This work considers a computationally and statistically e?cient parameter estimation method for a wide class of latent variable models—including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation—which exploits a certain tensor structure in their loworder observable moments (typically, of secondand third-order). Speci?cally, parameter estimation is reduced to the pro...

Tensor regression has shown to be advantageous in learning tasks with multi-directional relatedness. Given massive multiway data, traditional methods are often too slow to operate on or suffer from memory bottleneck. In this paper, we introduce subsampled tensor projected gradient to solve the problem. Our algorithm is impressively simple and efficient. It is built upon projected gradient metho...

The complete optical-gyration tensor for a monoclinic crystal of (2R, 3R)-(+)C4H6O6 has been determined by the tilter method at a wavelength of 680 nm. The tensor components in terms of rotatory power in relation to the principal axes of the indicatrix were found to be ρ◦ 11 = 79(7), ρ◦ 22 = 90(13), ρ◦ 33 = −70(4), ρ◦ 23 = −18(8)◦ mm−1 with ρ = −12.3(1.0)◦ mm−1 in the optic-axis directions. The...

We present limits on the fraction of large angle microwave anisotropies which could come from tensor perturbations. We use the COBE results as well as smaller scale CMB observations, measurements of galaxy correlations, abundances of galaxy clusters, and Lyα absorption cloud statistics. Our aim is to provide conservative limits on the tensor-to-scalar ratio for standard inflationary models. For...

Well known connections exist between the singular value decomposition of a matrix A and the Schur decomposition of its symmetric embedding sym(A) = ([ 0A ; A 0 ]). In particular, if σ is a singular value of A then +σ and −σ are eigenvalues of the symmetric embedding. The top and bottom halves of sym(A)’s eigenvectors are singular vectors for A. Power methods applied to A can be related to power...

In this article, the notions of non-abelian tensor and exterior products of two normal crossed submodules of a given crossed module of groups are introduced and some of their basic properties are established. In particular, we investigate some common properties between normal crossed modules and their tensor products, and present some bounds on the nilpotency class and solvability length of the...