Professor KARTHIK BHARATH's Outputs (30)

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.

Differential privacy over Riemannian manifolds (2021)
Presentation / Conference Contribution
Reimherr, M., Bharath, K., & Soto, C. (2021, December). Differential privacy over Riemannian manifolds. Presented at Thirty-fifth Conference on Neural Information Processing Systems (NeurIPS 2021), Online

In this work we consider the problem of releasing a differentially private statistical summary that resides on a Riemannian manifold. We present an extension of the Laplace or K-norm mechanism that utilizes intrinsic distances and volumes on the mani... Read More about Differential privacy over Riemannian manifolds.

Tangent functional canonical correlation analysis for densities and shapes, with applications to multimodal imaging data (2021)
Journal Article
Ho cho, M., Kurtek, S., & Bharath, K. (2022). Tangent functional canonical correlation analysis for densities and shapes, with applications to multimodal imaging data. Journal of Multivariate Analysis, 189, Article 104870. https://doi.org/10.1016/j.jmva.2021.104870

It is quite common for functional data arising from imaging data to assume values in infinite-dimensional manifolds. Uncovering associations between two or more such nonlinear functional data extracted from the same object across medical imaging moda... Read More about Tangent functional canonical correlation analysis for densities and shapes, with applications to multimodal imaging data.

Shape-Based Classification of Partially Observed Curves, With Applications to Anthropology (2021)
Journal Article
Matthews, G. J., Bharath, K., Kurtek, S., Brophy, J., Thiruvanthukal, G., & Harel, O. (2021). Shape-Based Classification of Partially Observed Curves, With Applications to Anthropology. Frontiers in Applied Mathematics and Statistics, 7, 1-14. https://doi.org/10.3389/fams.2021.759622

We consider the problem of classifying curves when they are observed only partially on their parameter domains. We propose computational methods for (i) completion of partially observed curves; (ii) assessment of completion variability through a nonp... Read More about Shape-Based Classification of Partially Observed Curves, With Applications to Anthropology.

Bayesian Framework for Simultaneous Registration and Estimation of Noisy, Sparse, and Fragmented Functional Data (2021)
Journal Article
Matuk, J., Bharath, K., Chkrebtii, O., & Kurtek, S. (2022). Bayesian Framework for Simultaneous Registration and Estimation of Noisy, Sparse, and Fragmented Functional Data. Journal of the American Statistical Association, 117(540), 1964-1980. https://doi.org/10.1080/01621459.2021.1893179

In many applications, smooth processes generate data that are recorded under a variety of observational regimes, including dense sampling and sparse or fragmented observations that are often contaminated with error. The statistical goal of registerin... Read More about Bayesian Framework for Simultaneous Registration and Estimation of Noisy, Sparse, and Fragmented Functional Data.

Invariance and identifiability issues for word embeddings (2019)
Presentation / Conference Contribution
Carrington, R., Bharath, K., & Preston, S. (2019, December). Invariance and identifiability issues for word embeddings. Presented at NeurIPS 2019, Vancouver, Canada

Word embeddings are commonly obtained as optimisers of a criterion function f of 1 a text corpus, but assessed on word-task performance using a different evaluation 2 function g of the test data. We contend that a possible source of disparity in 3 pe... Read More about Invariance and identifiability issues for word embeddings.

Mutually disjoint, maximally commuting set of physical observables for optimum state determination (2019)
Journal Article
Smitha Rao, H. S., Sirsi, S., & Bharath, K. (2019). Mutually disjoint, maximally commuting set of physical observables for optimum state determination. Physica Scripta, 94(10), 1-7. https://doi.org/10.1088/1402-4896/ab2a85

We consider the state determination problem using mutually unbiased bases (MUBs). For spin-1, spin-3/2 and spin-2 systems, analogous to Pauli operators of spin-1/2 system, which are experimentally implementable and correspond to the optimum measureme... Read More about Mutually disjoint, maximally commuting set of physical observables for optimum state determination.

Distribution on warp maps for alignment of open and closed curves (2019)
Journal Article
Bharath, K., & Kurtek, S. (2019). Distribution on warp maps for alignment of open and closed curves. Journal of the American Statistical Association, 115(531), 1378-1392. https://doi.org/10.1080/01621459.2019.1632066

Alignment of curve data is an integral part of their statistical analysis, and can be achieved using model-or optimization-based approaches. The parameter space is usually the set of monotone, continuous warp maps of a domain. Infinite-dimensional na... Read More about Distribution on warp maps for alignment of open and closed curves.

A geometric variational approach to Bayesian inference (2019)
Journal Article
Saha, A., Bharath, K., & Kurtek, S. (2020). A geometric variational approach to Bayesian inference. Journal of the American Statistical Association, 115(530), 822-835. https://doi.org/10.1080/01621459.2019.1585253

We propose a novel Riemannian geometric framework for variational inference in Bayesian models based on the nonparametric Fisher–Rao metric on the manifold of probability density functions. Under the square-root density representation, the manifold c... Read More about A geometric variational approach to Bayesian inference.

Radiologic image-based statistical shape analysis of brain tumors (2018)
Journal Article
Bharath, K., Kurtek, S., Rao, A., & Baladandayuthapani, V. (2018). Radiologic image-based statistical shape analysis of brain tumors. Journal of the Royal Statistical Society: Series C, 67(5), 1357-1378. https://doi.org/10.1111/rssc.12272

We propose a curve-based Riemannian-geometric approach for general shape-based statistical analyses of tumors obtained from radiologic images. A key component of the framework is a suitable metric that (1) enables comparisons of tumor shapes, (2) pro... Read More about Radiologic image-based statistical shape analysis of brain tumors.

POVM construction: a simple recipe with applications to symmetric states (2017)
Journal Article
Sirsi, S., Bharath, K., Shilpashree, S., & Rao, H. S. (in press). POVM construction: a simple recipe with applications to symmetric states. International Journal of Quantum Information, 15, https://doi.org/10.1142/S0219749917500423

We propose a simple method for constructing POVMs using any set of matrices which form an orthonormal basis for the space of complex matrices. Considering the orthonormal set of irreducible spherical tensors, we examine the properties of the construc... Read More about POVM construction: a simple recipe with applications to symmetric states.

Geometric multiaxial representation of N-qubit mixed symmetric separable states (2017)
Journal Article
Suma, S., Sirsi, S., Hegde, S., & Bharath, K. (2017). Geometric multiaxial representation of N-qubit mixed symmetric separable states. Physical Review A, 96(2), Article 022328. https://doi.org/10.1103/PhysRevA.96.022328

Study of an N qubit mixed symmetric separable states is a long standing challenging problem as there exist no unique separability criterion. In this regard, we take up the N-qubit mixed symmetric separable states for a detailed study as these states... Read More about Geometric multiaxial representation of N-qubit mixed symmetric separable states.