Related papers: Precision and Cholesky Factor Estimation for Gauss…
Gaussian process is an indispensable tool in clustering functional data, owing to it's flexibility and inherent uncertainty quantification. However, when the functional data is observed over a large grid (say, of length $p$), Gaussian…
In this paper, we focus on learning product graphs from multi-domain data. We assume that the product graph is formed by the Cartesian product of two smaller graphs, which we refer to as graph factors. We pose the product graph learning…
This paper presents a sequential randomized lowrank matrix factorization approach for incrementally predicting values of an unknown function at test points using the Gaussian Processes framework. It is well-known that in the Gaussian…
A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…
In this paper, we investigate the butterfly factorization problem, i.e., the problem of approximating a matrix by a product of sparse and structured factors. We propose a new formal mathematical description of such factors, that encompasses…
Finite Gaussian mixture models provide a powerful and widely employed probabilistic approach for clustering multivariate continuous data. However, the practical usefulness of these models is jeopardized in high-dimensional spaces, where…
In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…
The performance of sparse matrix computation highly depends on the matching of the matrix format with the underlying structure of the data being computed on. Different sparse matrix formats are suitable for different structures of data.…
The scalable calculation of matrix determinants has been a bottleneck to the widespread application of many machine learning methods such as determinantal point processes, Gaussian processes, generalised Markov random fields, graph models…
Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…
The vast quantity of information brought by big data as well as the evolving computer hardware encourages success stories in the machine learning community. In the meanwhile, it poses challenges for the Gaussian process (GP) regression, a…
Algorithms are presented for evaluating gradients and Hessians of logarithmic barrier functions for two types of convex cones: the cone of positive semidefinite matrices with a given sparsity pattern, and its dual cone, the cone of sparse…
This paper studies the covariance matrix estimation for high-dimensional time series within a new framework that combines low-rank factor and latent variable-specific cluster structures. The popular methods based on assuming the sparse…
Precision matrices are crucial in many fields such as social networks, neuroscience, and economics, representing the edge structure of Gaussian graphical models (GGMs), where a zero in an off-diagonal position of the precision matrix…
In this paper we present a method for matrix inversion based on Cholesky decomposition with reduced number of operations by avoiding computation of intermediate results; further, we use fixed point simulations to compare the numerical…
In this paper, we focus on activating only a few sensors, among many available, to estimate the state of a stochastic process of interest. This problem is important in applications such as target tracking and simultaneous localization and…
In Gaussian graphical models, the likelihood equations must typically be solved iteratively. We investigate two algorithms: A version of iterative proportional scaling which avoids inversion of large matrices, and an algorithm based on…
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…
Riemann manifold Hamiltonian Monte Carlo (RMHMC) has the potential to produce high-quality Markov chain Monte Carlo-output even for very challenging target distributions. To this end, a symmetric positive definite scaling matrix for RMHMC,…
The partial pivoted Cholesky approximation accurately represents matrices that are close to being low-rank. Meanwhile, the Vecchia approximation accurately represents matrices with inverse Cholesky factors that are close to being sparse.…