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Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is…
Marginalization techniques are presented for the Bayesian filtering problem under the assumption of Gaussian priors and posteriors and a set of sequentially more constraining state space model assumptions. The techniques provide the…
In this paper, we propose a new method of Bayesian measurement for spectral deconvolution, which regresses spectral data into the sum of unimodal basis function such as Gaussian or Lorentzian functions. Bayesian measurement is a framework…
This paper introduces the Gaussian multi-Graphical Model, a model to construct sparse graph representations of matrix- and tensor-variate data. We generalize prior work in this area by simultaneously learning this representation across…
Parton distribution functions (PDFs) form an essential part of particle physics calculations. Currently, the most precise predictions for these non-perturbative functions are generated through fits to global data. A problem that several PDF…
Manifestly invariant renormalization scheme for supersymmetric gauge theories is proposed. This scheme is applied to supersymmetric quantum electrodynamics.
The density matrix renormalization group method is generalized to one dimensional random systems. Using this method, the energy gap distribution of the spin-1/2 random antiferromagnetic Heisenberg chain is calculated. The results are…
Evaluation of likelihood functions for cosmological large scale structure data sets (including CMB, galaxy redshift surveys, etc.) naturally involves marginalization, i.e., integration, over an unknown underlying random signal field.…
The Kadanoff-Wilson-Fisher approach to renormalization is based upon studying the renormalization transform, which may be described as an action of the monoid $\mathbb{R}^{\times}_{\geq 1}$ on a suitable space of interactions. It is…
Most machine learning methods require careful selection of hyper-parameters in order to train a high performing model with good generalization abilities. Hence, several automatic selection algorithms have been introduced to overcome tedious…
A momentum-space approach of the density-matrix renormalization-group (DMRG) method is developed. Ground state energies of the Hubbard model are evaluated using this method and compared with exact diagonalization as well as quantum…
This article is intended to provide a pedagogical introduction to the supersymmetry method for performing ensemble-averaging in Gaussian random-matrix theory. The method is illustrated by a detailed calculation of the simplest non-trivial…
A method is presented for performing joint analyses of cosmological datasets, in which the weight assigned to each dataset is determined directly by it own statistical properties. The weights are considered in a Bayesian context as a set of…
We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet…
This paper proposes a generalization of Gaussian mixture models, where the mixture weight is allowed to behave as an unknown function of time. This model is capable of successfully capturing the features of the data, as demonstrated by…
The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point patterns. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the…
This paper proposes a strategy for regularized estimation in multi-way contingency tables, which are common in meta-analyses and multi-center clinical trials. Our approach is based on data augmentation, and appeals heavily to a novel class…
There are reasons to believe that the Standard Model is only an effective theory, with new Physics lying beyond it. Supersymmetric extensions are one possibility: they address some of the Standard Model's shortcomings, such as the…
Recovering physical properties of objects in motion is a core task across scientific and industrial applications. When the relative motion between the object and the sensing apparatus provides sufficient angular coverage, Computerized…
We describe an approach for identifying groups of dynamically similar locations in spatial time-series data based on a simple Markov transition model. We give maximum-likelihood, empirical Bayes, and fully Bayesian formulations of the…