Related papers: Rigorous Implications of the Low-Degree Heuristic

In this paper, we investigate the impact of compression on stochastic gradient algorithms for machine learning, a technique widely used in distributed and federated learning. We underline differences in terms of convergence rates between…

In natural language processing (NLP), the likelihood ratios (LRs) of N-grams are often estimated from the frequency information. However, a corpus contains only a fraction of the possible N-grams, and most of them occur infrequently. Hence,…

We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of…

This work presents a new variation of the commonly used Least Mean Squares Algorithm (LMS) for the identification of sparse signals with an a-priori known sparsity using a hard threshold operator in every iteration. It examines some useful…

Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed,…

We study the convergence of a random iterative sequence of a family of operators on infinite dimensional Hilbert spaces, inspired by the Stochastic Gradient Descent (SGD) algorithm in the case of the noiseless regression, as studied in [1].…

Several approximate inference algorithms have been proposed to minimize an alpha-divergence between an approximating distribution and a target distribution. Many of these algorithms introduce bias, the magnitude of which becomes problematic…

In the number partitioning problem (NPP) one aims to partition a given set of $N$ real numbers into two subsets with approximately equal sum. The NPP is a well-studied optimization problem and is famous for possessing a…

Large language model (LLM) evaluation platforms increasingly rely on pairwise human judgments. These data are noisy, sparse, and non-uniform, yet leaderboards are reported with limited uncertainty quantification. We study this as…

Score-based diffusion models have demonstrated outstanding empirical performance in machine learning and artificial intelligence, particularly in generating high-quality new samples from complex probability distributions. Improving the…

The execution of Large Language Models (LLMs) has been shown to produce nondeterministic results when run on Graphics Processing Units (GPUs), even when they are configured to produce deterministic results. This is due to the finite…

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…

We consider a distributed detection problem where measurements at each sensor follow a general parametric distribution. The network does not have a central processing unit or fusion center (FC). Thus, each node takes some measurements, does…

Universality, namely distributional invariance, is a well-known property for many random structures. For example, it is known to hold for a broad range of variational problems with random input. Much less is known about the algorithmic…

In many fields of science, generalized likelihood ratio tests are established tools for statistical inference. At the same time, it has become increasingly common that a simulator (or generative model) is used to describe complex processes…

Consider estimating a structured signal $\mathbf{x}_0$ from linear, underdetermined and noisy measurements $\mathbf{y}=\mathbf{A}\mathbf{x}_0+\mathbf{z}$, via solving a variant of the lasso algorithm: $\hat{\mathbf{x}}=\arg\min_\mathbf{x}\{…

We initiate the study of the algorithmic problem of certifying lower bounds on the discrepancy of random matrices: given an input matrix $A \in \mathbb{R}^{m \times n}$, output a value that is a lower bound on $\mathsf{disc}(A) = \min_{x…

We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…

Label Distribution Learning (LDL) assigns soft labels, a.k.a. degrees, to a sample. In reality, it is always laborious to obtain complete degrees, giving birth to the Incomplete LDL (InLDL). However, InLDL often suffers from performance…

We propose a new analysis framework for clustering $M$ items into an unknown number of $K$ distinct groups using noisy and actively collected responses. At each time step, an agent is allowed to query pairs of items and observe bandit…