arXiv subjects

Nadja Klein

Publications and source records attributed to Nadja Klein.

At least 55 records · Page 3Linked to original sources

arXiv2024

Investigating Calibration and Corruption Robustness of Post-hoc Pruned Perception CNNs: An Image Classification Benchmark Study

Convolutional Neural Networks (CNNs) have achieved state-of-the-art performance in many computer vision tasks. However, high computational and storage demands hinder their deployment into resource-constrained environments, such as embedded devices. Model pruning helps to meet these restrictions by reducing the model size, while maintaining superior performance. Meanwhile, safety-critical applications pose more than just resource and performance constraints. In particular, predictions must not be overly confident, i.e., provide properly calibrated uncertainty estimations (proper uncertainty calibration), and CNNs must be robust against corruptions like naturally occurring input perturbations (natural corruption robustness). This work investigates the important trade-off between uncertainty calibration, natural corruption robustness, and performance for current state-of-research post-hoc CNN pruning techniques in the context of image classification tasks. Our study reveals that post-hoc pruning substantially improves the model's uncertainty calibration, performance, and natural corruption robustness, sparking hope for safe and robust embedded CNNs.Furthermore, uncertainty calibration and natural corruption robustness are not mutually exclusive targets under pruning, as evidenced by the improved safety aspects obtained by post-hoc unstructured pruning with increasing compression.

cs.CV↗

arXiv2024

Density regression via Dirichlet process mixtures of normal structured additive regression models

Within Bayesian nonparametrics, dependent Dirichlet process mixture models provide a highly flexible approach for conducting inference about the conditional density function. However, several formulations of this class make either rather restrictive modelling assumptions or involve intricate algorithms for posterior inference, thus preventing their widespread use. In response to these challenges, we present a flexible, versatile, and computationally tractable model for density regression based on a single-weights dependent Dirichlet process mixture of normal distributions model for univariate continuous responses. We assume an additive structure for the mean of each mixture component and incorporate the effects of continuous covariates through smooth nonlinear functions. The key components of our modelling approach are penalised B-splines and their bivariate tensor product extension. Our proposed method also seamlessly accommodates parametric effects of categorical covariates, linear effects of continuous covariates, interactions between categorical and/or continuous covariates, varying coefficient terms, and random effects, which is why we refer our model as a Dirichlet process mixture of normal structured additive regression models. A noteworthy feature of our method is its efficiency in posterior simulation through Gibbs sampling, as closed-form full conditional distributions for all model parameters are available. Results from a simulation study demonstrate that our approach successfully recovers true conditional densities and other regression functionals in various challenging scenarios. Applications to a toxicology, disease diagnosis, and agricultural study are provided and further underpin the broad applicability of our modelling framework. An R package, DDPstar, implementing the proposed method is publicly available at https://bitbucket.org/mxrodriguez/ddpstar.

stat.ME↗

arXiv2024

Cost-Sensitive Uncertainty-Based Failure Recognition for Object Detection

Object detectors in real-world applications often fail to detect objects due to varying factors such as weather conditions and noisy input. Therefore, a process that mitigates false detections is crucial for both safety and accuracy. While uncertainty-based thresholding shows promise, previous works demonstrate an imperfect correlation between uncertainty and detection errors. This hinders ideal thresholding, prompting us to further investigate the correlation and associated cost with different types of uncertainty. We therefore propose a cost-sensitive framework for object detection tailored to user-defined budgets on the two types of errors, missing and false detections. We derive minimum thresholding requirements to prevent performance degradation and define metrics to assess the applicability of uncertainty for failure recognition. Furthermore, we automate and optimize the thresholding process to maximize the failure recognition rate w.r.t. the specified budget. Evaluation on three autonomous driving datasets demonstrates that our approach significantly enhances safety, particularly in challenging scenarios. Leveraging localization aleatoric uncertainty and softmax-based entropy only, our method boosts the failure recognition rate by 36-60\% compared to conventional approaches. Code is available at https://mos-ks.github.io/publications.

cs.CV↗

arXiv2024

Informed Spectral Normalized Gaussian Processes for Trajectory Prediction

Prior parameter distributions provide an elegant way to represent prior expert and world knowledge for informed learning. Previous work has shown that using such informative priors to regularize probabilistic deep learning (DL) models increases their performance and data-efficiency. However, commonly used sampling-based approximations for probabilistic DL models can be computationally expensive, requiring multiple inference passes and longer training times. Promising alternatives are compute-efficient last layer kernel approximations like spectral normalized Gaussian processes (SNGPs). We propose a novel regularization-based continual learning method for SNGPs, which enables the use of informative priors that represent prior knowledge learned from previous tasks. Our proposal builds upon well-established methods and requires no rehearsal memory or parameter expansion. We apply our informed SNGP model to the trajectory prediction problem in autonomous driving by integrating prior drivability knowledge. On two public datasets, we investigate its performance under diminishing training data and across locations, and thereby demonstrate an increase in data-efficiency and robustness to location-transfers over non-informed and informed baselines.

cs.LG↗

arXiv2024

Regression Copulas for Multivariate Responses

We propose a novel distributional regression model for a multivariate response vector based on a copula process over the covariate space. It uses the implicit copula of a Gaussian multivariate regression, which we call a ``regression copula''. To allow for large covariate vectors their coefficients are regularized using a novel multivariate extension of the horseshoe prior. Bayesian inference and distributional predictions are evaluated using efficient variational inference methods, allowing application to large datasets. An advantage of the approach is that the marginal distributions of the response vector can be estimated separately and accurately, resulting in predictive distributions that are marginally-calibrated. Two substantive applications of the methodology highlight its efficacy in multivariate modeling. The first is the econometric modeling and prediction of half-hourly regional Australian electricity prices. Here, our approach produces more accurate distributional forecasts than leading benchmark methods. The second is the evaluation of multivariate posteriors in likelihood-free inference (LFI) of a model for tree species abundance data, extending a previous univariate regression copula LFI method. In both applications, we demonstrate that our new approach exhibits a desirable marginal calibration property.

stat.ME↗

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↗

arXiv2024

Boosting Causal Additive Models

We present a boosting-based method to learn additive Structural Equation Models (SEMs) from observational data, with a focus on the theoretical aspects of determining the causal order among variables. We introduce a family of score functions based on arbitrary regression techniques, for which we establish necessary conditions to consistently favor the true causal ordering. Our analysis reveals that boosting with early stopping meets these criteria and thus offers a consistent score function for causal orderings. To address the challenges posed by high-dimensional data sets, we adapt our approach through a component-wise gradient descent in the space of additive SEMs. Our simulation study underlines our theoretical results for lower dimensions and demonstrates that our high-dimensional adaptation is competitive with state-of-the-art methods. In addition, it exhibits robustness with respect to the choice of the hyperparameters making the procedure easy to tune.

stat.ML↗

arXiv2024

Bayesian Effect Selection in Additive Models with an Application to Time-to-Event Data

Accurately selecting and estimating smooth functional effects in additive models with potentially many functions is a challenging task. We introduce a novel Demmler-Reinsch basis expansion to model the functional effects that allows us to orthogonally decompose an effect into its linear and nonlinear parts. We show that our representation allows to consistently estimate both parts as opposed to commonly employed mixed model representations. Equipping the reparameterized regression coefficients with normal beta prime spike and slab priors allows us to determine whether a continuous covariate has a linear, a nonlinear or no effect at all. We provide new theoretical results for the prior and a compelling explanation for its superior Markov chain Monte Carlo mixing performance compared to the spike-and-slab group lasso. We establish an efficient posterior estimation scheme and illustrate our approach along effect selection on the hazard rate of a time-to-event response in the geoadditive Cox regression model in simulations and data on survival with leukemia.

stat.ME↗

arXiv2023

Modeling the Ratio of Correlated Biomarkers Using Copula Regression

Modeling the ratio of two dependent components as a function of covariates is a frequently pursued objective in observational research. Despite the high relevance of this topic in medical studies, where biomarker ratios are often used as surrogate endpoints for specific diseases, existing models are based on oversimplified assumptions, assuming e.g.\@ independence or strictly positive associations between the components. In this paper, we close this gap in the literature and propose a regression model where the marginal distributions of the two components are linked by Frank copula. A key feature of our model is that it allows for both positive and negative correlations between the components, with one of the model parameters being directly interpretable in terms of Kendall's rank correlation coefficient. We study our method theoretically, evaluate finite sample properties in a simulation study and demonstrate its efficacy in an application to diagnosis of Alzheimer's disease via ratios of amyloid-beta and total tau protein biomarkers.

stat.ME↗

arXiv2023

Scalable Estimation for Structured Additive Distributional Regression Through Variational Inference

Structured additive distributional regression models offer a versatile framework for estimating complete conditional distributions by relating all parameters of a parametric distribution to covariates. Although these models efficiently leverage information in vast and intricate data sets, they often result in highly-parameterized models with many unknowns. Standard estimation methods, like Bayesian approaches based on Markov chain Monte Carlo methods, face challenges in estimating these models due to their complexity and costliness. To overcome these issues, we suggest a fast and scalable alternative based on variational inference. Our approach combines a parsimonious parametric approximation for the posteriors of regression coefficients, with the exact conditional posterior for hyperparameters. For optimization, we use a stochastic gradient ascent method combined with an efficient strategy to reduce the variance of estimators. We provide theoretical properties and investigate global and local annealing to enhance robustness, particularly against data outliers. Our implementation is very general, allowing us to include various functional effects like penalized splines or complex tensor product interactions. In a simulation study, we demonstrate the efficacy of our approach in terms of accuracy and computation time. Lastly, we present two real examples illustrating the modeling of infectious COVID-19 outbreaks and outlier detection in brain activity.

stat.ME↗

arXiv2023

Actor Heterogeneity and Explained Variance in Network Models -- A Scalable Approach through Variational Approximations

The analysis of network data has gained considerable interest in recent years. This also includes the analysis of large, high-dimensional networks with hundreds and thousands of nodes. While exponential random graph models serve as workhorse for network data analyses, their applicability to very large networks is problematic via classical inference such as maximum likelihood or exact Bayesian estimation owing to scaling and instability issues. The latter trace from the fact that classical network statistics consider nodes as exchangeable, i.e., actors in the network are assumed to be homogeneous. This is often questionable. One way to circumvent the restrictive assumption is to include actor-specific random effects, which account for unobservable heterogeneity. However, this increases the number of unknowns considerably, thus making the model highly-parameterized. As a solution even for very large networks, we propose a scalable approach based on variational approximations, which not only leads to numerically stable estimation but is also applicable to high-dimensional directed as well as undirected networks. We furthermore demonstrate that including node-specific covariates can reduce node heterogeneity, which we facilitate through versatile prior formulations and a new measure that we call posterior explained variance. We illustrate our approach in three diverse examples, covering network data from the Italian Parliament, international arms trading, and Facebook; and conduct detailed simulation studies.

stat.ME↗

arXiv2023

Heat increases experienced racial segregation in the United States

Segregation on the basis of ethnic groups stands as a pervasive and persistent social challenge in many cities across the globe. Public spaces provide opportunities for diverse encounters but recent research suggests individuals adjust their time spent in such places to cope with extreme temperatures. We evaluate to what extent such adaptation affects racial segregation and thus shed light on a yet unexplored channel through which global warming might affect social welfare. We use large-scale foot traffic data for millions of places in 315 US cities between 2018 and 2020 to estimate an index of experienced isolation in daily visits between whites and other ethnic groups. We find that heat increases segregation. Results from panel regressions imply that a week with temperatures above 33°C in a city like Los Angeles induces an upward shift of visit isolation by 0.7 percentage points, which equals about 14% of the difference in the isolation index of Los Angeles to the more segregated city of Atlanta. The segregation-increasing effect is particularly strong for individuals living in lower-income areas and at places associated with leisure activities. Combining our estimates with climate model projections, we find that stringent mitigation policy can have significant co-benefits in terms of cushioning increases in racial segregation in the future.

econ.GN↗

arXiv2023

The Deep Promotion Time Cure Model

We propose a novel method for predicting time-to-event in the presence of cure fractions based on flexible survivals models integrated into a deep neural network framework. Our approach allows for non-linear relationships and high-dimensional interactions between covariates and survival and is suitable for large-scale applications. Furthermore, we allow the method to incorporate an identified predictor formed of an additive decomposition of interpretable linear and non-linear effects and add an orthogonalization layer to capture potential higher dimensional interactions. We demonstrate the usefulness and computational efficiency of our method via simulations and apply it to a large portfolio of US mortgage loans. Here, we find not only a better predictive performance of our framework but also a more realistic picture of covariate effects.

stat.ML↗

arXiv2023

Scalable Estimation for Structured Additive Distributional Regression

Recently, fitting probabilistic models have gained importance in many areas but estimation of such distributional models with very large data sets is a difficult task. In particular, the use of rather complex models can easily lead to memory-related efficiency problems that can make estimation infeasible even on high-performance computers. We therefore propose a novel backfitting algorithm, which is based on the ideas of stochastic gradient descent and can deal virtually with any amount of data on a conventional laptop. The algorithm performs automatic selection of variables and smoothing parameters, and its performance is in most cases superior or at least equivalent to other implementations for structured additive distributional regression, e.g., gradient boosting, while maintaining low computation time. Performance is evaluated using an extensive simulation study and an exceptionally challenging and unique example of lightning count prediction over Austria. A very large dataset with over 9 million observations and 80 covariates is used, so that a prediction model cannot be estimated with standard distributional regression methods but with our new approach.

stat.CO↗

arXiv2022

Accounting for Time Dependency in Meta-Analyses of Concordance Probability Estimates

Recent years have seen the development of many novel scoring tools for disease prognosis and prediction. To become accepted for use in clinical applications, these tools have to be validated on external data. In practice, validation is often hampered by logistical issues, resulting in multiple small-sized validation studies. It is therefore necessary to synthesize the results of these studies using techniques for meta-analysis. Here we consider strategies for meta-analyzing the concordance probability for time-to-event data ("C-index"), which has become a popular tool to evaluate the discriminatory power of prediction models with a right-censored outcome. We show that standard meta-analysis of the C-index may lead to biased results, as the magnitude of the concordance probability depends on the length of the time interval used for evaluation (defined e.g. by the follow-up time, which might differ considerably between studies). To address this issue, we propose a set of methods for random-effects meta-regression that incorporate time directly as covariate in the model equation. In addition to analyzing nonlinear time trends via fractional polynomial, spline, and exponential decay models, we provide recommendations on suitable transformations of the C-index before meta-regression. Our results suggest that the C-index is best meta-analyzed using fractional polynomial meta-regression with logit-transformed C-index values. Classical random-effects meta-analysis (not considering time as covariate) is demonstrated to be a suitable alternative when follow-up times are small. Our findings have implications for the reporting of C-index values in future studies, which should include information on the length of the time interval underlying the calculations.

stat.ME↗

arXiv2022

Anisotropic multidimensional smoothing using Bayesian tensor product P-splines

We introduce a highly efficient fully Bayesian approach for anisotropic multidimensional smoothing. The main challenge in this context is the Markov chain Monte Carlo update of the smoothing parameters as their full conditional posterior comprises a pseudo-determinant that appears to be intractable at first sight. As a consequence, most existing implementations are computationally feasible only for the estimation of two-dimensional tensor product smooths, which is, however, too restrictive for many applications. In this paper, we break this barrier and derive closed-form expressions for the log-pseudo-determinant and its first and second order partial derivatives. These expressions are valid for arbitrary dimension and very efficient to evaluate, which allows us to set up an efficient MCMC sampler with adaptive Metropolis-Hastings updates for the smoothing parameters. We investigate different priors for the smoothing parameters and discuss the efficient derivation of lower-dimensional effects such as one-dimensional main effects and two-dimensional interactions. We show that the suggested approach outperforms previous suggestions in the literature in terms of accuracy, scalability and computational cost and demonstrate its applicability by consideration of an illustrating temperature data example from spatio-temporal statistics.

stat.CO↗

arXiv2022

Informed Priors for Knowledge Integration in Trajectory Prediction

Informed machine learning methods allow the integration of prior knowledge into learning systems. This can increase accuracy and robustness or reduce data needs. However, existing methods often assume hard constraining knowledge, that does not require to trade-off prior knowledge with observations, but can be used to directly reduce the problem space. Other approaches use specific, architectural changes as representation of prior knowledge, limiting applicability. We propose an informed machine learning method, based on continual learning. This allows the integration of arbitrary, prior knowledge, potentially from multiple sources, and does not require specific architectures. Furthermore, our approach enables probabilistic and multi-modal predictions, that can improve predictive accuracy and robustness. We exemplify our approach by applying it to a state-of-the-art trajectory predictor for autonomous driving. This domain is especially dependent on informed learning approaches, as it is subject to an overwhelming large variety of possible environments and very rare events, while requiring robust and accurate predictions. We evaluate our model on a commonly used benchmark dataset, only using data already available in a conventional setup. We show that our method outperforms both non-informed and informed learning methods, that are often used in the literature. Furthermore, we are able to compete with a conventional baseline, even using half as many observation examples.

cs.LG↗

arXiv2022

Distributional Adaptive Soft Regression Trees

Random forests are an ensemble method relevant for many problems, such as regression or classification. They are popular due to their good predictive performance (compared to, e.g., decision trees) requiring only minimal tuning of hyperparameters. They are built via aggregation of multiple regression trees during training and are usually calculated recursively using hard splitting rules. Recently regression forests have been incorporated into the framework of distributional regression, a nowadays popular regression approach aiming at estimating complete conditional distributions rather than relating the mean of an output variable to input features only - as done classically. This article proposes a new type of a distributional regression tree using a multivariate soft split rule. One great advantage of the soft split is that smooth high-dimensional functions can be estimated with only one tree while the complexity of the function is controlled adaptive by information criteria. Moreover, the search for the optimal split variable is obsolete. We show by means of extensive simulation studies that the algorithm has excellent properties and outperforms various benchmark methods, especially in the presence of complex non-linear feature interactions. Finally, we illustrate the usefulness of our approach with an example on probabilistic forecasts for the Sun's activity.

stat.ME↗