Differentially Private Sparse Covariance Matrix Estimation under Lower-Bounded Moment Assumption

Sparse estimation of a covariance matrix.

We suggest a method for estimating a covariance matrix on the basis of a sample of vectors drawn from a multivariate normal distribution. In particular, we penalize the likelihood with a lasso penalty on the entries of the covariance matrix. This penalty plays two important roles: it reduces the effective number of parameters, which is important even when the dimension of the vectors is smaller...

Adaptive Thresholding for Sparse Covariance Matrix Estimation

In this article we consider estimation of sparse covariance matrices and propose a thresholding procedure that is adaptive to the variability of individual entries. The estimators are fully data-driven and demonstrate excellent performance both theoretically and numerically. It is shown that the estimators adaptively achieve the optimal rate of convergence over a large class of sparse covarianc...

Sparse Covariance Matrix Estimation With Eigenvalue Constraints.

We propose a new approach for estimating high-dimensional, positive-definite covariance matrices. Our method extends the generalized thresholding operator by adding an explicit eigenvalue constraint. The estimated covariance matrix simultaneously achieves sparsity and positive definiteness. The estimator is rate optimal in the minimax sense and we develop an efficient iterative soft-thresholdin...

Estimation of Rigid Motion Parameters Using Moment Covariance Matrix

The estimation of rigid motion parameters has been investigated using Fourier transform and iterative techniques for over two decades. But the numerical efficiency remains a challenge. Especially for 3D case, there is no any analytical algorithm. In this work, we propose to use the moment covariance matrix to estimate the orthogonal transform (i.e., rigid motion in real world). This algorithm d...

Supplement to “Adaptive Thresholding for Sparse Covariance Matrix Estimation”