arXiv subjects

Peter Filzmoser

Publications and source records attributed to Peter Filzmoser.

At least 19 recordsLinked to original sources

arXiv2026

Explainable Outlier Detection for Multivariate Functional Data

This work addresses the challenges of robust covariance estimation and interpretable outlier detection for multivariate functional data with separable covariance structure. We develop a method that simultaneously improves robustness and interpretability in this context by establishing a connection between stochastic processes with separable covariance structures and the corresponding matrix-variate distribution of their basis representations. Leveraging this connection, we employ the recently developed matrix-variate counterpart of the Minimum Covariance Determinant estimator (MMCD) in conjunction with a truncated multivariate functional Mahalanobis semi-distance to robustly estimate mean and covariance for multivariate functional data. For interpretable outlier detection, we generalize multivariate outlier explanations based on Shapley values to decompose overall multivariate functional outlyingness into time-coordinate-specific contributions. Importantly, we reduce the otherwise exponential computational complexity (relative to the number of components) to linear complexity, while retaining the key properties of the Shapley value. This integrated framework combines robust Mahalanobis distances, MMCD estimators, and Shapley value-based outlyingness decomposition to provide a robust and interpretable approach for analyzing multivariate functional data with separable covariance structures. The effectiveness of this approach is demonstrated through both theoretical analysis and practical applications, including simulations and real-world examples.

stat.ME↗

arXiv2025

A New View to Mission Profiles

Mission profiles cover the conditions that a component, e.g., an electronic component of a vehicle, is exposed to during its lifecycle. Currently, these profiles typically provide descriptive summaries, such as histograms, of single stress parameters like temperature, humidity, or voltage. This is highly aggregated information. New requirements for electric and autonomous driving cars require much more information how applications are used. In this work, we present a new approach for mission profiles which contains detailed usage information. We suggest a functional description over time, which allows joint modeling of various characteristics such as temperature, humidity, and voltage. The entire lifecycle history is covered, and the method can control the temporal resolution, i.e., the level of details of a mission profile. As a result, more accurate mission profiles can be generated, user quantiles can be derived, and usage outliers can be identified. This model establishes a framework to exchange usage data between suppliers, original equipment manufacturers (OEMs), and end customers while data integrity and protection are assured.

stat.AP↗

arXiv2025

Outlier-Robust Multi-Group Gaussian Mixture Modeling with Flexible Group Reassignment

Do expert-defined or diagnostically-labeled data groups align with clusters inferred through statistical modeling? If not, where do discrepancies between predefined labels and model-based groupings occur and why? In this work, we introduce the multi-group Gaussian mixture model (MG-GMM), the first model developed to investigate these questions. It incorporates prior group information while allowing flexibility to reassign observations to alternative groups based on data-driven evidence. We achieve this by modeling the observations of each group as arising not from a single distribution, but from a Gaussian mixture comprising all group-specific distributions. Moreover, our model offers robustness against cellwise outliers that may obscure or distort the underlying group structure. We propose a novel penalized likelihood approach, called cellMG-GMM, to jointly estimate mixture probabilities, location and scale parameters of the MG-GMM, and detect outliers through a penalty term on the number of flagged cellwise outliers in the objective function. We show that our estimator has good breakdown properties in presence of cellwise outliers. We develop a computationally-efficient EM-based algorithm for cellMG-GMM, and demonstrate its strong performance in identifying and diagnosing observations at the intersection of multiple groups through simulations and diverse applications in medicine and oenology.

stat.ME↗

arXiv2024

Robust functional PCA for relative data

This paper introduces a robust approach to functional principal component analysis (FPCA) for relative data, particularly density functions. While recent papers have studied density data within the Bayes space framework, there has been limited focus on developing robust methods to effectively handle anomalous observations and large noise. To address this, we extend the Mahalanobis distance concept to Bayes spaces, proposing its regularized version that accounts for the constraints inherent in density data. Based on this extension, we introduce a new method, robust density principal component analysis (RDPCA), for more accurate estimation of functional principal components in the presence of outliers. The method's performance is validated through simulations and real-world applications, showing its ability to improve covariance estimation and principal component analysis compared to traditional methods.

stat.ME↗

arXiv2024

spar: Sparse Projected Averaged Regression in R

Package spar for R builds ensembles of predictive generalized linear models with high-dimensional predictors. It employs an algorithm utilizing variable screening and random projection tools to efficiently handle the computational challenges associated with large sets of predictors. The package is designed with a strong focus on extensibility. Screening and random projection techniques are implemented as S3 classes with user-friendly constructor functions, enabling users to easily integrate and develop new procedures. This design enhances the package's adaptability and makes it a powerful tool for a variety of high-dimensional applications.

stat.CO↗

arXiv2024

Enhancing Forecasts Using Real-Time Data Flow and Hierarchical Forecast Reconciliation, with Applications to the Energy Sector

A novel framework for hierarchical forecast updating is presented, addressing a critical gap in the forecasting literature. By assuming a temporal hierarchy structure, the innovative approach extends hierarchical forecast reconciliation to effectively manage the challenge posed by partially observed data. This crucial extension allows, in conjunction with real-time data, to obtain updated and coherent forecasts across the entire temporal hierarchy, thereby enhancing decision-making accuracy. The framework involves updating base models in response to new data, which produces revised base forecasts. A subsequent pruning step integrates the newly available data, allowing for the application of any forecast reconciliation method to obtain fully updated reconciled forecasts. Additionally, the framework not only ensures coherence among forecasts but also improves overall accuracy throughout the hierarchy. Its inherent flexibility and interpretability enable users to perform hierarchical forecast updating concisely. The methodology is extensively demonstrated in a simulation study with various settings and comparing different data-generating processes, hierarchies, and reconciliation methods. Practical applicability is illustrated through two case studies in the energy sector, energy generation and solar power data, where the framework yields superior results compared to base models that do not incorporate new data, leading to more precise decision-making outcomes.

stat.ME↗

arXiv2024

Data-Driven Random Projection and Screening for High-Dimensional Generalized Linear Models

We address the challenge of correlated predictors in high-dimensional GLMs, where regression coefficients range from sparse to dense, by proposing a data-driven random projection method. This is particularly relevant for applications where the number of predictors is (much) larger than the number of observations and the underlying structure -- whether sparse or dense -- is unknown. We achieve this by using ridge-type estimates for variable screening and random projection to incorporate information about the response-predictor relationship when performing dimensionality reduction. We demonstrate that a ridge estimator with a small penalty is effective for random projection and screening, but the penalty value must be carefully selected. Unlike in linear regression, where penalties approaching zero work well, this approach leads to overfitting in non-Gaussian families. Instead, we recommend a data-driven method for penalty selection. This data-driven random projection improves prediction performance over conventional random projections, even surpassing benchmarks like elastic net. Furthermore, an ensemble of multiple such random projections combined with probabilistic variable screening delivers the best aggregated results in prediction and variable ranking across varying sparsity levels in simulations at a rather low computational cost. Finally, three applications with count and binary responses demonstrate the method's advantages in interpretability and prediction accuracy.

stat.ME↗

arXiv2024

Cellwise robust and sparse principal component analysis

A first proposal of a sparse and cellwise robust PCA method is presented. Robustness to single outlying cells in the data matrix is achieved by substituting the squared loss function for the approximation error by a robust version. The integration of a sparsity-inducing $L_1$ or elastic net penalty offers additional modeling flexibility. For the resulting challenging optimization problem, an algorithm based on Riemannian stochastic gradient descent is developed, with the advantage of being scalable to high-dimensional data, both in terms of many variables as well as observations. The resulting method is called SCRAMBLE (Sparse Cellwise Robust Algorithm for Manifold-based Learning and Estimation). Simulations reveal the superiority of this approach in comparison to established methods, both in the casewise and cellwise robustness paradigms. Two applications from the field of tribology underline the advantages of a cellwise robust and sparse PCA method.

stat.CO↗

arXiv2024

Sparse outlier-robust PCA for multi-source data

Sparse and outlier-robust Principal Component Analysis (PCA) has been a very active field of research recently. Yet, most existing methods apply PCA to a single dataset whereas multi-source data-i.e. multiple related datasets requiring joint analysis-arise across many scientific areas. We introduce a novel PCA methodology that simultaneously (i) selects important features, (ii) allows for the detection of global sparse patterns across multiple data sources as well as local source-specific patterns, and (iii) is resistant to outliers. To this end, we develop a regularization problem with a penalty that accommodates global-local structured sparsity patterns, and where the ssMRCD estimator is used as plug-in to permit joint outlier-robust analysis across multiple data sources. We provide an efficient implementation of our proposal via the Alternating Direction Method of Multiplier and illustrate its practical advantages in simulation and in applications.

stat.ME↗

arXiv2024

Rediscovering Bottom-Up: Effective Forecasting in Temporal Hierarchies

Forecast reconciliation has become a prominent topic in recent forecasting literature, with a primary distinction made between cross-sectional and temporal hierarchies. This work focuses on temporal hierarchies, such as aggregating monthly time series data to annual data. We explore the impact of various forecast reconciliation methods on temporally aggregated ARIMA models, thereby bridging the fields of hierarchical forecast reconciliation and temporal aggregation both theoretically and experimentally. Our paper is the first to theoretically examine the effects of temporal hierarchical forecast reconciliation, demonstrating that the optimal method aligns with a bottom-up aggregation approach. To assess the practical implications and performance of the reconciled forecasts, we conduct a series of simulation studies, confirming that the findings extend to more complex models. This result helps explain the strong performance of the bottom-up approach observed in many prior studies. Finally, we apply our methods to real data examples, where we observe similar results.

stat.ME↗

arXiv2024

Robust covariance estimation and explainable outlier detection for matrix-valued data

This work introduces the Matrix Minimum Covariance Determinant (MMCD) method, a novel robust location and covariance estimation procedure designed for data that are naturally represented in the form of a matrix. Unlike standard robust multivariate estimators, which would only be applicable after a vectorization of the matrix-variate samples leading to high-dimensional datasets, the MMCD estimators account for the matrix-variate data structure and consistently estimate the mean matrix, as well as the rowwise and columnwise covariance matrices in the class of matrix-variate elliptical distributions. Additionally, we show that the MMCD estimators are matrix affine equivariant and achieve a higher breakdown point than the maximal achievable one by any multivariate, affine equivariant location/covariance estimator when applied to the vectorized data. An efficient algorithm with convergence guarantees is proposed and implemented. As a result, robust Mahalanobis distances based on MMCD estimators offer a reliable tool for outlier detection. Additionally, we extend the concept of Shapley values for outlier explanation to the matrix-variate setting, enabling the decomposition of the squared Mahalanobis distances into contributions of the rows, columns, or individual cells of matrix-valued observations. Notably, both the theoretical guarantees and simulations show that the MMCD estimators outperform robust estimators based on vectorized observations, offering better computational efficiency and improved robustness. Moreover, real-world data examples demonstrate the practical relevance of the MMCD estimators and the resulting robust Shapley values.

stat.ME↗

arXiv2023

Sparse Data-Driven Random Projection in Regression for High-Dimensional Data

We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic variable screening with random projection tools as a viable approach. More specifically, we introduce a new data-driven random projection tailored to the problem at hand and derive a theoretical bound on the gain in expected prediction error over conventional random projections. The variables to enter the projection are screened by accounting for predictor correlation. To reduce the dependence on fine-tuning choices, we aggregate over an ensemble of linear models. A thresholding parameter is introduced to obtain a higher degree of sparsity. Both this parameter and the number of models in the ensemble can be chosen by cross-validation. In extensive simulations, we compare the proposed method with other random projection tools and with classical sparse and dense methods and show that it is competitive in terms of prediction across a variety of scenarios with different sparsity and predictor covariance settings. We also show that the method with cross-validation is able to rank the variables satisfactorily. Finally, we showcase the method on two real data applications.

stat.ME↗

arXiv2023

Efficient Computation of Sparse and Robust Maximum Association Estimators

Robust statistical estimators offer resilience against outliers but are often computationally challenging, particularly in high-dimensional sparse settings. Modern optimization techniques are utilized for robust sparse association estimators without imposing constraints on the covariance structure. The approach splits the problem into a robust estimation phase, followed by optimization of a decoupled, biconvex problem to derive the sparse canonical vectors. An augmented Lagrangian algorithm, combined with a modified adaptive gradient descent method, induces sparsity through simultaneous updates of both canonical vectors. Results demonstrate improved precision over existing methods, with high-dimensional empirical examples illustrating the effectiveness of this approach. The methodology can also be extended to other robust sparse estimators.

stat.CO↗

arXiv2023

Identifying Important Pairwise Logratios in Compositional Data with Sparse Principal Component Analysis

Compositional data are characterized by the fact that their elemental information is contained in simple pairwise logratios of the parts that constitute the composition. While pairwise logratios are typically easy to interpret, the number of possible pairs to consider quickly becomes (too) large even for medium-sized compositions, which might hinder interpretability in further multivariate analyses. Sparse methods can therefore be useful to identify few, important pairwise logratios (respectively parts contained in them) from the total candidate set. To this end, we propose a procedure based on the construction of all possible pairwise logratios and employ sparse principal component analysis to identify important pairwise logratios. The performance of the procedure is demonstrated both with simulated and real-world data. In our empirical analyses, we propose three visual tools showing (i) the balance between sparsity and explained variability, (ii) stability of the pairwise logratios, and (iii) importance of the original compositional parts to aid practitioners with their model interpretation.

stat.ME↗

arXiv2023

Data Type Agnostic Visual Sensitivity Analysis

Modern science and industry rely on computational models for simulation, prediction, and data analysis. Spatial blind source separation (SBSS) is a model used to analyze spatial data. Designed explicitly for spatial data analysis, it is superior to popular non-spatial methods, like PCA. However, a challenge to its practical use is setting two complex tuning parameters, which requires parameter space analysis. In this paper, we focus on sensitivity analysis (SA). SBSS parameters and outputs are spatial data, which makes SA difficult as few SA approaches in the literature assume such complex data on both sides of the model. Based on the requirements in our design study with statistics experts, we developed a visual analytics prototype for data type agnostic visual sensitivity analysis that fits SBSS and other contexts. The main advantage of our approach is that it requires only dissimilarity measures for parameter settings and outputs. We evaluated the prototype heuristically with visualization experts and through interviews with two SBSS experts. In addition, we show the transferability of our approach by applying it to microclimate simulations. Study participants could confirm suspected and known parameter-output relations, find surprising associations, and identify parameter subspaces to examine in the future. During our design study and evaluation, we identified challenging future research opportunities.

cs.HC↗

arXiv2023

Minimum regularized covariance trace estimator and outlier detection for functional data

In this paper, we propose the Minimum Regularized Covariance Trace (MRCT) estimator, a novel method for robust covariance estimation and functional outlier detection. The MRCT estimator employs a subset-based approach that prioritizes subsets exhibiting greater centrality based on the generalization of the Mahalanobis distance, resulting in a fast-MCD type algorithm. Notably, the MRCT estimator handles high-dimensional data sets without the need for preprocessing or dimension reduction techniques, due to the internal smoothening whose amount is determined by the regularization parameter $\alpha > 0$. The selection of the regularization parameter $\alpha$ is automated. The proposed method adapts seamlessly to sparsely observed data by working directly with the finite matrix of basis coefficients. An extensive simulation study demonstrates the efficacy of the MRCT estimator in terms of robust covariance estimation and automated outlier detection, emphasizing the balance between noise exclusion and signal preservation achieved through appropriate selection of $\alpha$. The method converges fast in practice and performs favorably when compared to other functional outlier detection methods.

stat.ME↗

arXiv2023

Improving Forecasts for Heterogeneous Time Series by "Averaging", with Application to Food Demand Forecast

A common forecasting setting in real world applications considers a set of possibly heterogeneous time series of the same domain. Due to different properties of each time series such as length, obtaining forecasts for each individual time series in a straight-forward way is challenging. This paper proposes a general framework utilizing a similarity measure in Dynamic Time Warping to find similar time series to build neighborhoods in a k-Nearest Neighbor fashion, and improve forecasts of possibly simple models by averaging. Several ways of performing the averaging are suggested, and theoretical arguments underline the usefulness of averaging for forecasting. Additionally, diagnostics tools are proposed allowing a deep understanding of the procedure.

stat.ME↗

arXiv2023

Predictive change point detection for heterogeneous data

A change point detection (CPD) framework assisted by a predictive machine learning model called "Predict and Compare" is introduced and characterised in relation to other state-of-the-art online CPD routines which it outperforms in terms of false positive rate and out-of-control average run length. The method's focus is on improving standard methods from sequential analysis such as the CUSUM rule in terms of these quality measures. This is achieved by replacing typically used trend estimation functionals such as the running mean with more sophisticated predictive models (Predict step), and comparing their prognosis with actual data (Compare step). The two models used in the Predict step are the ARIMA model and the LSTM recursive neural network. However, the framework is formulated in general terms, so as to allow the use of other prediction or comparison methods than those tested here. The power of the method is demonstrated in a tribological case study in which change points separating the run-in, steady-state, and divergent wear phases are detected in the regime of very few false positives.

cs.LG↗