Related papers: Dimension-Free Correlated Sampling for the Hypersi…

We study the power of uniform sampling for $k$-Median in various metric spaces. We relate the query complexity for approximating $k$-Median, to a key parameter of the dataset, called the balancedness $\beta \in (0, 1]$ (with $1$ being…

We consider optimization problems with uncertain constraints that need to be satisfied probabilistically. When data are available, a common method to obtain feasible solutions for such problems is to impose sampled constraints, following…

Graph signal sampling is the problem of selecting a subset of representative graph vertices whose values can be used to interpolate missing values on the remaining graph vertices. Optimizing the choice of sampling set using concepts from…

We propose a high dimensional mean test framework for shrinking random variables, where the underlying random variables shrink to zero as the sample size increases. By pooling observations across overlapping subsets of dimensions, we…

To fast approximate maximum likelihood estimators with massive data, this paper studies the Optimal Subsampling Method under the A-optimality Criterion (OSMAC) for generalized linear models. The consistency and asymptotic normality of the…

We consider posterior sampling in the very common Bayesian hierarchical model in which observed data depends on high-dimensional latent variables that, in turn, depend on relatively few hyperparameters. When the full conditional over the…

Functional data analysis (FDA) methods have computational and theoretical appeals for some high dimensional data, but lack the scalability to modern large sample datasets. To tackle the challenge, we develop randomized algorithms for two…

Quantum sampling, a fundamental subroutine in numerous quantum algorithms, involves encoding a given probability distribution in the amplitudes of a pure state. Given the hefty cost of large-scale quantum storage, we initiate the study of…

In the hypothesis selection problem, we are given sample and query access to finite set of candidate distributions (hypotheses), $\mathcal{H} = \{H_1, \ldots, H_n\}$, and samples from an unknown distribution $P$, both over a domain…

Many data-fitting applications require the solution of an optimization problem involving a sum of large number of functions of high dimensional parameter. Here, we consider the problem of minimizing a sum of $n$ functions over a convex…

We investigate distribution testing with access to non-adaptive conditional samples. In the conditional sampling model, the algorithm is given the following access to a distribution: it submits a query set $S$ to an oracle, which returns a…

Decoding sits between a language model and everything we do with it, yet it is still treated as a heuristic knob-tuning exercise. We argue decoding should be understood as a principled optimisation layer: at each token, we solve a…

We revisit the optimization from samples (OPS) model, which studies the problem of optimizing objective functions directly from the sample data. Previous results showed that we cannot obtain a constant approximation ratio for the maximum…

Given a dataset of points in a metric space and an integer $k$, a diversity maximization problem requires determining a subset of $k$ points maximizing some diversity objective measure, e.g., the minimum or the average distance between two…

A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. Unfortunately, the resulting submodular optimization…

$\newcommand{\Re}{\mathbb{R}}$We study the minWSPD problem of computing the minimum-size well-separated pairs decomposition of a set of points, and show constant approximation algorithms in low-dimensional Euclidean space and doubling…

We study parallel sampling from high-dimensional strongly log-concave distributions. Langevin-based samplers converge rapidly in continuous time, but their discretizations are typically sequential and often require polynomially many steps…

Overlapping clusters are common in models of many practical data-segmentation applications. Suppose we are given $n$ elements to be clustered into $k$ possibly overlapping clusters, and an oracle that can interactively answer queries of the…

\textit{Mallows model} is a widely-used probabilistic framework for learning from ranking data, with applications ranging from recommendation systems and voting to aligning language models with human preferences~\cite{chen2024mallows,…

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…