7 papers
A Hyperfinite Framework for Score-Based Generative Modeling
Sunder Ram Krishnan
Score-based diffusion models are typically formulated using continuous-time stochastic differential equations and measure-theoretic stochastic calculus. In this paper, we develop a…
Rao-Blackwellized Coverage Estimation in Poisson Networks: A High-Fidelity Hybrid Framework
Sunder Ram Krishnan, Junaid Farooq, Kumar Vijay Mishra +3
While stochastic geometry provides a powerful framework for the analysis of cellular networks, standard Monte Carlo simulations often suffer from slow convergence due to the stocha…
Refining Cramér-Rao Bound With Multivariate Parameters: An Extrinsic Geometry Perspective
Sunder Ram Krishnan
We derive a vector generalization of the curvature-corrected Cramér--Rao bound (CRB) in the nonasymptotic regime using a Hilbert space square-root embedding. Building on previous…
Improving Cramér-Rao Bound And Its Variants: An Extrinsic Geometry Perspective
Sunder Ram Krishnan
This work presents a geometric refinement of the classical Cramér--Rao bound (CRB) in the non-asymptotic regime by incorporating curvature-aware corrections based on the second fu…
Cartan meets Cramér-Rao
Sunder Ram Krishnan
A Cartan-geometric, jet bundle formulation of curvature-aware variance bounds in parametric statistical estimation is developed. Building on our earlier extrinsic Hilbert space app…
Coherent Source Enumeration with Compact ULAs
Dibakar Sil, Sunder Ram Krishnan, Kumar Vijay Mishra
Source enumeration typically relies on subspace-based techniques that require accurate separation of signal and noise subspaces. However, prior works do not address coherent source…