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We study information-theoretic phase transitions for the detectability of latent geometry in bipartite random geometric graphs RGGs with Gaussian d-dimensional latent vectors while only a subset of edges carries latent information…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
Maximizing high-dimensional, non-convex functions through noisy observations is a notoriously hard problem, but one that arises in many applications. In this paper, we tackle this challenge by modeling the unknown function as a sample from…
Stochastic kriging has been widely employed for simulation metamodeling to predict the response surface of complex simulation models. However, its use is limited to cases where the design space is low-dimensional because, in general, the…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
Multi-index models - functions which only depend on the covariates through a non-linear transformation of their projection on a subspace - are a useful benchmark for investigating feature learning with neural nets. This paper examines the…
We determine the information-theoretic cutoff value on separation of cluster centers for exact recovery of cluster labels in a $K$-component Gaussian mixture model with equal cluster sizes. Moreover, we show that a semidefinite programming…
Single-cell sequencing technologies have significantly advanced molecular and cellular biology, offering unprecedented insights into cellular heterogeneity by allowing for the measurement of gene expression at an individual cell level.…
Motivated by a sampling problem basic to computational statistical inference, we develop a nearly optimal algorithm for a fundamental problem in spectral graph theory and numerical analysis. Given an $n\times n$ SDDM matrix ${\bf…
We introduce Latent Space Distribution Matching (LSDM), a novel framework for semi-supervised generative modeling of conditional distributions. LSDM operates in two stages: (i) learning a low-dimensional latent space from both paired and…
In high-dimensional graph learning problems, some topological properties of the graph, such as bounded node degree or tree structure, are typically assumed to hold so that the sample complexity of recovering the graph structure can be…
Accurate modeling of spatial dependence is pivotal in analyzing spatial data, influencing parameter estimation and predictions. The spatial structure of the data significantly impacts valid statistical inference. Existing models for areal…
This paper investigates the fundamental limits for detecting a high-dimensional sparse matrix contaminated by white Gaussian noise from both the statistical and computational perspectives. We consider $p\times p$ matrices whose rows and…
We study a semidefinite programming (SDP) relaxation of the maximum likelihood estimation for exactly recovering a hidden community of cardinality $K$ from an $n \times n$ symmetric data matrix $A$, where for distinct indices $i,j$, $A_{ij}…
Data-driven model discovery (DDMD) algorithms are powerful tools for extracting interpretable symbolic models from data. However, identifying the model that best balances goodness-of-fit and sparsity is often a laborious process requiring…
We study the complexity of smoothed agnostic learning, recently introduced by~\cite{CKKMS24}, in which the learner competes with the best classifier in a target class under slight Gaussian perturbations of the inputs. Specifically, we focus…
Stochastic gradient algorithm is a key ingredient of many machine learning methods, particularly appropriate for large-scale learning.However, a major caveat of large data is their incompleteness.We propose an averaged stochastic gradient…
This paper presents a novel method to make statistical inferences for both the model support and regression coefficients in a high-dimensional logistic regression model. Our method is based on the repro samples framework, in which we…
Many latent-variable applications, including community detection, collaborative filtering, genomic analysis, and NLP, model data as generated by low-rank matrices. Yet despite considerable research, except for very special cases, the number…
We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…