List of publications

1. The Completion of Covariance Kernels.
   Kartik G. Waghmare & Victor M. Panaretos, (2022).
   Summary. We consider the problem of positive-definite completion for covariance functions and establish the existence of the kernel analogue of the determinant-maximizing matrix completion. Using this concept, we develop a methodology for covariance estimation from partially observed functional data under intuitive and plausible assumptions.
   Published: The Annals of Statistics, 2022, 50(6), pp.3281-3306. [arXiv] [Errata] [R Package]

2. Continuously Indexed Graphical Models.
   Kartik G. Waghmare & Victor M. Panaretos, (2023).
   Summary. We demonstrate how Gaussian processes can be thought of as Gaussian graphical models corresponding to continuous index sets and propose a method for recovering the graph of a process from an estimate of its covariance upto an appropriate finite resolution.
   Published: Journal of the Royal Statistical Society: Series B., qkae086. [arXiv] [R Package] [Reproduction]

3. The Functional Graphical Lasso.
   Kartik G. Waghmare, Tomas Masak and Victor M. Panaretos, (2023).
   Summary. We propose an infinite-dimensional generalization of the graphical lasso for recovering conditional independence relationships between jointly distributed Hilbertian random elements (which includes random vectors, functions and surfaces) in the sparse high-dimensional regime. Importantly, we show how the maximum likelihood method can be applied to multivariate functional data.
   Submitted. [arXiv]

4. The Positive-Definite Completion Problem.
   Kartik G. Waghmare and Victor M. Panaretos, (2024).
   Summary. We consider the positive-definite completion problem for kernels in a general setting and establish many interesting results concerning its existence and uniqueness of solutions, which include many interesting algebraic and variational characterizations of special solutions. Importantly, we prove the existence of a canonical extension in the context of the classical extension problem of positive-definite functions.
   Published: Transactions of the American Mathematical Society, 2024, 377, 6549-6594. [arXiv]

5. A Karhunen-Loève Theorem for Random Flows in Hilbert spaces.
   Leonardo V. Santoro, Kartik G. Waghmare, and Victor M. Panaretos, (2024).
   Summary. We generalize the Karhunen-Loève theorem and thus, principal components analysis, to Hilbertian functional data.
   Published: Electronic Communications in Probabability, 2024, 29: 1-12. [arXiv]