arXiv subjects

Andreas Mayr

Publications and source records attributed to Andreas Mayr.

At least 19 recordsLinked to original sources

arXiv2026

G-RRM: Guiding Symbolic Solvers with Recurrent Reasoning Models

In this work, we focus on SE-RRMs, a symbol-equivariant instantiation of RRMs that exhibits improved extrapolation to larger problem sizes. We propose a neuro-symbolic approach, ``Guiding with Recurrent Reasoning Models'' (G-RRM), which integrates SE-RRMs with symbolic solvers for constraint satisfaction problems. SE-RRMs act as neural solvers that generate full solution proposals and guide classical symbolic solvers, such as backtracking or SAT-based methods like Glucose 4.1 and CaDiCaL 3.0.0, that produce globally correct solutions. Centrally, we investigate when neural guidance with G-RRM improves the search efficiency of symbolic solvers. % Our experiments show that the efficacy of G-RRM depends on two conditions: first, the problem instances must have an expansive combinatorial search space to expose potential gains, and second, the solver architecture must be capable of dynamically overwriting its branching choices to recover when neural hints are imperfect. When these conditions hold, guidance drives median conflict counts to zero and yields significant wall-clock speedups: on $9\times9$ Sudoku, where the SE-RRM correctly solves $91.1\%$ of instances, backtracking accelerates by $33.3\times$ and Glucose 4.1 by $1.70\times$ (median, $p<0.001$), with Glucose 4.1 retaining a $1.17\times$ speedup on perfect-hint $25\times25$ grids. In contrast, CaDiCaL 3.0.0, whose runtime is overhead-dominated and which always respects the injected branching hints rather than overwriting them, shows no significant speedup (median $1.02\times$, n.s.) and even a small significant mean slowdown ($0.90\times$) on $9\times9$. These results delineate the regimes in which neural guidance translates into practical speedups.

cs.AI↗

arXiv2026

Symbol-Equivariant Recurrent Reasoning Models

Reasoning problems such as Sudoku and ARC-AGI remain challenging for neural networks. The structured problem solving architecture family of Recurrent Reasoning Models (RRMs), including Hierarchical Reasoning Model (HRM) and Tiny Recursive Model (TRM), offer a compact alternative to large language models, but currently handle symbol symmetries only implicitly via costly data augmentation. We introduce Symbol-Equivariant Recurrent Reasoning Models (SE-RRMs), which enforce permutation equivariance at the architectural level through symbol-equivariant layers, guaranteeing identical solutions under symbol or color permutations. SE-RRMs outperform prior RRMs on 9x9 Sudoku and generalize from just training on 9x9 to smaller 4x4 and larger 16x16 and 25x25 instances, to which existing RRMs cannot extrapolate. On ARC-AGI-1 and ARC-AGI-2, SE-RRMs achieve competitive performance with substantially less data augmentation and only 2 million parameters, demonstrating that explicitly encoding symmetry improves the robustness and scalability of neural reasoning. Code is available at https://github.com/ml-jku/SE-RRM.

cs.LG↗

arXiv2025

Refuting "Debunking the GAMLSS Myth: Simplicity Reigns in Pulmonary Function Diagnostics"

We read with interest the above article by Zavorsky (2025, Respiratory Medicine, doi:10.1016/j.rmed.2024.107836) concerning reference equations for pulmonary function testing. The author compares a Generalized Additive Model for Location, Scale, and Shape (GAMLSS), which is the standard adopted by the Global Lung Function Initiative (GLI), with a segmented linear regression (SLR) model, for pulmonary function variables. The author presents an interesting comparison; however there are some fundamental issues with the approach. We welcome this opportunity for discussion of the issues that it raises. The author's contention is that (1) SLR provides "prediction accuracies on par with GAMLSS"; and (2) the GAMLSS model equations are "complicated and require supplementary spline tables", whereas the SLR is "more straightforward, parsimonious, and accessible to a broader audience". We respectfully disagree with both of these points.

stat.AP↗

arXiv2025

Detecting gene-environment interactions to guide personalized intervention: boosting distributional regression for polygenic scores

Polygenic risk scores can be used to model the individual genetic liability for human traits. Current methods primarily focus on modeling the mean of a phenotype neglecting the variance. However, genetic variants associated with phenotypic variance can provide important insights to gene-environment interaction studies. To overcome this, we propose snpboostlss, a cyclical gradient boosting algorithm for a Gaussian location-scale model to jointly derive sparse polygenic models for both the mean and the variance of a quantitative phenotype. To improve computational efficiency on high-dimensional and large-scale genotype data (large n and large p), we only consider a batch of most relevant variants in each boosting step. We investigate the effect of statins therapy (the environmental factor) on low-density lipoprotein in the UK Biobank cohort using the new snpboostlss algorithm. We are able to verify the interaction between statins usage and the polygenic risk scores for phenotypic variance in both cross sectional and longitudinal analyses. Particularly, following the spirit of target trial emulation, we observe that the treatment effect of statins is more substantial in people with higher polygenic risk scores for phenotypic variance, indicating gene-environment interaction. When applying to body mass index, the newly constructed polygenic risk scores for variance show significant interaction with physical activity and sedentary behavior. Therefore, the polygenic risk scores for phenotypic variance derived by snpboostlss have potential to identify individuals that could benefit more from environmental changes (e.g. medical intervention and lifestyle changes).

stat.AP↗

arXiv2025

LaM-SLidE: Latent Space Modeling of Spatial Dynamical Systems via Linked Entities

Generative models are spearheading recent progress in deep learning, showcasing strong promise for trajectory sampling in dynamical systems as well. However, whereas latent space modeling paradigms have transformed image and video generation, similar approaches are more difficult for most dynamical systems. Such systems -- from chemical molecule structures to collective human behavior -- are described by interactions of entities, making them inherently linked to connectivity patterns, entity conservation, and the traceability of entities over time. Our approach, LaM-SLidE (Latent Space Modeling of Spatial Dynamical Systems via Linked Entities), bridges the gap between: (1) keeping the traceability of individual entities in a latent system representation, and (2) leveraging the efficiency and scalability of recent advances in image and video generation, where pre-trained encoder and decoder enable generative modeling directly in latent space. The core idea of LaM-SLidE is the introduction of identifier representations (IDs) that enable the retrieval of entity properties and entity composition from latent system representations, thus fostering traceability. Experimentally, across different domains, we show that LaM-SLidE performs favorably in terms of speed, accuracy, and generalizability. Code is available at https://github.com/ml-jku/LaM-SLidE .

cs.LG↗

arXiv2024

Boosting Distributional Copula Regression for Bivariate Right-Censored Time-to-Event Data

We propose a highly flexible distributional copula regression model for bivariate time-to-event data in the presence of right-censoring. The joint survival function of the response is constructed using parametric copulas, allowing for a separate specification of the dependence structure between the time-to-event outcome variables and their respective marginal survival distributions. The latter are specified using well-known parametric distributions such as the log-Normal, log-Logistic (proportional odds model), or Weibull (proportional hazards model) distributions. Hence, the marginal univariate event times can be specified as parametric (also known as Accelerated Failure Time, AFT) models. Embedding our model into the class of generalized additive models for location, scale and shape, possibly all distribution parameters of the joint survival function can depend on covariates. We develop a component-wise gradient-based boosting algorithm for estimation. This way, our approach is able to conduct data-driven variable selection. To the best of our knowledge, this is the first implementation of multivariate AFT models via distributional copula regression with automatic variable selection via statistical boosting. A special merit of our approach is that it works for high-dimensional (p>>n) settings. We illustrate the practical potential of our method on a high-dimensional application related to semi-competing risks responses in ovarian cancer. All of our methods are implemented in the open source statistical software R as add-on functions of the package gamboostLSS.

stat.ME↗

arXiv2024

Bio-xLSTM: Generative modeling, representation and in-context learning of biological and chemical sequences

Language models for biological and chemical sequences enable crucial applications such as drug discovery, protein engineering, and precision medicine. Currently, these language models are predominantly based on Transformer architectures. While Transformers have yielded impressive results, their quadratic runtime dependency on the sequence length complicates their use for long genomic sequences and in-context learning on proteins and chemical sequences. Recently, the recurrent xLSTM architecture has been shown to perform favorably compared to Transformers and modern state-space model (SSM) architectures in the natural language domain. Similar to SSMs, xLSTMs have a linear runtime dependency on the sequence length and allow for constant-memory decoding at inference time, which makes them prime candidates for modeling long-range dependencies in biological and chemical sequences. In this work, we tailor xLSTM towards these domains and propose a suite of architectural variants called Bio-xLSTM. Extensive experiments in three large domains, genomics, proteins, and chemistry, were performed to assess xLSTM's ability to model biological and chemical sequences. The results show that models based on Bio-xLSTM a) can serve as proficient generative models for DNA, protein, and chemical sequences, b) learn rich representations for those modalities, and c) can perform in-context learning for proteins and small molecules.

q-bio.BM↗

arXiv2024

Ranking evaluation metrics from a group-theoretic perspective

Confronted with the challenge of identifying the most suitable metric to validate the merits of newly proposed models, the decision-making process is anything but straightforward. Given that comparing rankings introduces its own set of formidable challenges and the likely absence of a universal metric applicable to all scenarios, the scenario does not get any better. Furthermore, metrics designed for specific contexts, such as for Recommender Systems, sometimes extend to other domains without a comprehensive grasp of their underlying mechanisms, resulting in unforeseen outcomes and potential misuses. Complicating matters further, distinct metrics may emphasize different aspects of rankings, frequently leading to seemingly contradictory comparisons of model results and hindering the trustworthiness of evaluations. We unveil these aspects in the domain of ranking evaluation metrics. Firstly, we show instances resulting in inconsistent evaluations, sources of potential mistrust in commonly used metrics; by quantifying the frequency of such disagreements, we prove that these are common in rankings. Afterward, we conceptualize rankings using the mathematical formalism of symmetric groups detaching from possible domains where the metrics have been created; through this approach, we can rigorously and formally establish essential mathematical properties for ranking evaluation metrics, essential for a deeper comprehension of the source of inconsistent evaluations. We conclude with a discussion, connecting our theoretical analysis to the practical applications, highlighting which properties are important in each domain where rankings are commonly evaluated. In conclusion, our analysis sheds light on ranking evaluation metrics, highlighting that inconsistent evaluations should not be seen as a source of mistrust but as the need to carefully choose how to evaluate our models in the future.

cs.IR↗

arXiv2024

Enhanced variable selection for boosting sparser and less complex models in distributional copula regression

Structured additive distributional copula regression allows to model the joint distribution of multivariate outcomes by relating all distribution parameters to covariates. Estimation via statistical boosting enables accounting for high-dimensional data and incorporating data-driven variable selection, both of which are useful given the complexity of the model class. However, as known from univariate (distributional) regression, the standard boosting algorithm tends to select too many variables with minor importance, particularly in settings with large sample sizes, leading to complex models with difficult interpretation. To counteract this behavior and to avoid selecting base-learners with only a negligible impact, we combined the ideas of probing, stability selection and a new deselection approach with statistical boosting for distributional copula regression. In a simulation study and an application to the joint modelling of weight and length of newborns, we found that all proposed methods enhance variable selection by reducing the number of false positives. However, only stability selection and the deselection approach yielded similar predictive performance to classical boosting. Finally, the deselection approach is better scalable to larger datasets and led to a competitive predictive performance, which we further illustrated in a genomic cohort study from the UK Biobank by modelling the joint genetic predisposition for two phenotypes.

stat.ME↗

arXiv2024

A Balanced Statistical Boosting Approach for GAMLSS via New Step Lengths

Component-wise gradient boosting algorithms are popular for their intrinsic variable selection and implicit regularization, which can be especially beneficial for very flexible model classes. When estimating generalized additive models for location, scale and shape (GAMLSS) by means of a component-wise gradient boosting algorithm, an important part of the estimation procedure is to determine the relative complexity of the submodels corresponding to the different distribution parameters. Existing methods either suffer from a computationally expensive tuning procedure or can be biased by structural differences in the negative gradients' sizes, which, if encountered, lead to imbalances between the different submodels. Shrunk optimal step lengths have been suggested to replace the typical small fixed step lengths for a non-cyclical boosting algorithm limited to a Gaussian response variable in order to address this issue. In this article, we propose a new adaptive step length approach that accounts for the relative size of the fitted base-learners to ensure a natural balance between the different submodels. The new balanced boosting approach thus represents a computationally efficient and easily generalizable alternative to shrunk optimal step lengths. We implemented the balanced non-cyclical boosting algorithm for a Gaussian, a negative binomial as well as a Weibull distributed response variable and demonstrate the competitive performance of the new adaptive step length approach by means of a simulation study, in the analysis of count data modeling the number of doctor's visits as well as for survival data in an oncological trial.

stat.ME↗

arXiv2024

VN-EGNN: E(3)-Equivariant Graph Neural Networks with Virtual Nodes Enhance Protein Binding Site Identification

Being able to identify regions within or around proteins, to which ligands can potentially bind, is an essential step to develop new drugs. Binding site identification methods can now profit from the availability of large amounts of 3D structures in protein structure databases or from AlphaFold predictions. Current binding site identification methods heavily rely on graph neural networks (GNNs), usually designed to output E(3)-equivariant predictions. Such methods turned out to be very beneficial for physics-related tasks like binding energy or motion trajectory prediction. However, the performance of GNNs at binding site identification is still limited potentially due to the lack of dedicated nodes that model hidden geometric entities, such as binding pockets. In this work, we extend E(n)-Equivariant Graph Neural Networks (EGNNs) by adding virtual nodes and applying an extended message passing scheme. The virtual nodes in these graphs are dedicated quantities to learn representations of binding sites, which leads to improved predictive performance. In our experiments, we show that our proposed method VN-EGNN sets a new state-of-the-art at locating binding site centers on COACH420, HOLO4K and PDBbind2020.

cs.LG↗

arXiv2024

GNN-VPA: A Variance-Preserving Aggregation Strategy for Graph Neural Networks

Graph neural networks (GNNs), and especially message-passing neural networks, excel in various domains such as physics, drug discovery, and molecular modeling. The expressivity of GNNs with respect to their ability to discriminate non-isomorphic graphs critically depends on the functions employed for message aggregation and graph-level readout. By applying signal propagation theory, we propose a variance-preserving aggregation function (VPA) that maintains expressivity, but yields improved forward and backward dynamics. Experiments demonstrate that VPA leads to increased predictive performance for popular GNN architectures as well as improved learning dynamics. Our results could pave the way towards normalizer-free or self-normalizing GNNs.

cs.LG↗

arXiv2024

Boosting Distributional Copula Regression for Bivariate Binary, Discrete and Mixed Responses

Motivated by challenges in the analysis of biomedical data and observational studies, we develop statistical boosting for the general class of bivariate distributional copula regression with arbitrary marginal distributions, which is suited to model binary, count, continuous or mixed outcomes. In our framework, the joint distribution of arbitrary, bivariate responses is modelled through a parametric copula. To arrive at a model for the entire conditional distribution, not only the marginal distribution parameters but also the copula parameters are related to covariates through additive predictors. We suggest efficient and scalable estimation by means of an adapted component-wise gradient boosting algorithm with statistical models as base-learners. A key benefit of boosting as opposed to classical likelihood or Bayesian estimation is the implicit data-driven variable selection mechanism as well as shrinkage without additional input or assumptions from the analyst. To the best of our knowledge, our implementation is the only one that combines a wide range of covariate effects, marginal distributions, copula functions, and implicit data-driven variable selection. We showcase the versatility of our approach on data from genetic epidemiology, healthcare utilization and childhood undernutrition. Our developments are implemented in the R package gamboostLSS, fostering transparent and reproducible research.

stat.ME↗

arXiv2023

Redundancy-aware unsupervised rankings for collections of gene sets

The biological roles of gene sets are used to group them into collections. These collections are often characterized by being high-dimensional, overlapping, and redundant families of sets, thus precluding a straightforward interpretation and study of their content. Bioinformatics looked for solutions to reduce their dimension or increase their intepretability. One possibility lies in aggregating overlapping gene sets to create larger pathways, but the modified biological pathways are hardly biologically justifiable. We propose to use importance scores to rank the pathways in the collections studying the context from a set covering perspective. The proposed Shapley values-based scores consider the distribution of the singletons and the size of the sets in the families; Furthermore, a trick allows us to circumvent the usual exponential complexity of Shapley values' computation. Finally, we address the challenge of including a redundancy awareness in the obtained rankings where, in our case, sets are redundant if they show prominent intersections. The rankings can be used to reduce the dimension of collections of gene sets, such that they show lower redundancy and still a high coverage of the genes. We further investigate the impact of our selection on Gene Sets Enrichment Analysis. The proposed method shows a practical utility in bioinformatics to increase the interpretability of the collections of gene sets and a step forward to include redundancy into Shapley values computations.

q-bio.QM↗

arXiv2022

Redundancy-aware unsupervised ranking based on game theory -- application to gene enrichment analysis

Gene set collections are a common ground to study the enrichment of genes for specific phenotypic traits. Gene set enrichment analysis aims to identify genes that are over-represented in gene sets collections and might be associated with a specific phenotypic trait. However, as this involves a massive number of hypothesis testing, it is often questionable whether a pre-processing step to reduce gene sets collections' sizes is helpful. Moreover, the often highly overlapping gene sets and the consequent low interpretability of gene sets' collections demand for a reduction of the included gene sets. Inspired by this bioinformatics context, we propose a method to rank sets within a family of sets based on the distribution of the singletons and their size. We obtain sets' importance scores by computing Shapley values without incurring into the usual exponential number of evaluations of the value function. Moreover, we address the challenge of including a redundancy awareness in the rankings obtained where, in our case, sets are redundant if they show prominent intersections. We finally evaluate our approach for gene sets collections; the rankings obtained show low redundancy and high coverage of the genes. The unsupervised nature of the proposed ranking does not allow for an evident increase in the number of significant gene sets for specific phenotypic traits when reducing the size of the collections. However, we believe that the rankings proposed are of use in bioinformatics to increase interpretability of the gene sets collections and a step forward to include redundancy into Shapley values computations.

q-bio.GN↗

arXiv2022

Boosting Multivariate Structured Additive Distributional Regression Models

We develop a model-based boosting approach for multivariate distributional regression within the framework of generalized additive models for location, scale, and shape. Our approach enables the simultaneous modeling of all distribution parameters of an arbitrary parametric distribution of a multivariate response conditional on explanatory variables, while being applicable to potentially high-dimensional data. Moreover, the boosting algorithm incorporates data-driven variable selection, taking various different types of effects into account. As a special merit of our approach, it allows for modelling the association between multiple continuous or discrete outcomes through the relevant covariates. After a detailed simulation study investigating estimation and prediction performance, we demonstrate the full flexibility of our approach in three diverse biomedical applications. The first is based on high-dimensional genomic cohort data from the UK Biobank, considering a bivariate binary response (chronic ischemic heart disease and high cholesterol). Here, we are able to identify genetic variants that are informative for the association between cholesterol and heart disease. The second application considers the demand for health care in Australia with the number of consultations and the number of prescribed medications as a bivariate count response. The third application analyses two dimensions of childhood undernutrition in Nigeria as a bivariate response and we find that the correlation between the two undernutrition scores is considerably different depending on the child's age and the region the child lives in.

stat.ME↗

arXiv2022

Unsupervised Features Ranking via Coalitional Game Theory for Categorical Data

Not all real-world data are labeled, and when labels are not available, it is often costly to obtain them. Moreover, as many algorithms suffer from the curse of dimensionality, reducing the features in the data to a smaller set is often of great utility. Unsupervised feature selection aims to reduce the number of features, often using feature importance scores to quantify the relevancy of single features to the task at hand. These scores can be based only on the distribution of variables and the quantification of their interactions. The previous literature, mainly investigating anomaly detection and clusters, fails to address the redundancy-elimination issue. We propose an evaluation of correlations among features to compute feature importance scores representing the contribution of single features in explaining the dataset's structure. Based on Coalitional Game Theory, our feature importance scores include a notion of redundancy awareness making them a tool to achieve redundancy-free feature selection. We show that the deriving features' selection outperforms competing methods in lowering the redundancy rate while maximizing the information contained in the data. We also introduce an approximated version of the algorithm to reduce the complexity of Shapley values' computations.

cs.LG↗

arXiv2022

Boosting Distributional Copula Regression

Capturing complex dependence structures between outcome variables (e.g., study endpoints) is of high relevance in contemporary biomedical data problems and medical research. Distributional copula regression provides a flexible tool to model the joint distribution of multiple outcome variables by disentangling the marginal response distributions and their dependence structure. In a regression setup each parameter of the copula model, i.e. the marginal distribution parameters and the copula dependence parameters, can be related to covariates via structured additive predictors. We propose a framework to fit distributional copula regression models via a model-based boosting algorithm. Model-based boosting is a modern estimation technique that incorporates useful features like an intrinsic variable selection mechanism, parameter shrinkage and the capability to fit regression models in high dimensional data setting, i.e. situations with more covariates than observations. Thus, model-based boosting does not only complement existing Bayesian and maximum-likelihood based estimation frameworks for this model class but rather enables unique intrinsic mechanisms that can be helpful in many applied problems. The performance of our boosting algorithm in the context of copula regression models with continuous margins is evaluated in simulation studies that cover low- and high-dimensional data settings and situations with and without dependence between the responses. Moreover, distributional copula boosting is used to jointly analyze and predict the length and the weight of newborns conditional on sonographic measurements of the fetus before delivery together with other clinical variables.

stat.ME↗