arXiv subjects

Michael Muma

Publications and source records attributed to Michael Muma.

At least 19 recordsLinked to original sources

arXiv2026

Virtual Dummies: Enabling Scalable FDR-Controlled Variable Selection via Sequential Sampling of Null Features

High-dimensional variable selection, particularly in genomics, requires error-controlling procedures that scale to millions of predictors. The Terminating-Random Experiments (T-Rex) selector achieves false discovery rate (FDR) control by aggregating results of early terminated random experiments, each combining original predictors with i.i.d. synthetic null variables (dummies). At biobank scales, however, explicit dummy augmentation requires terabytes of memory. We demonstrate that this bottleneck is not fundamental. Formalizing the information flow of forward selection through a filtration, we show that compatible selectors interact with unselected dummies solely through projections onto an adaptively evolving low-dimensional subspace. For rotationally invariant dummy distributions, we derive an adaptive stick-breaking construction sampling these projections from their exact conditional distribution given the selection history, thereby eliminating dummy matrix materialization. We prove a pathwise universality theorem: under mild delocalization conditions, selection paths driven by generic standardized i.i.d. dummies converge to the same Gaussian limit. We instantiate the theory through Virtual Dummy LARS (VD-LARS), reducing memory and runtime by several orders of magnitude while preserving the exact selection law and FDR guarantees of the T-Rex selector. Experiments on realistic genome-wide association study data confirm that VD-T-Rex controls FDR and achieves power at scales where all competing methods either fail or time out.

stat.ME↗

arXiv2026

FDR Control for Complex-Valued Data with Application in Single Snapshot Multi-Source Detection and DOA Estimation

False discovery rate (FDR) control is a popular approach for maintaining the integrity of statistical analyses, especially in high-dimensional data settings, where multiple comparisons increase the risk of false positives. FDR control has been extensively researched for real-valued data. However, the complex data case, which is relevant for many signal processing applications, remains widely unexplored. We therefore present a fast and FDR-controlling variable selector for complex-valued high-dimensional data. The proposed Complex-Valued Terminating-Random Experiments (CT-Rex) selector controls a user-defined target FDR while maximizing the number of selected variables. This is achieved by optimally fusing the solutions of multiple early terminated complex-valued random experiments. We benchmark the performance in sparse complex regression simulation studies and showcase an example of FDR-controlled compressed-sensing-based single snapshot multi-source detection and direction of arrival (DOA) estimation. The proposed work applies to a wide range of research areas, such as DOA estimation, communications, mechanical engineering, and magnetic resonance imaging, bridging a critical gap in signal processing for complex-valued data.

eess.SP↗

arXiv2026

Learning False Discovery Rate Control via Model-Based Neural Networks

Controlling the false discovery rate (FDR) in high-dimensional variable selection requires balancing rigorous error control with statistical power. Existing methods with provable guarantees are often overly conservative, creating a persistent gap between the realized false discovery proportion (FDP) and the target FDR level. We introduce a learning-augmented enhancement of the T-Rex Selector framework that narrows this gap. Our approach replaces the analytical FDP estimator with a neural network trained solely on diverse synthetic datasets, enabling a substantially tighter and more accurate approximation of the FDP. This refinement allows the procedure to operate much closer to the desired FDR level, thereby increasing discovery power while maintaining effective approximate control. Through extensive simulations and a challenging synthetic genome-wide association study (GWAS), we demonstrate that our method achieves superior detection of true variables compared to existing approaches.

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arXiv2025

Reproducible Physiological Features in Affective Computing: A Preliminary Analysis on Arousal Modeling

In Affective Computing, a key challenge lies in reliably linking subjective emotional experiences with objective physiological markers. This preliminary study addresses the issue of reproducibility by identifying physiological features from cardiovascular and electrodermal signals that are associated with continuous self-reports of arousal levels. Using the Continuously Annotated Signal of Emotion dataset, we analyzed 164 features extracted from cardiac and electrodermal signals of 30 participants exposed to short emotion-evoking videos. Feature selection was performed using the Terminating-Random Experiments (T-Rex) method, which performs variable selection systematically controlling a user-defined target False Discovery Rate. Remarkably, among all candidate features, only two electrodermal-derived features exhibited reproducible and statistically significant associations with arousal, achieving a 100\% confirmation rate. These results highlight the necessity of rigorous reproducibility assessments in physiological features selection, an aspect often overlooked in Affective Computing. Our approach is particularly promising for applications in safety-critical environments requiring trustworthy and reliable white box models, such as mental disorder recognition and human-robot interaction systems.

cs.HC↗

arXiv2025

Cross-Channel Unlabeled Sensing over a Union of Signal Subspaces

Cross-channel unlabeled sensing addresses the problem of recovering a multi-channel signal from measurements that were shuffled across channels. This work expands the cross-channel unlabeled sensing framework to signals that lie in a union of subspaces. The extension allows for handling more complex signal structures and broadens the framework to tasks like compressed sensing. These mismatches between samples and channels often arise in applications such as whole-brain calcium imaging of freely moving organisms or multi-target tracking. We improve over previous models by deriving tighter bounds on the required number of samples for unique reconstruction, while supporting more general signal types. The approach is validated through an application in whole-brain calcium imaging, where organism movements disrupt sample-to-neuron mappings. This demonstrates the utility of our framework in real-world settings with imprecise sample-channel associations, achieving accurate signal reconstruction.

eess.SP↗

arXiv2024

False Discovery Rate Control for Fast Screening of Large-Scale Genomics Biobanks

Genomics biobanks are information treasure troves with thousands of phenotypes (e.g., diseases, traits) and millions of single nucleotide polymorphisms (SNPs). The development of methodologies that provide reproducible discoveries is essential for the understanding of complex diseases and precision drug development. Without statistical reproducibility guarantees, valuable efforts are spent on researching false positives. Therefore, scalable multivariate and high-dimensional false discovery rate (FDR)-controlling variable selection methods are urgently needed, especially, for complex polygenic diseases and traits. In this work, we propose the Screen-T-Rex selector, a fast FDR-controlling method based on the recently developed T-Rex selector. The method is tailored to screening large-scale biobanks and it does not require choosing additional parameters (sparsity parameter, target FDR level, etc). Numerical simulations and a real-world HIV-1 drug resistance example demonstrate that the performance of the Screen-T-Rex selector is superior, and its computation time is multiple orders of magnitude lower compared to current benchmark knockoff methods.

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arXiv2024

The Informed Elastic Net for Fast Grouped Variable Selection and FDR Control in Genomics Research

Modern genomics research relies on genome-wide association studies (GWAS) to identify the few genetic variants among potentially millions that are associated with diseases of interest. Only reproducible discoveries of groups of associations improve our understanding of complex polygenic diseases and enable the development of new drugs and personalized medicine. Thus, fast multivariate variable selection methods that have a high true positive rate (TPR) while controlling the false discovery rate (FDR) are crucial. Recently, the T-Rex+GVS selector, a version of the T-Rex selector that uses the elastic net (EN) as a base selector to perform grouped variable election, was proposed. Although it significantly increased the TPR in simulated GWAS compared to the original T-Rex, its comparably high computational cost limits scalability. Therefore, we propose the informed elastic net (IEN), a new base selector that significantly reduces computation time while retaining the grouped variable selection property. We quantify its grouping effect and derive its formulation as a Lasso-type optimization problem, which is solved efficiently within the T-Rex framework by the terminated LARS algorithm. Numerical simulations and a GWAS study demonstrate that the proposed T-Rex+GVS (IEN) exhibits the desired grouping effect, reduces computation time, and achieves the same TPR as T-Rex+GVS (EN) but with lower FDR, which makes it a promising method for large-scale GWAS.

stat.ME↗

arXiv2024

Solving FDR-Controlled Sparse Regression Problems with Five Million Variables on a Laptop

Currently, there is an urgent demand for scalable multivariate and high-dimensional false discovery rate (FDR)-controlling variable selection methods to ensure the repro-ducibility of discoveries. However, among existing methods, only the recently proposed Terminating-Random Experiments (T-Rex) selector scales to problems with millions of variables, as encountered in, e.g., genomics research. The T-Rex selector is a new learning framework based on early terminated random experiments with computer-generated dummy variables. In this work, we propose the Big T-Rex, a new implementation of T-Rex that drastically reduces its Random Access Memory (RAM) consumption to enable solving FDR-controlled sparse regression problems with millions of variables on a laptop. We incorporate advanced memory-mapping techniques to work with matrices that reside on solid-state drive and two new dummy generation strategies based on permutations of a reference matrix. Our nu-merical experiments demonstrate a drastic reduction in memory demand and computation time. We showcase that the Big T-Rex can efficiently solve FDR-controlled Lasso-type problems with five million variables on a laptop in thirty minutes. Our work empowers researchers without access to high-performance clusters to make reproducible discoveries in large-scale high-dimensional data.

eess.SP↗

arXiv2024

High-Dimensional False Discovery Rate Control for Dependent Variables

Algorithms that ensure reproducible findings from large-scale, high-dimensional data are pivotal in numerous signal processing applications. In recent years, multivariate false discovery rate (FDR) controlling methods have emerged, providing guarantees even in high-dimensional settings where the number of variables surpasses the number of samples. However, these methods often fail to reliably control the FDR in the presence of highly dependent variable groups, a common characteristic in fields such as genomics and finance. To tackle this critical issue, we introduce a novel framework that accounts for general dependency structures. Our proposed dependency-aware T-Rex selector integrates hierarchical graphical models within the T-Rex framework to effectively harness the dependency structure among variables. Leveraging martingale theory, we prove that our variable penalization mechanism ensures FDR control. We further generalize the FDR-controlling framework by stating and proving a clear condition necessary for designing both graphical and non-graphical models that capture dependencies. Additionally, we formulate a fully integrated optimal calibration algorithm that concurrently determines the parameters of the graphical model and the T-Rex framework, such that the FDR is controlled while maximizing the number of selected variables. Numerical experiments and a breast cancer survival analysis use-case demonstrate that the proposed method is the only one among the state-of-the-art benchmark methods that controls the FDR and reliably detects genes that have been previously identified to be related to breast cancer. An open-source implementation is available within the R package TRexSelector on CRAN.

stat.ME↗

arXiv2024

FDR-Controlled Portfolio Optimization for Sparse Financial Index Tracking

In high-dimensional data analysis, such as financial index tracking or biomedical applications, it is crucial to select the few relevant variables while maintaining control over the false discovery rate (FDR). In these applications, strong dependencies often exist among the variables (e.g., stock returns), which can undermine the FDR control property of existing methods like the model-X knockoff method or the T-Rex selector. To address this issue, we have expanded the T-Rex framework to accommodate overlapping groups of highly correlated variables. This is achieved by integrating a nearest neighbors penalization mechanism into the framework, which provably controls the FDR at the user-defined target level. A real-world example of sparse index tracking demonstrates the proposed method's ability to accurately track the S&P 500 index over the past 20 years based on a small number of stocks. An open-source implementation is provided within the R package TRexSelector on CRAN.

q-fin.PM↗

arXiv2024

False Discovery Rate Control for Gaussian Graphical Models via Neighborhood Screening

Gaussian graphical models emerge in a wide range of fields. They model the statistical relationships between variables as a graph, where an edge between two variables indicates conditional dependence. Unfortunately, well-established estimators, such as the graphical lasso or neighborhood selection, are known to be susceptible to a high prevalence of false edge detections. False detections may encourage inaccurate or even incorrect scientific interpretations, with major implications in applications, such as biomedicine or healthcare. In this paper, we introduce a nodewise variable selection approach to graph learning and provably control the false discovery rate of the selected edge set at a self-estimated level. A novel fusion method of the individual neighborhoods outputs an undirected graph estimate. The proposed method is parameter-free and does not require tuning by the user. Benchmarks against competing false discovery rate controlling methods in numerical experiments considering different graph topologies show a significant gain in performance.

stat.ML↗

arXiv2024

Sparse PCA with False Discovery Rate Controlled Variable Selection

Sparse principal component analysis (PCA) aims at mapping large dimensional data to a linear subspace of lower dimension. By imposing loading vectors to be sparse, it performs the double duty of dimension reduction and variable selection. Sparse PCA algorithms are usually expressed as a trade-off between explained variance and sparsity of the loading vectors (i.e., number of selected variables). As a high explained variance is not necessarily synonymous with relevant information, these methods are prone to select irrelevant variables. To overcome this issue, we propose an alternative formulation of sparse PCA driven by the false discovery rate (FDR). We then leverage the Terminating-Random Experiments (T-Rex) selector to automatically determine an FDR-controlled support of the loading vectors. A major advantage of the resulting T-Rex PCA is that no sparsity parameter tuning is required. Numerical experiments and a stock market data example demonstrate a significant performance improvement.

stat.ML↗

arXiv2023

Fast and Robust Sparsity-Aware Block Diagonal Representation

The block diagonal structure of an affinity matrix is a commonly desired property in cluster analysis because it represents clusters of feature vectors by non-zero coefficients that are concentrated in blocks. However, recovering a block diagonal affinity matrix is challenging in real-world applications, in which the data may be subject to outliers and heavy-tailed noise that obscure the hidden cluster structure. To address this issue, we first analyze the effect of different fundamental outlier types in graph-based cluster analysis. A key idea that simplifies the analysis is to introduce a vector that represents a block diagonal matrix as a piece-wise linear function of the similarity coefficients that form the affinity matrix. We reformulate the problem as a robust piece-wise linear fitting problem and propose a Fast and Robust Sparsity-Aware Block Diagonal Representation (FRS-BDR) method, which jointly estimates cluster memberships and the number of blocks. Comprehensive experiments on a variety of real-world applications demonstrate the effectiveness of FRS-BDR in terms of clustering accuracy, robustness against corrupted features, computation time and cluster enumeration performance.

cs.LG↗

arXiv2023

Identifying the Complete Correlation Structure in Large-Scale High-Dimensional Data Sets with Local False Discovery Rates

The identification of the dependent components in multiple data sets is a fundamental problem in many practical applications. The challenge in these applications is that often the data sets are high-dimensional with few observations or available samples and contain latent components with unknown probability distributions. A novel mathematical formulation of this problem is proposed, which enables the inference of the underlying correlation structure with strict false positive control. In particular, the false discovery rate is controlled at a pre-defined threshold on two levels simultaneously. The deployed test statistics originate in the sample coherence matrix. The required probability models are learned from the data using the bootstrap. Local false discovery rates are used to solve the multiple hypothesis testing problem. Compared to the existing techniques in the literature, the developed technique does not assume an a priori correlation structure and work well when the number of data sets is large while the number of observations is small. In addition, it can handle the presence of distributional uncertainties, heavy-tailed noise, and outliers.

stat.ME↗

arXiv2023

Emergency Response Person Localization and Vital Sign Estimation Using a Semi-Autonomous Robot Mounted SFCW Radar

The large number and scale of natural and man-made disasters have led to an urgent demand for technologies that enhance the safety and efficiency of search and rescue teams. Semi-autonomous rescue robots are beneficial, especially when searching inaccessible terrains, or dangerous environments, such as collapsed infrastructures. For search and rescue missions in degraded visual conditions or non-line of sight scenarios, radar-based approaches may contribute to acquire valuable, and otherwise unavailable information. This article presents a complete signal processing chain for radar-based multi-person detection, 2D-MUSIC localization and breathing frequency estimation. The proposed method shows promising results on a challenging emergency response dataset that we collected using a semi-autonomous robot equipped with a commercially available through-wall radar system. The dataset is composed of 62 scenarios of various difficulty levels with up to five persons captured in different postures, angles and ranges including wooden and stone obstacles that block the radar line of sight. Ground truth data for reference locations, respiration, electrocardiogram, and acceleration signals are included. The full emergency response benchmark data set as well as all codes to reproduce our results, are publicly available at https://doi.org/10.21227/4bzd-jm32.

eess.SP↗

arXiv2022

Shuffled Multi-Channel Sparse Signal Recovery

Mismatches between samples and their respective channel or target commonly arise in several real-world applications. For instance, whole-brain calcium imaging of freely moving organisms, multiple-target tracking or multi-person contactless vital sign monitoring may be severely affected by mismatched sample-channel assignments. To systematically address this fundamental problem, we pose it as a signal reconstruction problem where we have lost correspondences between the samples and their respective channels. Assuming that we have a sensing matrix for the underlying signals, we show that the problem is equivalent to a structured unlabeled sensing problem, and establish sufficient conditions for unique recovery. To the best of our knowledge, a sampling result for the reconstruction of shuffled multi-channel signals has not been considered in the literature and existing methods for unlabeled sensing cannot be directly applied. We extend our results to the case where the signals admit a sparse representation in an overcomplete dictionary (i.e., the sensing matrix is not precisely known), and derive sufficient conditions for the reconstruction of shuffled sparse signals. We propose a robust reconstruction method that combines sparse signal recovery with robust linear regression for the two-channel case. The performance and robustness of the proposed approach is illustrated in an application related to whole-brain calcium imaging. The proposed methodology can be generalized to sparse signal representations other than the ones considered in this work to be applied in a variety of real-world problems with imprecise measurement or channel assignment.

eess.SP↗

arXiv2022

Robust and Efficient Aggregation for Distributed Learning

Distributed learning paradigms, such as federated and decentralized learning, allow for the coordination of models across a collection of agents, and without the need to exchange raw data. Instead, agents compute model updates locally based on their available data, and subsequently share the update model with a parameter server or their peers. This is followed by an aggregation step, which traditionally takes the form of a (weighted) average. Distributed learning schemes based on averaging are known to be susceptible to outliers. A single malicious agent is able to drive an averaging-based distributed learning algorithm to an arbitrarily poor model. This has motivated the development of robust aggregation schemes, which are based on variations of the median and trimmed mean. While such procedures ensure robustness to outliers and malicious behavior, they come at the cost of significantly reduced sample efficiency. This means that current robust aggregation schemes require significantly higher agent participation rates to achieve a given level of performance than their mean-based counterparts in non-contaminated settings. In this work we remedy this drawback by developing statistically efficient and robust aggregation schemes for distributed learning.

cs.LG↗

arXiv2021

The Terminating-Random Experiments Selector: Fast High-Dimensional Variable Selection with False Discovery Rate Control

We propose the Terminating-Random Experiments (T-Rex) selector, a fast variable selection method for high-dimensional data. The T-Rex selector controls a user-defined target false discovery rate (FDR) while maximizing the number of selected variables. This is achieved by fusing the solutions of multiple early terminated random experiments. The experiments are conducted on a combination of the original predictors and multiple sets of randomly generated dummy predictors. A finite sample proof based on martingale theory for the FDR control property is provided. Numerical simulations confirm that the FDR is controlled at the target level while allowing for high power. We prove that the dummies can be sampled from any univariate probability distribution with finite expectation and variance. The computational complexity of the proposed method is linear in the number of variables. The T-Rex selector outperforms state-of-the-art methods for FDR control in numerical experiments and on a simulated genome-wide association study (GWAS), while its sequential computation time is more than two orders of magnitude lower than that of the strongest benchmark methods. The open source R package TRexSelector containing the implementation of the T-Rex selector is available on CRAN.

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