Outputs (26)

Sampling and Estimation on Manifolds using the Langevin Diffusion (2025)
Journal Article
Bharath, K., Lewis, A., Sharma, A., & Tretyakov, M. V. (2025). Sampling and Estimation on Manifolds using the Langevin Diffusion. Journal of Machine Learning Research, 26, 1-50

Error bounds are derived for sampling and estimation using a discretization of an intrin-sically defined Langevin diffusion with invariant measure dµ ϕ ∝ e −ϕ dvol g on a compact Riemannian manifold. Two estimators of linear functionals of µ ϕ based... Read More about Sampling and Estimation on Manifolds using the Langevin Diffusion.

Probabilistic size-and-shape functional mixed models (2024)
Presentation / Conference Contribution
Wang, F., Bharath, K., Chkrebtii, O., & Kurtek, S. (2024, December). Probabilistic size-and-shape functional mixed models. Presented at Thirty-Eighth Annual Conference on Neural Information Processing Systems, Vancouver, Canada

The reliable recovery and uncertainty quantification of a fixed effect function µ in a functional mixed model, for modelling population-and object-level variability in noisily observed functional data, is a notoriously challenging task: variations al... Read More about Probabilistic size-and-shape functional mixed models.

Topo-Geometric Analysis of Variability in Point Clouds using Persistence Landscapes (2024)
Journal Article
Matuk, J., Kurtek, S., & Bharath, K. (2024). Topo-Geometric Analysis of Variability in Point Clouds using Persistence Landscapes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 46(12), 11035-11046. https://doi.org/10.1109/TPAMI.2024.3451328

Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects known as... Read More about Topo-Geometric Analysis of Variability in Point Clouds using Persistence Landscapes.

A diffusion approach to Stein's method on Riemannian manifolds (2024)
Journal Article
Le, H., Lewis, A., Bharath, K., & Fallaize, C. (2024). A diffusion approach to Stein's method on Riemannian manifolds. Bernoulli, 30(2), 1079-1104. https://doi.org/10.3150/23-bej1625

We detail an approach to developing Stein’s method for bounding integral metrics on probability measures defined on a Riemannian manifold M. Our approach exploits the relationship between the generator of a diffusion on M having a target invariant me... Read More about A diffusion approach to Stein's method on Riemannian manifolds.

Tumor radiogenomics in gliomas with Bayesian layered variable selection (2023)
Journal Article
Mohammed, S., Kurtek, S., Bharath, K., Rao, A., & Baladandayuthapani, V. (2023). Tumor radiogenomics in gliomas with Bayesian layered variable selection. Medical Image Analysis, 90, Article 102964. https://doi.org/10.1016/j.media.2023.102964

We propose a statistical framework to analyze radiological magnetic resonance imaging (MRI) and genomic data to identify the underlying radiogenomic associations in lower grade gliomas (LGG). We devise a novel imaging phenotype by dividing the tumor... Read More about Tumor radiogenomics in gliomas with Bayesian layered variable selection.

Probabilistic Learning of Treatment Trees in Cancer (2023)
Journal Article
Yao, T.-H., Wu, Z., Bharath, K., Li, J., & Baladandayuthapani, V. (2023). Probabilistic Learning of Treatment Trees in Cancer. Annals of Applied Statistics, 17(3), 1884-1908. https://doi.org/10.1214/22-AOAS1696

Accurate identification of synergistic treatment combinations and their underlying biological mechanisms is critical across many disease domains, especially cancer. In translational oncology research, preclinical systems, such as patient-derived xeno... Read More about Probabilistic Learning of Treatment Trees in Cancer.

Spatially penalized registration of multivariate functional data (2023)
Journal Article
Guo, X., Kurtek, S., & Bharath, K. (2023). Spatially penalized registration of multivariate functional data. Spatial Statistics, 56, Article 100760. https://doi.org/10.1016/j.spasta.2023.100760

Registration of multivariate functional data involves handling of both cross-component and cross-observation phase variations. Allowing for the two phase variations to be modelled as general diffeomorphic time warpings, in this work we focus on the h... Read More about Spatially penalized registration of multivariate functional data.

Shape and Structure Preserving Differential Privacy (2022)
Presentation / Conference Contribution
Soto, C., Bharath, K., Reimherr, M., & Slavkovic, A. (2022, November). Shape and Structure Preserving Differential Privacy. Poster presented at Thirty-sixth Conference on Neural Information Processing Systems (NeurIPS 2022), New Orleans, USA

It is common for data structures such as images and shapes of 2D objects to be represented as points on a manifold. The utility of a mechanism to produce sanitized differentially private estimates from such data is intimately linked to how compatible... Read More about Shape and Structure Preserving Differential Privacy.

Variograms for kriging and clustering of spatial functional data with phase variation (2022)
Journal Article
Guo, X., Kurtek, S., & Bharath, K. (2022). Variograms for kriging and clustering of spatial functional data with phase variation. Spatial Statistics, 51, Article 100687. https://doi.org/10.1016/j.spasta.2022.100687

Spatial, amplitude and phase variations in spatial functional data are confounded. Conclusions from the popular functional trace-variogram, which quantifies spatial variation, can be misleading when analyzing misaligned functional data with phase var... Read More about Variograms for kriging and clustering of spatial functional data with phase variation.

RADIOHEAD: Radiogenomic analysis incorporating tumor heterogeneity in imaging through densities (2021)
Journal Article
Mohammed, S., Bharath, K., Kurtek, S., Rao, A., & Baladandayuthapani, V. (2021). RADIOHEAD: Radiogenomic analysis incorporating tumor heterogeneity in imaging through densities. Annals of Applied Statistics, 15(4), 1808-1830. https://doi.org/10.1214/21-AOAS1458

Recent technological advancements have enabled detailed investigation of associations between the molecular architecture and tumor heterogeneity through multisource integration of radiological imaging and genomic (radiogenomic) data. In this paper we... Read More about RADIOHEAD: Radiogenomic analysis incorporating tumor heterogeneity in imaging through densities.