37 citations · 48 across the 15 of their papers we have counts for
24 papers
Convergence of Momentum-Based Optimization Algorithms with Time-Varying Parameters
Mathukumalli Vidyasagar
In this paper, we present a unified algorithm for stochastic optimization that makes use of a "momentum" term; in other words, the stochastic gradient depends not only on the curre…
A Tutorial Introduction to Reinforcement Learning
Mathukumalli Vidyasagar
In this paper, we present a brief survey of Reinforcement Learning (RL), with particular emphasis on Stochastic Approximation (SA) as a unifying theme. The scope of the paper inclu…
Convergence of the Stochastic Heavy Ball Method With Approximate Gradients and/or Block Updating
Uday Kiran Reddy Tadipatri, Mathukumalli Vidyasagar
In this paper, we establish the convergence of the stochastic Heavy Ball (SHB) algorithm under more general conditions than in the current literature. Specifically, (i) The stochas…
Estimating large causal polytrees from small samples
Sourav Chatterjee, Mathukumalli Vidyasagar
We consider the problem of estimating a large causal polytree from a relatively small i.i.d. sample. This is motivated by the problem of determining causal structure when the numbe…
Convergence of Batch Updating Methods with Approximate Gradients and/or Noisy Measurements: Theory and Computational Results
Tadipatri Uday Kiran Reddy, M. Vidyasagar
In this paper, we present a unified and general framework for analyzing the batch updating approach to nonlinear, high-dimensional optimization. The framework encompasses all the c…
Convergence of Stochastic Approximation via Martingale and Converse Lyapunov Methods
M. Vidyasagar
In this paper, we study the almost sure boundedness and the convergence of the stochastic approximation (SA) algorithm. At present, most available convergence proofs are based on t…
SUTRA: A Novel Approach to Modelling Pandemics with Applications to COVID-19
Manindra Agrawal, Madhuri Kanitkar, Deepu Phillip +5
The Covid-19 pandemic has two key properties: (i) asymptomatic cases (both detected and undetected) that can result in new infections, and (ii) time-varying characteristics due to…
Estimating Hidden Asymptomatics, Herd Immunity Threshold and Lockdown Effects using a COVID-19 Specific Model
Shaurya Kaushal, Abhineet Singh Rajput, Soumyadeep Bhattacharya +4
A quantitative COVID-19 model that incorporates hidden asymptomatic patients is developed, and an analytic solution in parametric form is given. The model incorporates the impact o…
New and Explicit Constructions of Unbalanced Ramanujan Bipartite Graphs
Shantanu Prasad Burnwal, Kaneenika Sinha, Mathukumalli Vidyasagar
The objectives of this article are three-fold. Firstly, we present for the first time explicit constructions of an infinite family of \textit{unbalanced} Ramanujan bigraphs. Second…
Deterministic Completion of Rectangular Matrices Using Asymmetric Ramanujan Graphs: Exact and Stable Recovery
Shantanu Prasad Burnwal, Mathukumalli Vidyasagar
In this paper we study the matrix completion problem: Suppose is unknown except for a known upper bound on its rank. By measuring a small n…
Compressed Sensing Using Binary Matrices of Nearly Optimal Dimensions
Mahsa Lotfi, Mathukumalli Vidyasagar
In this paper, we study the problem of compressed sensing using binary measurement matrices and -norm minimization (basis pursuit) as the recovery algorithm. We derive new…
An Approach to One-Bit Compressed Sensing Based on Probably Approximately Correct Learning Theory
Mehmet Eren Ahsen, Mathukumalli Vidyasagar
In this paper, the problem of one-bit compressed sensing (OBCS) is formulated as a problem in probably approximately correct (PAC) learning. It is shown that the Vapnik-Chervonenki…
CLOT Norm Minimization for Continuous Hands-off Control
Niharika Challapalli, Masaaki Nagahara, Mathukumalli Vidyasagar
In this paper, we consider hands-off control via minimization of the CLOT (Combined -One and Two) norm. The maximum hands-off control is the -optimal (or the sparsest) cont…
A Fast Noniterative Algorithm for Compressive Sensing Using Binary Measurement Matrices
Mahsa Lotfi, Mathukumalli Vidyasagar
In this paper we present a new algorithm for compressive sensing that makes use of binary measurement matrices and achieves exact recovery of ultra sparse vectors, in a single pass…
Continuous Hands-off Control by CLOT Norm Minimization
Niharika Challapalli, Masaaki Nagahara, Mathukumalli Vidyasagar
In this paper, we consider hands-off control via minimization of the CLOT (Combined L-One and Two) norm. The maximum hands-off control is the L0-optimal (or the sparsest) control a…
Tight Performance Bounds for Compressed Sensing With Conventional and Group Sparsity
Shashank Ranjan, Mathukumalli Vidyasagar
In this paper, we study the problem of recovering a group sparse vector from a small number of linear measurements. In the past the common approach has been to use various "group s…
Error Bounds for Compressed Sensing Algorithms With Group Sparsity: A Unified Approach
M. Eren Ahsen, M. Vidyasagar
In compressed sensing, in order to recover a sparse or nearly sparse vector from possibly noisy measurements, the most popular approach is -norm minimization. Upper bounds…
Two New Approaches to Compressed Sensing Exhibiting Both Robust Sparse Recovery and the Grouping Effect
Mehmet Eren Ahsen, Niharika Challapalli, Mathukumalli Vidyasagar
In this paper we introduce a new optimization formulation for sparse regression and compressed sensing, called CLOT (Combined L-One and Two), wherein the regularizer is a convex co…
Machine Learning Methods in the Computational Biology of Cancer
Mathukumalli Vidyasagar
The objectives of this "perspective" paper are to review some recent advances in sparse feature selection for regression and classification, as well as compressed sensing, and to d…
Near-Ideal Behavior of Compressed Sensing Algorithms
Mehmet Eren Ahsen, Mathukumalli Vidyasagar
In a recent paper, it is shown that the LASSO algorithm exhibits "near-ideal behavior," in the following sense: Suppose where satisfies the restricted isometry pro…
An Elementary Derivation of the Large Deviation Rate Function for Finite State Markov Chains
Mathukumalli Vidyasagar
Large deviation theory is a branch of probability theory that is devoted to a study of the "rate" at which empirical estimates of various quantities converge to their true values.…
Reverse Engineering Gene Interaction Networks Using the Phi-Mixing Coefficient
Nitin Kumar Singh, M. Eren Ahsen, Shiva Mankala +3
Constructing gene interaction networks (GINs) from high-throughput gene expression data is an important and challenging problem in systems biology. Existing algorithms produce netw…
Mixing Coefficients Between Discrete and Real Random Variables: Computation and Properties
Mehmet Eren Ahsen, Mathukumalli Vidyasagar
In this paper we study the problem of estimating the alpha-, beta- and phi-mixing coefficients between two random variables, that can either assume values in a finite set or the se…
A Metric Between Probability Distributions on Finite Sets of Different Cardinalities and Applications to Order Reduction
Mathukumalli Vidyasagar
With increasing use of digital control it is natural to view control inputs and outputs as stochastic processes assuming values over finite alphabets rather than in a Euclidean spa…