Matthias Schmid

Saeed Maleki, John Crassidis, Yang Cheng et al.

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.

David Köhler, David Rügamer, Matthias Schmid

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.

Pardha Sai Krishna Ala, Ameya Salvi, Venkat Krovi et al.

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

Saeed Maleki, Yang Cheng, John Crassidis et al.

This work provides a theoretical framework for the pose estimation problem using total least squares for vector observations from landmark features. First, the optimization framework is formulated with observation vectors extracted from point cloud features. Then, error-covariance expressions are derived. The attitude and position solutions obtained via the derived optimization framework are proven to reach the bounds defined by the Cramér-Rao lower bound under the small-angle approximation of attitude errors. The measurement data for the simulation of this problem is provided through a series of vector observation scans, and 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. Here, previous derivations are expanded for the pose estimation problem to include more generic correlations in the errors than previous cases involving an isotropic noise assumption. The proposed solution is simulated in a Monte-Carlo framework to validate the error-covariance analysis.

Andreas Mayr, Benjamin Hofner, Elisabeth Waldmann et al.

Statistical boosting algorithms have triggered a lot of research during the last decade. They combine a powerful machine-learning approach with classical statistical modelling, offering various practical advantages like automated variable selection and implicit regularization of effect estimates. They are extremely flexible, as the underlying base-learners (regression functions defining the type of effect for the explanatory variables) can be combined with any kind of loss function (target function to be optimized, defining the type of regression setting). In this review article, we highlight the most recent methodological developments on statistical boosting regarding variable selection, functional regression and advanced time-to-event modelling. Additionally, we provide a short overview on relevant applications of statistical boosting in biomedicine.

Janek Thomas, Andreas Mayr, Bernd Bischl et al.

We present a new algorithm for boosting generalized additive models for location, scale and shape (GAMLSS) that allows to incorporate stability selection, an increasingly popular way to obtain stable sets of covariates while controlling the per-family error rate (PFER). The model is fitted repeatedly to subsampled data and variables with high selection frequencies are extracted. To apply stability selection to boosted GAMLSS, we develop a new "noncyclical" fitting algorithm that incorporates an additional selection step of the best-fitting distribution parameter in each iteration. This new algorithms has the additional advantage that optimizing the tuning parameters of boosting is reduced from a multi-dimensional to a one-dimensional problem with vastly decreased complexity. The performance of the novel algorithm is evaluated in an extensive simulation study. We apply this new algorithm to a study to estimate abundance of common eider in Massachusetts, USA, featuring excess zeros, overdispersion, non-linearity and spatio-temporal structures. Eider abundance is estimated via boosted GAMLSS, allowing both mean and overdispersion to be regressed on covariates. Stability selection is used to obtain a sparse set of stable predictors.

Elisabeth Waldmann, David Taylor-Robinson, Nadja Klein et al.

Joint Models for longitudinal and time-to-event data have gained a lot of attention in the last few years as they are a helpful technique to approach common a data structure in clinical studies where longitudinal outcomes are recorded alongside event times. Those two processes are often linked and the two outcomes should thus be modeled jointly in order to prevent the potential bias introduced by independent modelling. Commonly, joint models are estimated in likelihood based expectation maximization or Bayesian approaches using frameworks where variable selection is problematic and which do not immediately work for high-dimensional data. In this paper, we propose a boosting algorithm tackling these challenges by being able to simultaneously estimate predictors for joint models and automatically select the most influential variables even in high-dimensional data situations. We analyse the performance of the new algorithm in a simulation study and apply it to the Danish cystic fibrosis registry which collects longitudinal lung function data on patients with cystic fibrosis together with data regarding the onset of pulmonary infections. This is the first approach to combine state-of-the art algorithms from the field of machine-learning with the model class of joint models, providing a fully data-driven mechanism to select variables and predictor effects in a unified framework of boosting joint models.

Matthias Schmid, Marvin Wright, Andreas Ziegler

Random survival forests (RSF) are a powerful method for risk prediction of right-censored outcomes in biomedical research. RSF use the log-rank split criterion to form an ensemble of survival trees. The most common approach to evaluate the prediction accuracy of a RSF model is Harrell's concordance index for survival data ('C index'). Conceptually, this strategy implies that the split criterion in RSF is different from the evaluation criterion of interest. This discrepancy can be overcome by using Harrell's C for both node splitting and evaluation. We compare the difference between the two split criteria analytically and in simulation studies with respect to the preference of more unbalanced splits, termed end-cut preference (ECP). Specifically, we show that the log-rank statistic has a stronger ECP compared to the C index. In simulation studies and with the help of two medical data sets we demonstrate that the accuracy of RSF predictions, as measured by Harrell's C, can be improved if the log-rank statistic is replaced by the C index for node splitting. This is especially true in situations where the censoring rate or the fraction of informative continuous predictor variables is high. Conversely, log-rank splitting is preferable in noisy scenarios. Both C-based and log-rank splitting are implemented in the R~package ranger. We recommend Harrell's C as split criterion for use in smaller scale clinical studies and the log-rank split criterion for use in large-scale 'omics' studies.

Andreas Mayr, Matthias Schmid

The development of molecular signatures for the prediction of time-to-event outcomes is a methodologically challenging task in bioinformatics and biostatistics. Although there are numerous approaches for the derivation of marker combinations and their evaluation, the underlying methodology often suffers from the problem that different optimization criteria are mixed during the feature selection, estimation and evaluation steps. This might result in marker combinations that are only suboptimal regarding the evaluation criterion of interest. To address this issue, we propose a unified framework to derive and evaluate biomarker combinations. Our approach is based on the concordance index for time-to-event data, which is a non-parametric measure to quantify the discrimatory power of a prediction rule. Specifically, we propose a component-wise boosting algorithm that results in linear biomarker combinations that are optimal with respect to a smoothed version of the concordance index. We investigate the performance of our algorithm in a large-scale simulation study and in two molecular data sets for the prediction of survival in breast cancer patients. Our numerical results show that the new approach is not only methodologically sound but can also lead to a higher discriminatory power than traditional approaches for the derivation of gene signatures.