PROJECT TITLE :

Efficient Minimax Estimation of a Class of High-Dimensional Sparse Precision Matrices

ABSTRACT:

Estimation of the covariance matrix and its inverse, the precision matrix, in high-dimensional situations is of great interest in many applications. In this paper, we focus on the estimation of a class of sparse precision matrices which are assumed to be approximately inversely closed for the case that the dimensionality $p$ can be much larger than the sample size $n$, which is fundamentally different from the classical case that $p < n$. Different in nature from state-of-the-art methods that are based on penalized likelihood maximization or constrained error minimization, based on the truncated Neumann series representation, we propose a computationally efficient precision matrix estimator that has a computational complexity of $O(p^{3})$. We prove that the proposed estimator is consistent in probability and in $L^{2}$ under the spectral norm. Moreover, its convergence is shown to be rate-optimal in the sense of minimax risk. We further prove that the proposed estimator is model selection consistent by establishing a convergence result under the entry-wise $infty$-norm. Simulations demonstrate the encouraging finite sample size performance and computational advantage of the proposed estimator. The proposed estimator is also applied to a real breast cancer data and shown to outperform existing precision matrix estimators.


Did you like this research project?

To get this research project Guidelines, Training and Code... Click Here


PROJECT TITLE :Efficient Secure Outsourcing of Large-Scale Sparse Linear Systems of Equations - 2018ABSTRACT:Solving large-scale sparse linear systems of equations (SLSEs) is one in all the foremost common and basic problems in
PROJECT TITLE :Distributed Feature Selection for Efficient Economic Big Data Analysis - 2018ABSTRACT:With the rapidly increasing popularity of economic activities, a large amount of economic data is being collected. Although
PROJECT TITLE :Efficient Wideband DOA Estimation Through Function Evaluation Techniques - 2018ABSTRACT:This Project presents an economical analysis methodology for the functions involved within the computation of direction-of-arrival
PROJECT TITLE :Efficient System Tracking With Decomposable Graph-Structured Inputs and Application to Adaptive Equalization With Cyclostationary Inputs - 2018ABSTRACT:This Project introduces the graph-structured recursive least
PROJECT TITLE :Efficient Partial-Sum Network Architectures for List Successive-Cancellation Decoding of Polar Codes - 2018ABSTRACT:List successive cancellation decoder (LSCD) architectures have been recently proposed for the decoding

Ready to Complete Your Academic MTech Project Work In Affordable Price ?

Project Enquiry