53 citations · 293 across the 32 of their papers we have counts for
12 papers · 1 filter
Online Stochastic Gradient Descent Learns Linear Dynamical Systems from A Single Trajectory
Navid Reyhanian, Jarvis Haupt
This work investigates the problem of estimating the weight matrices of a stable time-invariant linear dynamical system from a single sequence of noisy measurements. We show that i…
Convexifying Sparse Interpolation with Infinitely Wide Neural Networks: An Atomic Norm Approach
Akshay Kumar, Jarvis Haupt
This work examines the problem of exact data interpolation via sparse (neuron count), infinitely wide, single hidden layer neural networks with leaky rectified linear unit activati…
Provable Online CP/PARAFAC Decomposition of a Structured Tensor via Dictionary Learning
Sirisha Rambhatla, Xingguo Li, Jarvis Haupt
We consider the problem of factorizing a structured 3-way tensor into its constituent Canonical Polyadic (CP) factors. This decomposition, which can be viewed as a generalization o…
A Dictionary Based Generalization of Robust PCA
Sirisha Rambhatla, Xingguo Li, Jarvis Haupt
We analyze the decomposition of a data matrix, assumed to be a superposition of a low-rank component and a component which is sparse in a known dictionary, using a convex demixing…
NOODL: Provable Online Dictionary Learning and Sparse Coding
Sirisha Rambhatla, Xingguo Li, Jarvis Haupt
We consider the dictionary learning problem, where the aim is to model the given data as a linear combination of a few columns of a matrix known as a dictionary, where the sparse w…
A Dictionary-Based Generalization of Robust PCA with Applications to Target Localization in Hyperspectral Imaging
Sirisha Rambhatla, Xingguo Li, Jineng Ren +1
We consider the decomposition of a data matrix assumed to be a superposition of a low-rank matrix and a component which is sparse in a known dictionary, using a convex demixing met…
On Tighter Generalization Bound for Deep Neural Networks: CNNs, ResNets, and Beyond
Xingguo Li, Junwei Lu, Zhaoran Wang +2
We establish a margin based data dependent generalization error bound for a general family of deep neural networks in terms of the depth and width, as well as the Jacobian of the n…
On Landscape of Lagrangian Functions and Stochastic Search for Constrained Nonconvex Optimization
Zhehui Chen, Xingguo Li, Lin F. Yang +2
We study constrained nonconvex optimization problems in machine learning, signal processing, and stochastic control. It is well-known that these problems can be rewritten to a mini…
Near Optimal Sketching of Low-Rank Tensor Regression
Jarvis Haupt, Xingguo Li, David P. Woodruff
We study the least squares regression problem \begin{align*} \min_{Θ\in \mathcal{S}_{\odot D,R}} \|AΘ-b\|_2, \end{align*} where is the set of for whic…
Symmetry, Saddle Points, and Global Optimization Landscape of Nonconvex Matrix Factorization
Xingguo Li, Junwei Lu, Raman Arora +4
We propose a general theory for studying the \xl{landscape} of nonconvex \xl{optimization} with underlying symmetric structures \tz{for a class of machine learning problems (e.g.,…
On Fast Convergence of Proximal Algorithms for SQRT-Lasso Optimization: Don't Worry About Its Nonsmooth Loss Function
Xingguo Li, Haoming Jiang, Jarvis Haupt +4
Many machine learning techniques sacrifice convenient computational structures to gain estimation robustness and modeling flexibility. However, by exploring the modeling structures…
Nonconvex Sparse Learning via Stochastic Optimization with Progressive Variance Reduction
Xingguo Li, Raman Arora, Han Liu +2
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which t…