arXiv subjects

Søren Højsgaard

Publications and source records attributed to Søren Højsgaard.

5 recordsLinked to original sources

arXiv2023

On some algorithms for estimation in Gaussian graphical models

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 convex duality and operating on the covariance matrix by neighbourhood coordinate descent, corresponding to the graphical lasso with zero penalty. For large, sparse graphs, the iterative proportional scaling algorithm appears feasible and has simple convergence properties. The algorithm based on neighbourhood coordinate descent is extremely fast and less dependent on sparsity, but needs a positive definite starting value to converge. We give an algorithm for finding such a starting value for graphs with low colouring number. As a consequence, we also obtain a simplified proof for existence of the maximum likelihood estimator in such cases.

stat.CO↗

arXiv2023

Computer Algebra in R Bridges a Gap Between Mathematics and Data in the Teaching of Statistics and Data Science

The capability of R to do symbolic mathematics is enhanced by the caracas package. This package uses the Python computer algebra library SymPy as a back-end but caracas is tightly integrated in the R environment. This enables the R user with symbolic mathematics within R at a high abstraction level rather than using text strings and text string manipulation as the case would be if using SymPy from R directly. We demonstrate how mathematics and statistics can benefit from bridging computer algebra and data via R. This is done thought a number of examples and we propose some topics for small student projects. The caracas package integrates well with e.g. Rmarkdown, and as such creation of scientific reports and teaching is supported.

stat.AP↗

arXiv2022

Unity Smoothing for Handling Inconsistent Evidence in Bayesian Networks and Unity Propagation for Faster Inference

We propose Unity Smoothing (US) for handling inconsistencies between a Bayesian network model and new unseen observations. We show that prediction accuracy, using the junction tree algorithm with US is comparable to that of Laplace smoothing. Moreover, in applications were sparsity of the data structures is utilized, US outperforms Laplace smoothing in terms of memory usage. Furthermore, we detail how to avoid redundant calculations that must otherwise be performed during the message passing scheme in the junction tree algorithm which we refer to as Unity Propagation (UP). Experimental results shows that it is always faster to exploit UP on top of the Lauritzen-Spigelhalter message passing scheme for the junction tree algorithm.

cs.LG↗

arXiv2021

sparta: Sparse Tables and their Algebra with a View Towards High Dimensional Graphical Models

A graphical model is a multivariate (potentially very high dimensional) probabilistic model, which is formed by combining lower dimensional components. Inference (computation of conditional probabilities) is based on message passing algorithms that utilize conditional independence structures. In graphical models for discrete variables with finite state spaces, there is a fundamental problem in high dimensions: A discrete distribution is represented by a table of values, and in high dimensions such tables can become prohibitively large. In inference, such tables must be multiplied which can lead to even larger tables. The sparta package meets this challenge by implementing methods that efficiently handles multiplication and marginalization of sparse tables. The package was written in the R programming language and is freely available from the Comprehensive R Archive Network (CRAN). The companion package jti, also on CRAN, was developed to showcase the potential of sparta in connection to the Junction Tree Algorithm. We show, that jti is able to handle highly complex graphical models which are otherwise infeasible due to lack of computer memory, using sparta as a backend for table operations.

stat.CO↗

arXiv2021

Computer Algebra in R with caracas

The capability of R to do symbolic mathematics is enhanced by the caracas package. This package uses the Python computer algebra library SymPy as a back-end but caracas is tightly integrated in the R environment, thereby enabling the R user with symbolic mathematics within R. Key components of the caracas package are illustrated in this paper. Examples are taken from statistics and mathematics. The caracas package integrates well with e.g. Rmarkdown, and as such creation of scientific reports and teaching is supported.

stat.AP↗