Kernel learning plays an important role in many machine learning tasks. However, algorithms for learning a kernel matrix often scale poorly, with running times that are cubic in the number of data… (More)

In this paper, we study low-rank matrix nearness problems, with a focus on learning low-rank positive semidefinite (kernel) matrices for machine learning applications. We propose efficient algorithms… (More)

The `1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying… (More)

The `1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix even under high-dimensional… (More)

An equiangular tight frame (ETF) is a d × N matrix that has unit-norm columns and orthogonal rows of norm √ N/d. Its key property is that the absolute inner products between pairs of columns are (i)… (More)

The l1 regularized Gaussian maximum likelihood estimator has bee n shown to have strong statistical guarantees in recovering a sparse i nverse covariance matrix, or alternatively the underlying graph… (More)

In this paper, we present new algorithms that can replace the diagonal entries of a Hermitian matrix by any set of diagonal entries that majorize the original set without altering the eigenvalues of… (More)

In this paper we present the use of the ACL2 theorem prover to formalize and mechanically check a new proof of Dickson’s lemma about monomial sequences. Dickson’s lemma can be used to establish the… (More)

The GLASSO algorithm has been proposed by Friedman, Hastie and Tibshirani in 2008 to solve the `1 regularized inverse covariance matrix estimation problem. The conditional dependency structure which… (More)