54 citations · 200 across the 55 of their papers we have counts for
17 papers · 1 filter
Mirror Flow Matching with Heavy-Tailed Priors for Generative Modeling on Convex Domains
Yunrui Guan, Krishnakumar Balasubramanian, Shiqian Ma
We study generative modeling on convex domains using flow matching and mirror maps, and identify two fundamental challenges. First, standard log-barrier mirror maps induce heavy-ta…
Riemannian Proximal Sampler for High-accuracy Sampling on Manifolds
Yunrui Guan, Krishnakumar Balasubramanian, Shiqian Ma
We introduce the Riemannian Proximal Sampler, a method for sampling from densities defined on Riemannian manifolds. The performance of this sampler critically depends on two key or…
Online Covariance Estimation in Nonsmooth Stochastic Approximation
Liwei Jiang, Abhishek Roy, Krishna Balasubramanian +3
We consider applying stochastic approximation (SA) methods to solve nonsmooth variational inclusion problems. Existing studies have shown that the averaged iterates of SA methods e…
Stochastic Optimization Algorithms for Instrumental Variable Regression with Streaming Data
Xuxing Chen, Abhishek Roy, Yifan Hu +1
We develop and analyze algorithms for instrumental variable regression by viewing the problem as a conditional stochastic optimization problem. In the context of least-squares inst…
Regularized Stein Variational Gradient Flow
Ye He, Krishnakumar Balasubramanian, Bharath K. Sriperumbudur +1
The Stein Variational Gradient Descent (SVGD) algorithm is a deterministic particle method for sampling. However, a mean-field analysis reveals that the gradient flow corresponding…
Mirror Descent Strikes Again: Optimal Stochastic Convex Optimization under Infinite Noise Variance
Nuri Mert Vural, Lu Yu, Krishnakumar Balasubramanian +2
We study stochastic convex optimization under infinite noise variance. Specifically, when the stochastic gradient is unbiased and has uniformly bounded -th moment, for some…
Nonparametric Modeling of Higher-Order Interactions via Hypergraphons
Krishnakumar Balasubramanian
We study statistical and algorithmic aspects of using hypergraphons, that are limits of large hypergraphs, for modeling higher-order interactions. Although hypergraphons are extrem…
Statistical Inference for Polyak-Ruppert Averaged Zeroth-order Stochastic Gradient Algorithm
Yanhao Jin, Tesi Xiao, Krishnakumar Balasubramanian
Statistical machine learning models trained with stochastic gradient algorithms are increasingly being deployed in critical scientific applications. However, computing the stochast…
On the Ergodicity, Bias and Asymptotic Normality of Randomized Midpoint Sampling Method
Ye He, Krishnakumar Balasubramanian, Murat A. Erdogdu
The randomized midpoint method, proposed by [SL19], has emerged as an optimal discretization procedure for simulating the continuous time Langevin diffusions. Focusing on the case…
Escaping Saddle-Points Faster under Interpolation-like Conditions
Abhishek Roy, Krishnakumar Balasubramanian, Saeed Ghadimi +1
In this paper, we show that under over-parametrization several standard stochastic optimization algorithms escape saddle-points and converge to local-minimizers much faster. One of…
Fractal Gaussian Networks: A sparse random graph model based on Gaussian Multiplicative Chaos
Subhroshekhar Ghosh, Krishnakumar Balasubramanian, Xiaochuan Yang
We propose a novel stochastic network model, called Fractal Gaussian Network (FGN), that embodies well-defined and analytically tractable fractal structures. Such fractal structure…
An Analysis of Constant Step Size SGD in the Non-convex Regime: Asymptotic Normality and Bias
Lu Yu, Krishnakumar Balasubramanian, Stanislav Volgushev +1
Structured non-convex learning problems, for which critical points have favorable statistical properties, arise frequently in statistical machine learning. Algorithmic convergence…
Zeroth-Order Algorithms for Nonconvex Minimax Problems with Improved Complexities
Zhongruo Wang, Krishnakumar Balasubramanian, Shiqian Ma +1
In this paper, we study zeroth-order algorithms for minimax optimization problems that are nonconvex in one variable and strongly-concave in the other variable. Such minimax optimi…
Multi-Point Bandit Algorithms for Nonstationary Online Nonconvex Optimization
Abhishek Roy, Krishnakumar Balasubramanian, Saeed Ghadimi +1
Bandit algorithms have been predominantly analyzed in the convex setting with function-value based stationary regret as the performance measure. In this paper, motivated by online…
Low-Rank Principal Eigenmatrix Analysis
Krishna Balasubramanian, Elynn Y. Chen, Jianqing Fan +1
Sparse PCA is a widely used technique for high-dimensional data analysis. In this paper, we propose a new method called low-rank principal eigenmatrix analysis. Different from spar…
On the Optimality of Kernel-Embedding Based Goodness-of-Fit Tests
Krishnakumar Balasubramanian, Tong Li, Ming Yuan
The reproducing kernel Hilbert space (RKHS) embedding of distributions offers a general and flexible framework for testing problems in arbitrary domains and has attracted considera…
Smooth Sparse Coding via Marginal Regression for Learning Sparse Representations
Krishnakumar Balasubramanian, Kai Yu, Guy Lebanon
We propose and analyze a novel framework for learning sparse representations, based on two statistical techniques: kernel smoothing and marginal regression. The proposed approach p…