Author name cluster

Hans-Georg Müller

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

4 papers

1 author row

NeurIPS Conference 2025 Conference Paper

Fréchet Geodesic Boosting

Yidong Zhou
Su Iao
Hans-Georg Müller

Gradient boosting has become a cornerstone of machine learning, enabling base learners such as decision trees to achieve exceptional predictive performance. While existing algorithms primarily handle scalar or Euclidean outputs, increasingly prevalent complex-structured data, such as distributions, networks, and manifold-valued outputs, present challenges for traditional methods. Such non-Euclidean data lack algebraic structures such as addition, subtraction, or scalar multiplication required by standard gradient boosting frameworks. To address these challenges, we introduce Fréchet geodesic boosting (FGBoost), a novel approach tailored for outputs residing in geodesic metric spaces. FGBoost leverages geodesics as proxies for residuals and constructs ensembles in a way that respects the intrinsic geometry of the output space. Through theoretical analysis, extensive simulations, and real-world applications, we demonstrate the strong performance and adaptability of FGBoost, showcasing its potential for modeling complex data.

PDF Details

NeurIPS Conference 2025 Conference Paper

Functional data analysis for multivariate distributions through Wasserstein slicing

Han Chen
Hans-Georg Müller

The modeling of samples of distributions is a major challenge since distributions do not form a vector space. While various approaches exist for univariate distributions, including transformations to a Hilbert space, far less is known about the multivariate case. We utilize a transformation approach to map multivariate distributions to a Hilbert space via a Wasserstein slicing method that is invertible. This approach combines functional data analysis tools, such as functional principal component analysis and modes of variation, with the facility to map back to interpretable distributions. We also provide convergence guarantees for the Hilbert space representations under a broad class of such transforms. The method is illustrated using joint systolic and diastolic blood pressure data.

PDF Details

JMLR Journal 2022 Journal Article

Network Regression with Graph Laplacians

Yidong Zhou
Hans-Georg Müller

Network data are increasingly available in various research fields, motivating statistical analysis for populations of networks, where a network as a whole is viewed as a data point. The study of how a network changes as a function of covariates is often of paramount interest. However, due to the non-Euclidean nature of networks, basic statistical tools available for scalar and vector data are no longer applicable. This motivates an extension of the notion of regression to the case where responses are network data. Here we propose to adopt conditional Fréchet means implemented as M-estimators that depend on weights derived from both global and local least squares regression, extending the Fréchet regression framework to networks that are quantified by their graph Laplacians. The challenge is to characterize the space of graph Laplacians to justify the application of Fréchet regression. This characterization then leads to asymptotic rates of convergence for the corresponding M-estimators by applying empirical process methods. We demonstrate the usefulness and good practical performance of the proposed framework with simulations and with network data arising from resting-state fMRI in neuroimaging, as well as New York taxi records. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2022. ( edit, beta )

PDF Details

YNIMG Journal 2021 Journal Article

Modeling sparse longitudinal data in early neurodevelopment

Yaqing Chen
Paromita Dubey
Hans-Georg Müller
Muriel Bruchhage
Jane-Ling Wang
Sean Deoni

Early childhood is a period marked by rapid brain growth accompanied by cognitive and motor development. However, it remains unclear how early developmental skills relate to neuroanatomical growth across time with no growth quantile trajectories of typical brain development currently available to place and compare individual neuroanatomical development. Even though longitudinal neuroimaging data have become more common, they are often sparse, making dynamic analyses at subject level a challenging task. Using the Principal Analysis through Conditional Expectation (PACE) approach geared towards sparse longitudinal data, we investigate the evolution of gray matter, white matter and cerebrospinal fluid volumes in a cohort of 446 children between the ages of 1 and 120 months. For each child, we calculate their dynamic age-varying association between the growing brain and scores that assess cognitive functioning, applying the functional varying coefficient model. Using local Fréchet regression, we construct age-varying growth percentiles to reveal the evolution of brain development across the population. To further demonstrate its utility, we apply PACE to predict individual trajectories of brain development.

Details DOI