arXiv subjects

Matthias Schmid

Publications and source records attributed to Matthias Schmid.

At least 19 recordsLinked to original sources

arXiv2026

Estimating conditional Mann-Whitney effects using pseudo-observation-based regression

The Mann-Whitney effect is an effect measure for the order of two sample-specific outcome variables. It has the interpretation of a probability and also a connection to the area under the ROC curve. In the literature it has been considered for both ordinal and right-censored time-to-event outcomes. For both cases, the present paper introduces a distribution-free regression model that relates the Mann-Whitney effect to a linear combination of covariates. To fit the model, we develop a pseudo-observation-based procedure yielding consistent and asymptotically normal coefficient estimates. In addition, we propose bootstrap-based hypothesis tests to infer the effects of the covariates on the Mann-Whitney effect. A simulation study on the small-sample behavior of the proposed method demonstrates that the novel hypothesis tests keep up with the z-test of a Cox regression model. The new methods are used to analyze progression-free survival in breast cancer patients enrolled for the randomized phase III SUCCESS-A trial.

stat.ME↗

arXiv2025

Physics constrained learning of stochastic characteristics

Accurate state estimation requires careful consideration of uncertainty surrounding the process and measurement models; these characteristics are usually not well-known and need an experienced designer to select the covariance matrices. An error in the selection of covariance matrices could impact the accuracy of the estimation algorithm and may sometimes cause the filter to diverge. Identifying noise characteristics has long been a challenging problem due to uncertainty surrounding noise sources and difficulties in systematic noise modeling. Most existing approaches try identifying unknown covariance matrices through an optimization algorithm involving innovation sequences. In recent years, learning approaches have been utilized to determine the stochastic characteristics of process and measurement models. We present a learning-based methodology with different loss functions to identify noise characteristics and test these approaches' performance for real-time vehicle state estimation

stat.ML↗

arXiv2025

Characterizing gaussian mixture of motion modes for skid-steer vehicle state estimation

Skid-steered wheel mobile robots (SSWMRs) are characterized by the unique domination of the tire-terrain skidding for the robot to move. The lack of reliable friction models cascade into unreliable motion models, especially the reduced ordered variants used for state estimation and robot control. Ensemble modeling is an emerging research direction where the overall motion model is broken down into a family of local models to distribute the performance and resource requirement and provide a fast real-time prediction. To this end, a gaussian mixture model based modeling identification of model clusters is adopted and implemented within an interactive multiple model (IMM) based state estimation. The framework is adopted and implemented for angular velocity as the estimated state for a mid scaled skid-steered wheel mobile robot platform.

cs.RO↗

arXiv2025

A categorization of performance measures for estimated non-linear associations between an outcome and continuous predictors

In regression analysis, associations between continuous predictors and the outcome are often assumed to be linear. However, modeling the associations as non-linear can improve model fit. Many flexible modeling techniques, like (fractional) polynomials and spline-based approaches, are available. Such methods can be systematically compared in simulation studies, which require suitable performance measures to evaluate the accuracy of the estimated curves against the true data-generating functions. Although various measures have been proposed in the literature, no systematic overview exists so far. To fill this gap, we introduce a categorization of performance measures for evaluating estimated non-linear associations between an outcome and continuous predictors. This categorization includes many commonly used measures. The measures can not only be used in simulation studies, but also in application studies to compare different estimates to each other. We further illustrate and compare the behavior of different performance measures through some examples and a Shiny app.

stat.ME↗

arXiv2025

Flexible tree-structured regression for clustered data with an application to quality of life in older adults

Tree-structured models are a powerful alternative to parametric regression models if non-linear effects and interactions are present in the data. Yet, classical tree-structured models might not be appropriate if data comes in clusters of units, which requires taking the dependence of observations into account. This is, for example, the case in cross-national studies, as presented here, where country-specific effects should not be neglected. To address this issue, we present a flexible tree-structured approach that achieves a sparse modeling of unit-specific effects and identifies subgroups (based on individual-level covariates) that differ with regard to the outcome. The methodological advances were motivated by the analysis of quality of life in older adults using data from the survey of Health, Ageing and Retirement in Europe. Application of the proposed model yields promising results and illustrated the accessibility of the approach. A comparison to alternative methods with regard to variable selection and goodness-of-fit was performed in several simulation experiments.

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arXiv2024

Modeling the restricted mean survival time using pseudo-value random forests

The restricted mean survival time (RMST) has become a popular measure to summarize event times in longitudinal studies. Defined as the area under the survival function up to a time horizon $\tau$ > 0, the RMST can be interpreted as the life expectancy within the time interval [0, $\tau$]. In addition to its straightforward interpretation, the RMST also allows for the definition of valid estimands for the causal analysis of treatment contrasts in medical studies. In this work, we introduce a non-parametric approach to model the RMST conditional on a set of baseline variables (including, e.g., treatment variables and confounders). Our method is based on a direct modeling strategy for the RMST, using leave-one-out jackknife pseudo-values within a random forest regression framework. In this way, it can be employed to obtain precise estimates of both patient-specific RMST values and confounder-adjusted treatment contrasts. Since our method (termed "pseudo-value random forest", PVRF) is model-free, RMST estimates are not affected by restrictive assumptions like the proportional hazards assumption. Particularly, PVRF offers a high flexibility in detecting relevant covariate effects from higher-dimensional data, thereby expanding the range of existing pseudo-value modeling techniques for RMST estimation. We investigate the properties of our method using simulations and illustrate its use by an application to data from the SUCCESS-A breast cancer trial. Our numerical experiments demonstrate that PVRF yields accurate estimates of both patient-specific RMST values and RMST-based treatment contrasts.

stat.ME↗

arXiv2024

Online identification of skidding modes with interactive multiple model estimation

Skid-steered wheel mobile robots (SSWMRs) operate in a variety of outdoor environments exhibiting motion behaviors dominated by the effects of complex wheel-ground interactions. Characterizing these interactions is crucial both from the immediate robot autonomy perspective (for motion prediction and control) as well as a long-term predictive maintenance and diagnostics perspective. An ideal solution entails capturing precise state measurements for decisions and controls, which is considerably difficult, especially in increasingly unstructured outdoor regimes of operations for these robots. In this milieu, a framework to identify pre-determined discrete modes of operation can considerably simplify the motion model identification process. To this end, we propose an interactive multiple model (IMM) based filtering framework to probabilistically identify predefined robot operation modes that could arise due to traversal in different terrains or loss of wheel traction.

cs.RO↗

arXiv2024

Achieving interpretable machine learning by functional decomposition of black-box models into explainable predictor effects

Machine learning (ML) has seen significant growth in both popularity and importance. The high prediction accuracy of ML models is often achieved through complex black-box architectures that are difficult to interpret. This interpretability problem has been hindering the use of ML in fields like medicine, ecology and insurance, where an understanding of the inner workings of the model is paramount to ensure user acceptance and fairness. The need for interpretable ML models has boosted research in the field of interpretable machine learning (IML). Here we propose a novel approach for the functional decomposition of black-box predictions, which is considered a core concept of IML. The idea of our method is to replace the prediction function by a surrogate model consisting of simpler subfunctions. Similar to additive regression models, these functions provide insights into the direction and strength of the main feature contributions and their interactions. Our method is based on a novel concept termed stacked orthogonality, which ensures that the main effects capture as much functional behavior as possible and do not contain information explained by higher-order interactions. Unlike earlier functional IML approaches, it is neither affected by extrapolation nor by hidden feature interactions. To compute the subfunctions, we propose an algorithm based on neural additive modeling and an efficient post-hoc orthogonalization procedure.

stat.ML↗

arXiv2024

Control Informed Design of the IAC Autonomous Racecar for Operation at the Dynamic Envelope

This article introduces the hardware-software co-design of the control system for an autonomy-enabled formula-style high-speed racecar that will be utilized as the deployment platform for high-level autonomy in the first ever head-to-head driverless race called the Indy Autonomous Challenge. The embedded control system needs to facilitate autonomous functionality, including perception, localization, and by-wire actuation, at high speeds and dynamic limits of the vehicle. Rapid maneuvering during the race, however, excites transient dynamics of the vehicle and the actuators. Compared to current autonomous driving focused on highway cruising and urban traffic, transient vehicle control imposes new challenges to the algorithm and system design. The presented work introduces the cascaded control structure employed by the IAC prototype to fully exploit the time scale separation between different control tasks. It is demonstrated by example way how the model-based control strategies and simulation are utilized to inform the decisions in the actuation, computation, perception, and software pipeline design decisions for the first-of-its-kind IAC racecar.

eess.SY↗

arXiv2024

Confidence intervals for tree-structured varying coefficients

The tree-structured varying coefficient model (TSVC) is a flexible regression approach that allows the effects of covariates to vary with the values of the effect modifiers. Relevant effect modifiers are identified inherently using recursive partitioning techniques. To quantify uncertainty in TSVC models, we propose a procedure to construct confidence intervals of the estimated partition-specific coefficients. This task constitutes a selective inference problem as the coefficients of a TSVC model result from data-driven model building. To account for this issue, we introduce a parametric bootstrap approach, which is tailored to the complex structure of TSVC. Finite sample properties, particularly coverage proportions, of the proposed confidence intervals are evaluated in a simulation study. For illustration, we consider applications to data from COVID-19 patients and from patients suffering from acute odontogenic infection. The proposed approach may also be adapted for constructing confidence intervals for other tree-based methods.

stat.ME↗

arXiv2024

An Overview of Automated Vehicle Longitudinal Platoon Formation Strategies

Automated vehicle (AV) platooning has the potential to improve the safety, operational, and energy efficiency of surface transportation systems by limiting or eliminating human involvement in the driving tasks. The theoretical validity of the AV platooning strategies has been established and practical applications are being tested under real-world conditions. The emergence of sensors, communication, and control strategies has resulted in rapid and constant evolution of AV platooning strategies. In this paper, we review the state-of-the-art knowledge in AV longitudinal platoon formation using a five-component platooning framework, which includes vehicle model, information-receiving process, information flow topology, spacing policy, and controller and discuss the advantages and limitations of the components. Based on the discussion about existing strategies and associated limitations, potential future research directions are presented.

eess.SY↗

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.

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arXiv2023

Detection of nonlinearity, discontinuity and interactions in generalized regression models

In generalized regression models the effect of continuous covariates is commonly assumed to be linear. This assumption, however, may be too restrictive in applications and may lead to biased effect estimates and decreased predictive ability. While a multitude of alternatives for the flexible modeling of continuous covariates have been proposed, methods that provide guidance for choosing a suitable functional form are still limited. To address this issue, we propose a detection algorithm that evaluates several approaches for modeling continuous covariates and guides practitioners to choose the most appropriate alternative. The algorithm utilizes a unified framework for tree-structured modeling which makes the results easily interpretable. We assessed the performance of the algorithm by conducting a simulation study. To illustrate the proposed algorithm, we analyzed data of patients suffering from chronic kidney disease.

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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.

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arXiv2022

Optimal Pose Estimation and Covariance Analysis with Simultaneous Localization and Mapping Applications

This work provides a theoretical analysis for optimally solving the pose estimation problem using total least squares for vector observations from landmark features, which is central to applications involving simultaneous localization and mapping. First, the optimization process is formulated with observation vectors extracted from point-cloud features. Then, error-covariance expressions are derived. The attitude and position estimates obtained via the derived optimization process are proven to reach the bounds defined by the Cramér-Rao lower bound under the small-angle approximation of attitude errors. A fully populated observation noise-covariance matrix is assumed as the weight in the cost function to cover the most general case of the sensor uncertainty. This includes more generic correlations in the errors than previous cases involving an isotropic noise assumption. The proposed solution is verified using Monte Carlo simulations and an experiment with an actual LIDAR to validate the error-covariance analysis.

cs.RO↗

arXiv2022

Error-Covariance Analysis of Monocular Pose Estimation Using Total Least Squares

This study presents a theoretical structure for the monocular pose estimation problem using the total least squares. The unit-vector line-of-sight observations of the features are extracted from the monocular camera images. First, the optimization framework is formulated for the pose estimation problem with observation vectors extracted from unit vectors from the camera center-of-projection, pointing towards the image features. The attitude and position solutions obtained via the derived optimization framework are proven to reach the Cramér-Rao lower bound under the small angle approximation of the attitude errors. Specifically, The Fisher Information Matrix and the Cramér-Rao bounds are evaluated and compared to the analytical derivations of the error-covariance expressions to rigorously prove the optimality of the estimates. The sensor data for the measurement model is provided through a series of vector observations, and two fully populated noise-covariance matrices are assumed for the body and reference observation data. The inverse of the former matrices appear in terms of a series of weight matrices in the cost function. The proposed solution is simulated in a Monte-Carlo framework with 10,000 samples to validate the error-covariance analysis.

cs.CV↗

arXiv2022

Model-based recursive partitioning for discrete event times

Model-based recursive partitioning (MOB) is a semi-parametric statistical approach allowing the identification of subgroups that can be combined with a broad range of outcome measures including continuous time-to-event outcomes. When time is measured on a discrete scale, methods and models need to account for this discreetness as otherwise subgroups might be spurious and effects biased. The test underlying the splitting criterion of MOB, the M-fluctuation test, assumes independent observations. However, for fitting discrete time-to-event models the data matrix has to be modified resulting in an augmented data matrix violating the independence assumption. We propose MOB for discrete Survival data (MOB-dS) which controls the type I error rate of the test used for data splitting and therefore the rate of identifying subgroups although none is present. MOB-ds uses a permutation approach accounting for dependencies in the augmented time-to-event data to obtain the distribution under the null hypothesis of no subgroups being present. Through simulations we investigate the type I error rate of the new MOB-dS and the standard MOB for different patterns of survival curves and event rates. We find that the type I error rates of the test is well controlled for MOB-dS, but observe some considerable inflations of the error rate for MOB. To illustrate the proposed methods, MOB-dS is applied to data on unemployment duration.

stat.ME↗

arXiv2022

A Failure Identification and Recovery Framework for a Planar Reconfigurable Cable Driven Parallel Robot

In cable driven parallel robots (CDPRs), a single cable malfunction usually induces complete failure of the entire robot. However, the lost static workspace (due to failure) can often be recovered through reconfiguration of the cable attachment points on the frame. This capability is introduced by adding kinematic redundancies to the robot in the form of moving linear sliders that are manipulated in a real-time redundancy resolution controller. The presented work combines this controller with an online failure detection framework to develop a complete fault tolerant control scheme for automatic task recovery. This solution provides robustness by combining pose estimation of the end-effector with the failure detection through the application of an Interactive Multiple Model (IMM) algorithm relying only on end-effector information. The failure and pose estimation scheme is then tied into the redundancy resolution approach to produce a seamless automatic task (trajectory) recovery approach for cable failures.

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