arXiv subjects

Thomas Kneib

Publications and source records attributed to Thomas Kneib.

At least 37 records · Page 2Linked to original sources

arXiv2025

Capturing heterogeneous time-variation in covariate effects in non-proportional hazard regression models

A central focus in survival analysis is examining how covariates influence survival time. These covariate effects are often found to be either time-varying, heterogeneous - such as being specific to patients, treatments, or subgroups - or exhibit both characteristics simultaneously. While the standard model, the Cox proportional hazards model, allows neither time-varying nor heterogeneous effects, several extensions to the Cox model as well as alternative modeling frameworks have been introduced. However, no unified framework for incorporating heterogeneously time-varying effects of covariates has been proposed yet. Such effects occur when a covariate influences survival not only in a heterogeneous and time-varying manner, but when the time-variation is also heterogeneous. We propose to model such effects by introducing heterogeneously time-varying coefficients to piecewise exponential additive mixed models. We deploy functional random effects, also known as factor smooths, to model such coefficients as the interaction effect of heterogeneity and time-variation. Our approach allows for non-linear time-effects due to being based on penalized splines and uses an efficient random effects basis to model the heterogeneity. Using a penalized basis prevents overfitting in case of absence of such effects. In addition, the penalization mostly solves the problem of choosing the number of intervals which is usually present in unregularized piecewise exponential approaches. We demonstrate the superiority of our approach in comparison to competitors by means of a simulation study. Finally, the practical application and relevance are outlined by presenting a brain tumor case study.

stat.ME↗

arXiv2025

TreeLearn: A deep learning method for segmenting individual trees from ground-based LiDAR forest point clouds

Laser-scanned point clouds of forests make it possible to extract valuable information for forest management. To consider single trees, a forest point cloud needs to be segmented into individual tree point clouds. Existing segmentation methods are usually based on hand-crafted algorithms, such as identifying trunks and growing trees from them, and face difficulties in dense forests with overlapping tree crowns. In this study, we propose TreeLearn, a deep learning-based approach for tree instance segmentation of forest point clouds. TreeLearn is trained on already segmented point clouds in a data-driven manner, making it less reliant on predefined features and algorithms. Furthermore, TreeLearn is implemented as a fully automatic pipeline and does not rely on extensive hyperparameter tuning, which makes it easy to use. Additionally, we introduce a new manually segmented benchmark forest dataset containing 156 full trees. The data is generated by mobile laser scanning and contributes to create a larger and more diverse data basis for model development and fine-grained instance segmentation evaluation. We trained TreeLearn on forest point clouds of 6665 trees, labeled using the Lidar360 software. An evaluation on the benchmark dataset shows that TreeLearn performs as well as the algorithm used to generate its training data. Furthermore, the performance can be vastly improved by fine-tuning the model using manually annotated datasets. We evaluate TreeLearn on our benchmark dataset and the Wytham Woods dataset, outperforming the recent SegmentAnyTree, ForAINet and TLS2Trees methods. The TreeLearn code and all datasets that were created in the course of this work are made publicly available.

cs.CV↗

arXiv2024

A Machine Learning and Explainable AI Framework Tailored for Unbalanced Experimental Catalyst Discovery

The successful application of machine learning (ML) in catalyst design relies on high-quality and diverse data to ensure effective generalization to novel compositions, thereby aiding in catalyst discovery. However, due to complex interactions, catalyst design has long relied on trial-and-error, a costly and labor-intensive process leading to scarce data that is heavily biased towards undesired, low-yield catalysts. Despite the rise of ML in this field, most efforts have not focused on dealing with the challenges presented by such experimental data. To address these challenges, we introduce a robust machine learning and explainable AI (XAI) framework to accurately classify the catalytic yield of various compositions and identify the contributions of individual components. This framework combines a series of ML practices designed to handle the scarcity and imbalance of catalyst data. We apply the framework to classify the yield of various catalyst compositions in oxidative methane coupling, and use it to evaluate the performance of a range of ML models: tree-based models, logistic regression, support vector machines, and neural networks. These experiments demonstrate that the methods used in our framework lead to a significant improvement in the performance of all but one of the evaluated models. Additionally, the decision-making process of each ML model is analyzed by identifying the most important features for predicting catalyst performance using XAI methods. Our analysis found that XAI methods, providing class-aware explanations, such as Layer-wise Relevance Propagation, identified key components that contribute specifically to high-yield catalysts. These findings align with chemical intuition and existing literature, reinforcing their validity. We believe that such insights can assist chemists in the development and identification of novel catalysts with superior performance.

physics.chem-ph↗

arXiv2024

Probabilistic Topic Modelling with Transformer Representations

Topic modelling was mostly dominated by Bayesian graphical models during the last decade. With the rise of transformers in Natural Language Processing, however, several successful models that rely on straightforward clustering approaches in transformer-based embedding spaces have emerged and consolidated the notion of topics as clusters of embedding vectors. We propose the Transformer-Representation Neural Topic Model (TNTM), which combines the benefits of topic representations in transformer-based embedding spaces and probabilistic modelling. Therefore, this approach unifies the powerful and versatile notion of topics based on transformer embeddings with fully probabilistic modelling, as in models such as Latent Dirichlet Allocation (LDA). We utilize the variational autoencoder (VAE) framework for improved inference speed and modelling flexibility. Experimental results show that our proposed model achieves results on par with various state-of-the-art approaches in terms of embedding coherence while maintaining almost perfect topic diversity. The corresponding source code is available at https://github.com/ArikReuter/TNTM.

cs.LG↗

arXiv2024

Neural Additive Models for Location Scale and Shape: A Framework for Interpretable Neural Regression Beyond the Mean

Deep neural networks (DNNs) have proven to be highly effective in a variety of tasks, making them the go-to method for problems requiring high-level predictive power. Despite this success, the inner workings of DNNs are often not transparent, making them difficult to interpret or understand. This lack of interpretability has led to increased research on inherently interpretable neural networks in recent years. Models such as Neural Additive Models (NAMs) achieve visual interpretability through the combination of classical statistical methods with DNNs. However, these approaches only concentrate on mean response predictions, leaving out other properties of the response distribution of the underlying data. We propose Neural Additive Models for Location Scale and Shape (NAMLSS), a modelling framework that combines the predictive power of classical deep learning models with the inherent advantages of distributional regression while maintaining the interpretability of additive models. The code is available at the following link: https://github.com/AnFreTh/NAMpy

stat.ML↗

arXiv2023

"Spatial Joint Models through Bayesian Structured Piece-wise Additive Joint Modelling for Longitudinal and Time-to-Event Data"

Joint models for longitudinal and time-to-event data have seen many developments in recent years. Though spatial joint models are still rare and the traditional proportional hazards formulation of the time-to-event part of the model is accompanied by computational challenges. We propose a joint model with a piece-wise exponential formulation of the hazard using the counting process representation of a hazard and structured additive predictors able to estimate (non-)linear, spatial and random effects. Its capabilities are assessed in a simulation study comparing our approach to an established one and highlighted by an example on physical functioning after cardiovascular events from the German Ageing Survey. The Structured Piecewise Additive Joint Model yielded good estimation performance, also and especially in spatial effects, while being double as fast as the chosen benchmark approach and performing stable in imbalanced data setting with few events.

stat.ME↗

arXiv2022

Multivariate Distributional Stochastic Frontier Models

The primary objective of Stochastic Frontier (SF) Analysis is the deconvolution of the estimated composed error terms into noise and inefficiency. Assuming a parametric production function (e.g. Cobb-Douglas, Translog, etc.), might lead to false inefficiency estimates. To overcome this limiting assumption, the production function can be modelled utilizing P-splines. Application of this powerful and flexible tool enables modelling of a wide range of production functions. Additionally, one can allow the parameters of the composed error distribution to depend on covariates in a functional form. The SF model can then be cast into the framework of a Generalized Additive Model for Location, Scale and Shape (GAMLSS). Furthermore, a decision-making unit (DMU) typically produces multiple outputs. It does this by operating several sub-DMUs, which each employ a production process to produce a single output. Therefore, the production processes of the sub-DMUs are typically not independent. Consequently, the inefficiencies may be expected to be dependent, too. In this paper, the Distributional Stochastic Frontier Model (DSFM) is introduced. The multivariate distribution of the composed error term is modeled using a copula. As a result, the presented model is a generalization of the model for seemingly unrelated stochastic frontier regressions by Lai and Huang (2013).

stat.ME↗

arXiv2022

Probabilistic Time Series Forecasts with Autoregressive Transformation Models

Probabilistic forecasting of time series is an important matter in many applications and research fields. In order to draw conclusions from a probabilistic forecast, we must ensure that the model class used to approximate the true forecasting distribution is expressive enough. Yet, characteristics of the model itself, such as its uncertainty or its feature-outcome relationship are not of lesser importance. This paper proposes Autoregressive Transformation Models (ATMs), a model class inspired by various research directions to unite expressive distributional forecasts using a semi-parametric distribution assumption with an interpretable model specification. We demonstrate the properties of ATMs both theoretically and through empirical evaluation on several simulated and real-world forecasting datasets.

cs.LG↗

arXiv2022

Twitmo: A Twitter Data Topic Modeling and Visualization Package for R

We present Twitmo, a package that provides a broad range of methods to collect, pre-process, analyze and visualize geo-tagged Twitter data. Twitmo enables the user to collect geo-tagged Tweets from Twitter and and provides a comprehensive and user-friendly toolbox to generate topic distributions from Latent Dirichlet Allocations (LDA), correlated topic models (CTM) and structural topic models (STM). Functions are included for pre-processing of text, model building and prediction. In addition, one of the innovations of the package is the automatic pooling of Tweets into longer pseudo-documents using hashtags and cosine similarities for better topic coherence. The package additionally comes with functionality to visualize collected data sets and fitted models in static as well as interactive ways and offers built-in support for model visualizations via LDAvis providing great convenience for researchers in this area. The Twitmo package is an innovative toolbox that can be used to analyze public discourse of various topics, political parties or persons of interest in space and time.

cs.IR↗

arXiv2022

Bayesian Conditional Transformation Models

Recent developments in statistical regression methodology shift away from pure mean regression towards distributional regression models. One important strand thereof is that of conditional transformation models (CTMs). CTMs infer the entire conditional distribution directly by applying a transformation function to the response conditionally on a set of covariates towards a simple log-concave reference distribution. Thereby, CTMs allow not only variance, kurtosis or skewness but the complete conditional distribution to depend on the explanatory variables. We propose a Bayesian notion of conditional transformation models (BCTMs) focusing on exactly observed continuous responses, but also incorporating extensions to randomly censored and discrete responses. Rather than relying on Bernstein polynomials that have been considered in likelihood-based CTMs, we implement a spline-based parametrization for monotonic effects that are supplemented with smoothness priors. Furthermore, we are able to benefit from the Bayesian paradigm via easily obtainable credible intervals and other quantities without relying on large sample approximations. A simulation study demonstrates the competitiveness of our approach against its likelihood-based counterpart but also Bayesian additive models of location, scale and shape and Bayesian quantile regression. Two applications illustrate the versatility of BCTMs in problems involving real world data, again including the comparison with various types of competitors.

stat.ME↗

arXiv2022

Bayesian Discrete Conditional Transformation Models

We propose a novel Bayesian model framework for discrete ordinal and count data based on conditional transformations of the responses. The conditional transformation function is estimated from the data in conjunction with an a priori chosen reference distribution. For count responses, the resulting transformation model is novel in the sense that it is a Bayesian fully parametric yet distribution-free approach that can additionally account for excess zeros with additive transformation function specifications. For ordinal categoric responses, our cumulative link transformation model allows the inclusion of linear and nonlinear covariate effects that can additionally be made category-specific, resulting in (non-)proportional odds or hazards models and more, depending on the choice of the reference distribution. Inference is conducted by a generic modular Markov chain Monte Carlo algorithm where multivariate Gaussian priors enforce specific properties such as smoothness on the functional effects. To illustrate the versatility of Bayesian discrete conditional transformation models, applications to counts of patent citations in the presence of excess zeros and on treating forest health categories in a discrete partial proportional odds model are presented.

stat.ME↗

arXiv2022

Distributional Gradient Boosting Machines

We present a unified probabilistic gradient boosting framework for regression tasks that models and predicts the entire conditional distribution of a univariate response variable as a function of covariates. Our likelihood-based approach allows us to either model all conditional moments of a parametric distribution, or to approximate the conditional cumulative distribution function via Normalizing Flows. As underlying computational backbones, our framework is based on XGBoost and LightGBM. Modelling and predicting the entire conditional distribution greatly enhances existing tree-based gradient boosting implementations, as it allows to create probabilistic forecasts from which prediction intervals and quantiles of interest can be derived. Empirical results show that our framework achieves state-of-the-art forecast accuracy.

stat.ML↗

arXiv2021

Using the Softplus Function to Construct Alternative Link Functions in Generalized Linear Models and Beyond

Response functions linking regression predictors to properties of the response distribution are fundamental components in many statistical models. However, the choice of these functions is typically based on the domain of the modeled quantities and is not further scrutinized. For example, the exponential response function is usually assumed for parameters restricted to be positive although it implies a multiplicative model which may not necessarily be desired. Consequently, applied researchers might easily face misleading results when relying on defaults without further investigation. As an alternative to the exponential response function, we propose the use of the softplus function to construct alternative link functions for parameters restricted to be positive. As a major advantage, we can construct differentiable link functions corresponding closely to the identity function for positive values of the regression predictor, which implies an quasi-additive model and thus allows for an additive interpretation of the estimated effects by practitioners. We demonstrate the applicability of the softplus response function using both simulations and real data. In four applications featuring count data regression and Bayesian distributional regression, we contrast our approach to the commonly used exponential response function.

stat.ME↗

arXiv2021

A multivariate Gaussian random field prior against spatial confounding

Spatial models are used in a variety research areas, such as environmental sciences, epidemiology, or physics. A common phenomenon in many spatial regression models is spatial confounding. This phenomenon takes place when spatially indexed covariates modeling the mean of the response are correlated with the spatial random effect. As a result, estimates for regression coefficients of the covariates can be severely biased and interpretation of these is no longer valid. Recent literature has shown that typical solutions for reducing spatial confounding can lead to misleading and counterintuitive results. In this paper, we develop a computationally efficient spatial model in a Bayesian framework integrating novel prior structure that reduces spatial confounding. Starting from the univariate case, we extend our prior structure to case of multiple spatially confounded covariates. In a simulation study, we show that our novel model flexibly detects and reduces spatial confounding in spatial datasets, and it performs better than typically used methods such as restricted spatial regression. These results are promising for any applied researcher who wishes to interpret covariate effects in spatial regression models. As a real data illustration, we study the effect of elevation and temperature on the mean of daily precipitation in Germany.

stat.ME↗

arXiv2021

Flexible Bayesian Modeling of Counts: Constructing Penalized Complexity Priors

Many of the data, particularly in medicine and disease mapping are count. Indeed, the under or overdispersion problem in count data distrusts the performance of the classical Poisson model. For taking into account this problem, in this paper, we introduce a new Bayesian structured additive regression model, called gamma count, with enough flexibility in modeling dispersion. Setting convenient prior distributions on the model parameters is a momentous issue in Bayesian statistics that characterize the nature of our uncertainty parameters. Relying on a recently proposed class of penalized complexity priors, motivated from a general set of construction principles, we derive the prior structure. The model can be formulated as a latent Gaussian model, and consequently, we can carry out the fast computation by using the integrated nested Laplace approximation method. We investigate the proposed methodology simulation study. Different expropriate prior distribution are examined to provide reasonable sensitivity analysis. To explain the applicability of the proposed model, we analyzed two real-world data sets related to the larynx mortality cancer in Germany and the handball champions league.

stat.ME↗

arXiv2021

Adaptive shrinkage of smooth functional effects towards a predefined functional subspace

In this paper, we propose a new horseshoe-type prior hierarchy for adaptively shrinking spline-based functional effects towards a predefined vector space of parametric functions. Instead of shrinking each spline coefficient towards zero, we use an adapted horseshoe prior to control the deviation from the predefined vector space. For this purpose, the modified horseshoe prior is set up with one scale parameter per spline and not one per coefficient. The presented prior allows for a large number of basis functions to capture all kinds of functional effects while the estimated functional effect is prevented from a highly oscillating overfit. We achieve this by integrating a smoothing penalty similar to the random walk prior commonly applied in Bayesian P-spline priors. In a simulation study, we demonstrate the properties of the new prior specification and compare it to other approaches from the literature. Furthermore, we showcase the applicability of the proposed method by estimating the energy consumption in Germany over the course of a day. For inference, we rely on Markov chain Monte Carlo simulations combining Gibbs sampling for the spline coefficients with slice sampling for all scale parameters in the model.

stat.ME↗

arXiv2020

Beyond unidimensional poverty analysis using distributional copula models for mixed ordered-continuous outcomes

Poverty is a multidimensional concept often comprising a monetary outcome and other welfare dimensions such as education, subjective well-being or health, that are measured on an ordinal scale. In applied research, multidimensional poverty is ubiquitously assessed by studying each poverty dimension independently in univariate regression models or by combining several poverty dimensions into a scalar index. This inhibits a thorough analysis of the potentially varying interdependence between the poverty dimensions. We propose a multivariate copula generalized additive model for location, scale and shape (copula GAMLSS or distributional copula model) to tackle this challenge. By relating the copula parameter to covariates, we specifically examine if certain factors determine the dependence between poverty dimensions. Furthermore, specifying the full conditional bivariate distribution, allows us to derive several features such as poverty risks and dependence measures coherently from one model for different individuals. We demonstrate the approach by studying two important poverty dimensions: income and education. Since the level of education is measured on an ordinal scale while income is continuous, we extend the bivariate copula GAMLSS to the case of mixed ordered-continuous outcomes. The new model is integrated into the GJRM package in R and applied to data from Indonesia. Particular emphasis is given to the spatial variation of the income-education dependence and groups of individuals at risk of being simultaneously poor in both education and income dimensions.

stat.ME↗

arXiv2020

Multivariate Conditional Transformation Models

Regression models describing the joint distribution of multivariate response variables conditional on covariate information have become an important aspect of contemporary regression analysis. However, a limitation of such models is that they often rely on rather simplistic assumptions, e.g. a constant dependency structure that is not allowed to vary with the covariates or the restriction to linear dependence between the responses only. We propose a general framework for multivariate conditional transformation models that overcomes these limitations and describes the entire distribution in a tractable and interpretable yet flexible way conditional on nonlinear effects of covariates. The framework can be embedded into likelihood-based inference, including results on asymptotic normality, and allows the dependence structure to vary with covariates. In addition, the framework scales well beyond bivariate response situations, which were the main focus of most earlier investigations. We illustrate the application of multivariate conditional transformation models in a trivariate analysis of childhood undernutrition and demonstrate empirically that our approach can be beneficial compared to existing benchmarks such that complex truly multivariate data-generating processes can be inferred from observations.

stat.ME↗