arXiv subjects

Kurt Hornik

Publications and source records attributed to Kurt Hornik.

9 recordsLinked to original sources

arXiv2025

Hyperspherical Variational Autoencoders Using Efficient Spherical Cauchy Distribution

We propose spherical Cauchy (spCauchy) latent variables for variational autoencoders on hyperspherical latent spaces. The spCauchy family has heavy-tailed global behavior and admits an exact differentiable reparameterization by applying a M\"obius transformation to uniform samples on the sphere. We show that, in the high-concentration limit, spCauchy recovers the local tangent-space geometry of the von Mises-Fisher (vMF) distribution under an explicit concentration parameter mapping, while avoiding the high-order Bessel-function evaluations required by vMF implementations. For training, the Kullback-Leibler divergence to a uniform spherical prior admits rapidly convergent series, stable quadrature, and high-concentration asymptotic forms. We further establish monotonicity of the concentration-dependent KL core and derive analytic brackets with closed-form surrogates and error control, supporting stable approximation in extreme regimes. Stress-test benchmarks show that the resulting latent-layer objective remains stable and faster to evaluate than vMF baselines on CPU and GPU. Experiments on image and molecular sequence data demonstrate that spCauchy-VAEs provide a robust and scalable alternative for generative modeling with hyperspherical latent representations.

stat.ML↗

arXiv2024

Regularized Adjusted Plus-Minus Models for Evaluating and Scouting Football (Soccer) Players using Possession Sequences

This paper presents a novel framework for evaluating players in association football (soccer). Our method uses possession sequences, i.e. sequences of consecutive on-ball actions, for deriving estimates for player strengths. On the surface, the methodology is similar to classical adjusted plus-minus rating models using mainly regularized regression techniques. However, by analyzing possessions, our framework is able to distinguish on-ball and off-ball contributions of players to the game. From a methodological viewpoint, the framework explores four different penalization schemes, which exploit football-specific structures such as the grouping of players into position groups as well as into common strength groups. These four models lead to four ways to rate players by considering the respective estimate of each model corresponding to the player. The ratings are used to analyze the 2017/18 season of the Spanish La Liga. We compare similarities as well as particular use cases of each of the penalized models and provide guidance for practitioners when using the individual model specifications. Finally, we conclude our analysis by providing a domain-specific statistical evaluation framework, which highlights the potential of the penalized regression approaches for evaluating players.

stat.AP↗

arXiv2023

CRAN Task Views: The Next Generation

CRAN Task Views have been available on the Comprehensive R Archive Network since 2005. They provide guidance about which CRAN packages are relevant for tasks related to a certain topic, and can also facilitate automatic installation of all corresponding packages. Motivated by challenges from the growth of CRAN and the R community as a whole since 2005, all of the task views infrastructure and workflows were rethought and relaunched in 2021/22 in order to facilitate maintenance and to foster deeper interactions with the R community. The redesign encompasses the establishment of a group of CRAN Task View Editors, moving all task view sources to dedicated GitHub repositories, adopting well-documented workflows with a code of conduct, and leveraging R/Markdown files (rather than XML) for the content of the task views.

stat.CO↗

arXiv2019

colorspace: A Toolbox for Manipulating and Assessing Colors and Palettes

The R package colorspace provides a flexible toolbox for selecting individual colors or color palettes, manipulating these colors, and employing them in statistical graphics and data visualizations. In particular, the package provides a broad range of color palettes based on the HCL (Hue-Chroma-Luminance) color space. The three HCL dimensions have been shown to match those of the human visual system very well, thus facilitating intuitive selection of color palettes through trajectories in this space. Using the HCL color model general strategies for three types of palettes are implemented: (1) Qualitative for coding categorical information, i.e., where no particular ordering of categories is available. (2) Sequential for coding ordered/numeric information, i.e., going from high to low (or vice versa). (3) Diverging for coding ordered/numeric information around a central neutral value, i.e., where colors diverge from neutral to two extremes. To aid selection and application of these palettes the package also contains scales for use with ggplot2, shiny (and tcltk) apps for interactive exploration, visualizations of palette properties, accompanying manipulation utilities (like desaturation and lighten/darken), and emulation of color vision deficiencies.

stat.CO↗

arXiv2015

Computing a consensus journal meta-ranking using paired comparisons and adaptive lasso estimators

In a "publish-or-perish culture", the ranking of scientific journals plays a central role in assessing performance in the current research environment. With a wide range of existing methods and approaches to deriving journal rankings, meta-rankings have gained popularity as a means of aggregating different information sources. In this paper, we propose a method to create a consensus meta-ranking using heterogeneous journal rankings. Using a parametric model for paired comparison data we estimate quality scores for 58 journals in the OR/MS community, which together with a shrinkage procedure allows for the identification of clusters of journals with similar quality. The use of paired comparisons provides a flexible framework for deriving a consensus score while eliminating the problem of data missingness.

stat.AP↗

arXiv2013

Model trees with topic model preprocessing: An approach for data journalism illustrated with the WikiLeaks Afghanistan war logs

The WikiLeaks Afghanistan war logs contain nearly $77,000$ reports of incidents in the US-led Afghanistan war, covering the period from January 2004 to December 2009. The recent growth of data on complex social systems and the potential to derive stories from them has shifted the focus of journalistic and scientific attention increasingly toward data-driven journalism and computational social science. In this paper we advocate the usage of modern statistical methods for problems of data journalism and beyond, which may help journalistic and scientific work and lead to additional insight. Using the WikiLeaks Afghanistan war logs for illustration, we present an approach that builds intelligible statistical models for interpretable segments in the data, in this case to explore the fatality rates associated with different circumstances in the Afghanistan war. Our approach combines preprocessing by Latent Dirichlet Allocation (LDA) with model trees. LDA is used to process the natural language information contained in each report summary by estimating latent topics and assigning each report to one of them. Together with other variables these topic assignments serve as splitting variables for finding segments in the data to which local statistical models for the reported number of fatalities are fitted. Segmentation and fitting is carried out with recursive partitioning of negative binomial distributions. We identify segments with different fatality rates that correspond to a small number of topics and other variables as well as their interactions. Furthermore, we carve out the similarities between segments and connect them to stories that have been covered in the media. This gives an unprecedented description of the war in Afghanistan and serves as an example of how data journalism, computational social science and other areas with interest in database data can benefit from modern statistical techniques.

stat.AP↗

arXiv2013

Influencing elections with statistics: Targeting voters with logistic regression trees

In political campaigning substantial resources are spent on voter mobilization, that is, on identifying and influencing as many people as possible to vote. Campaigns use statistical tools for deciding whom to target ("microtargeting"). In this paper we describe a nonpartisan campaign that aims at increasing overall turnout using the example of the 2004 US presidential election. Based on a real data set of 19,634 eligible voters from Ohio, we introduce a modern statistical framework well suited for carrying out the main tasks of voter targeting in a single sweep: predicting an individual's turnout (or support) likelihood for a particular cause, party or candidate as well as data-driven voter segmentation. Our framework, which we refer to as LORET (for LOgistic REgression Trees), contains standard methods such as logistic regression and classification trees as special cases and allows for a synthesis of both techniques. For our case study, we explore various LORET models with different regressors in the logistic model components and different partitioning variables in the tree components; we analyze them in terms of their predictive accuracy and compare the effect of using the full set of available variables against using only a limited amount of information. We find that augmenting a standard set of variables (such as age and voting history) with additional predictor variables (such as the household composition in terms of party affiliation) clearly improves predictive accuracy. We also find that LORET models based on tree induction beat the unpartitioned models. Furthermore, we illustrate how voter segmentation arises from our framework and discuss the resulting profiles from a targeting point of view.

stat.AP↗

arXiv2008

Selective association rule generation

Mining association rules is a popular and well researched method for discovering interesting relations between variables in large databases. A practical problem is that at medium to low support values often a large number of frequent itemsets and an even larger number of association rules are found in a database. A widely used approach is to gradually increase minimum support and minimum confidence or to filter the found rules using increasingly strict constraints on additional measures of interestingness until the set of rules found is reduced to a manageable size. In this paper we describe a different approach which is based on the idea to first define a set of ``interesting'' itemsets (e.g., by a mixture of mining and expert knowledge) and then, in a second step to selectively generate rules for only these itemsets. The main advantage of this approach over increasing thresholds or filtering rules is that the number of rules found is significantly reduced while at the same time it is not necessary to increase the support and confidence thresholds which might lead to missing important information in the database.

cs.DB↗

arXiv2008

New probabilistic interest measures for association rules

Mining association rules is an important technique for discovering meaningful patterns in transaction databases. Many different measures of interestingness have been proposed for association rules. However, these measures fail to take the probabilistic properties of the mined data into account. In this paper, we start with presenting a simple probabilistic framework for transaction data which can be used to simulate transaction data when no associations are present. We use such data and a real-world database from a grocery outlet to explore the behavior of confidence and lift, two popular interest measures used for rule mining. The results show that confidence is systematically influenced by the frequency of the items in the left hand side of rules and that lift performs poorly to filter random noise in transaction data. Based on the probabilistic framework we develop two new interest measures, hyper-lift and hyper-confidence, which can be used to filter or order mined association rules. The new measures show significantly better performance than lift for applications where spurious rules are problematic.

cs.DB↗