase retrieval problem, where we try to recover a $d_1\times d_2$ low-rank matrix from a series of phaseless linear measurements. This is a fourth-order inverse problem, as we are trying to recover factors of matrix…

We consider the problem of recovering elements of a low-dimensional model from linear measurements. From signal and image processing to inverse problems in data science, this question has been at the center of many applications. Lately,…

We study the statistical complexity of private linear regression under an unknown, potentially ill-conditioned covariate distribution. Somewhat surprisingly, under privacy constraints the intrinsic complexity is \emph{not} captured by the…

This work provides tight upper- and lower-bounds for the problem of mean estimation under $\epsilon$-differential privacy in the local model, when the input is composed of $n$ i.i.d. drawn samples from a normal distribution with variance…

Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…

We consider the problem of recovering the support of a sparse signal using noisy projections. While extensive work has been done on the dense measurement matrix setting, the sparse setting remains less explored. In this work, we establish…

We show a new lower bound on the sample complexity of $(\varepsilon, \delta)$-differentially private algorithms that accurately answer statistical queries on high-dimensional databases. The novelty of our bound is that it depends optimally…

This paper is concerned with the problem of recovering a structured signal from a relatively small number of corrupted random measurements. Sharp phase transitions have been numerically observed in practice when different convex programming…

We give lower bounds for the problem of stable sparse recovery from /adaptive/ linear measurements. In this problem, one would like to estimate a vector $x \in \R^n$ from $m$ linear measurements $A_1x,..., A_mx$. One may choose each vector…

We consider the problem of recovery of an unknown multivariate signal $f$ observed in a $d$-dimensional Gaussian white noise model of intensity $\varepsilon$. We assume that $f$ belongs to a class of smooth functions ${\cal F}^d\subset…

In this paper, we study the Empirical Risk Minimization (ERM) problem in the non-interactive Local Differential Privacy (LDP) model. Previous research on this problem \citep{smith2017interaction} indicates that the sample complexity, to…

In large-scale statistical learning, data collection and model fitting are moving increasingly toward peripheral devices---phones, watches, fitness trackers---away from centralized data collection. Concomitant with this rise in…

In the field of machine learning, many problems can be formulated as the minimax problem, including reinforcement learning, generative adversarial networks, to just name a few. So the minimax problem has attracted a huge amount of…

We consider non-parametric density estimation in the framework of local approximate differential privacy. In contrast to centralized privacy scenarios with a trusted curator, in the local setup anonymization must be guaranteed already on…

We study the problem of recovering a hidden community of cardinality $K$ from an $n \times n$ symmetric data matrix $A$, where for distinct indices $i,j$, $A_{ij} \sim P$ if $i, j$ both belong to the community and $A_{ij} \sim Q$ otherwise,…

This paper considers the problem of label recovery in random graphs and matrices. Motivated by transitive behavior in real-world networks (i.e., ``the friend of my friend is my friend''), a recent line of work considers spatially-embedded…

Privacy preserving mechanisms such as differential privacy inject additional randomness in the form of noise in the data, beyond the sampling mechanism. Ignoring this additional noise can lead to inaccurate and invalid inferences. In this…

Recovering an unknown complex signal from the magnitude of linear combinations of the signal is referred to as phase retrieval. We present an exact performance analysis of a recently proposed convex-optimization-formulation for this…

We study a spectral initialization method that serves a key role in recent work on estimating signals in nonconvex settings. Previous analysis of this method focuses on the phase retrieval problem and provides only performance bounds. In…

The phase retrieval problem has garnered significant attention since the development of the PhaseLift algorithm, which is a convex program that operates in a lifted space of matrices. Because of the substantial computational cost due to…