相关论文: Breaking The Dimension Dependence in Sparse Distri…

We study oblivious sketching for $k$-sparse linear regression under various loss functions such as an $\ell_p$ norm, or from a broad class of hinge-like loss functions, which includes the logistic and ReLU losses. We show that for sparse…

Let A be an M by N matrix (M < N) which is an instance of a real random Gaussian ensemble. In compressed sensing we are interested in finding the sparsest solution to the system of equations A x = y for a given y. In general, whenever the…

We present a new adaptive algorithm for learning discrete distributions under distribution drift. In this setting, we observe a sequence of independent samples from a discrete distribution that is changing over time, and the goal is to…

We study the problem of list-decodable sparse mean estimation. Specifically, for a parameter $\alpha \in (0, 1/2)$, we are given $m$ points in $\mathbb{R}^n$, $\lfloor \alpha m \rfloor$ of which are i.i.d. samples from a distribution $D$…

We develop a technique to design efficiently computable estimators for sparse linear regression in the simultaneous presence of two adversaries: oblivious and adaptive. We design several robust algorithms that outperform the state of the…

In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…

The goal of (stable) sparse recovery is to recover a $k$-sparse approximation $x*$ of a vector $x$ from linear measurements of $x$. Specifically, the goal is to recover $x*$ such that ||x-x*||_p <= C min_{k-sparse x'} ||x-x'||_q for some…

The sparse regression problem, also known as best subset selection problem, can be cast as follows: Given a set $S$ of $n$ points in $\mathbb{R}^d$, a point $y\in \mathbb{R}^d$, and an integer $2 \leq k \leq d$, find an affine combination…

In this paper, we shall optimize the efficiency of Metropolis algorithms for multidimensional target distributions with scaling terms possibly depending on the dimension. We propose a method for determining the appropriate form for the…

Diffusion-based generative models have emerged as highly effective methods for synthesizing high-quality samples. Recent works have focused on analyzing the convergence of their generation process with minimal assumptions, either through…

We consider a sparse high dimensional regression model where the goal is to recover a $k$-sparse unknown vector $\beta^*$ from $n$ noisy linear observations of the form $Y=X\beta^*+W \in \mathbb{R}^n$ where $X \in \mathbb{R}^{n \times p}$…

Many algorithms in machine learning and computational geometry require, as input, the intrinsic dimension of the manifold that supports the probability distribution of the data. This parameter is rarely known and therefore has to be…

In supervised learning, training and test datasets are often sampled from distinct distributions. Domain adaptation techniques are thus required. Covariate shift adaptation yields good generalization performance when domains differ only by…

We study a plug in least squares estimator for the change point parameter where change is in the mean of a high dimensional random vector under subgaussian or subexponential distributions. We obtain sufficient conditions under which this…

The recent work by Dong & Yang (2023) showed for misspecified sparse linear bandits, one can obtain an $O\left(\epsilon\right)$-optimal policy using a polynomial number of samples when the sparsity is a constant, where $\epsilon$ is the…

Minimax $L_2$ risks for high-dimensional nonparametric regression are derived under two sparsity assumptions: (1) the true regression surface is a sparse function that depends only on $d=O(\log n)$ important predictors among a list of $p$…

We present differentially private algorithms for high-dimensional mean estimation. Previous private estimators on distributions over $\mathbb{R}^d$ suffer from a curse of dimensionality, as they require $\Omega(d^{1/2})$ samples to achieve…

We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension…

We study the problem of assigning transmission ranges to radio stations placed arbitrarily in a $d$-dimensional ($d$-D) Euclidean space in order to achieve a strongly connected communication network with minimum total power consumption. The…

We consider a standard distributed optimisation setting where $N$ machines, each holding a $d$-dimensional function $f_i$, aim to jointly minimise the sum of the functions $\sum_{i = 1}^N f_i (x)$. This problem arises naturally in…