Outputs (26)

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.