Matrix factorization algorithms are frequently used in the machine learning community to find low dimensional representations of data. We introduce a novel generative Bayesian probabilistic model for unsupervised matrix and tensor factorization. The model consists of several interacting LDA models, one for each modality. We describe an efficient collapsed Gibbs sampler for inference. We also de...

We discuss an NNLO realization of the general mass scheme S-ACOT-χ for treatment of heavy-flavor production in neutral current deep-inelastic scattering. The connection of this scheme to the QCD factorization theorem with massive quarks is elucidated. As a new feature, kinematical constraints on collinear production of heavy quarks that are crucial near the heavy-quark threshold are included in...

Energy transfer between a macromolecule or supramolecular assembly and a host medium is considered from the perspective of Newton's equations and Lie-Trotter factorization. The development starts by demonstrating that the energy of the molecule evolves slowly relative to the time scale of atomic collisions-vibrations. The energy is envisioned to be a coarse-grained variable that coevolves with ...

This paper studies the use of a generalized hierarchical basis transformation at each level of a multilevel block factorization. The factorization may be used as a preconditioner to the conjugate gradient method, or the structure it sets up may be used to define a multigrid method. The basis transformation is performed with an averaged piecewise constant interpolant and is applicable to unstruc...

In a previous work, we proposed an informed Non-negative Matrix Factorization (NMF) with a specific parametrization which involves constraints about some known components of the factorization. In this paper we extend the above work by adding some information provided by a physical dispersion model. In particular, we derive a special structure of one of the factorizing matrices, which provides a...

In this paper, we investigate the predictive power of different prosodic factorization schemes with respect to pitch movement. We will use this to propose an extension of a standard diphone database with diphones that have been recorded in different prosodic contexts. The goal of this research is to reduce the amount of pitch modification required, thereby improving the segmental quality of the...

We investigate the problem of factoring a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where finding a factorization corresponds to finding edges in different layers and also values of hidden units. We prove that under certain assumptions on a sparse li...

Spectrogram factorization is a recent and promising alternative to sinusoidal or source/filter modeling for analysis/resynthesis systems aimed at musical creation. This paper presents a framework designed to perform a wide range of sound manipulations based on Non-negative Matrix Factorization (NMF), including a set of new techniques for creating artificial cross-components not present in the o...