We consider moment matching techniques for estimation in latent Dirichlet allocation (LDA). By drawing explicit links between LDA and discrete versions of independent component analysis (ICA), we first derive a new set of cumulantbased tensors, with an improved sample complexity. Moreover, we reuse standard ICA techniques such as joint diagonalization of tensors to improve over existing methods...

A constructive proof of identification of multilinear decompositions of multiway arrays is presented. It can be applied to show identification in a variety of multivariate latent structures. Examples are finite-mixture models and hidden Markov models. The key step to show identification is the joint diagonalization of a set of matrices in the same nonorthogonal basis. An estimator of the latent...

We propose a new non-perturbative technique for calculating the field-theory S matrix directly from the eigenstates of the Hamiltonian. Our method involves a discretized momentum space and a momentum cutoff, thereby truncating the Hilbert space and making numerical diagonalization of the Hamiltonian achievable. We show how to do this in the context of a simplified λφ theory in two space-time di...

This paper deals with estimation of structured signals such as damped sinusoids, exponentials, polynomials, and their products from single channel data. It is shown that building tensors from this kind of data results in tensors with hidden block structure which can be recovered through the tensor diagonalization. The tensor diagonalization means multiplying tensors by several matrices along it...

We identify an integrable one-dimensional inhomogeneous three-site open spin chain which arises in the problem of diagonalization of twist-three quark-gluon evolution equations in QCD in the chiral-odd sector. Making use of the existence of a non-trivial 'hidden' integral of motion the problem of diagonalization of the evolution kernels is reduced to the study of a second order finite-differenc...

Going back to the seminal paper [FSS84] by Furst, Saxe, and Sipser, analogues between polynomial time classes and constant depth circuit classes have been considered in a number of papers. Oracles separating polynomial time classes have been obtained by diagonalization making essential use of lower bounds for circuit classes. In this note we show how separating oracles can be obtained uniformly...

Simultaneous diagonalization of several matrices can be implemented by a Jacobi-like technique. This note gives the required Jacobi angles in close form.