arXiv subjects

Mads Lindskou

Publications and source records attributed to Mads Lindskou.

3 recordsLinked to original sources

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

Detecting Outliers in High-dimensional Data with Mixed Variable Types using Conditional Gaussian Regression Models

Outlier detection has gained increasing interest in recent years, due to newly emerging technologies and the huge amount of high-dimensional data that are now available. Outlier detection can help practitioners to identify unwanted noise and/or locate interesting abnormal observations. To address this, we developed a novel method for outlier detection for use in, possibly high-dimensional, datasets with both discrete and continuous variables. We exploit the family of decomposable graphical models in order to model the relationship between the variables and use this to form an exact likelihood ratio test for an observation that is considered an outlier. We show that our method outperforms the state-of-the-art Isolation Forest algorithm on a real data example.

math.ST↗