A variational perspective on diffusion-based generative models and score matching
Discrete-time diffusion-based generative models and score matching methods have shown
promising results in modeling high-dimensional image data. Recently, Song et al.(2021) …
promising results in modeling high-dimensional image data. Recently, Song et al.(2021) …
Proximal langevin algorithm: Rapid convergence under isoperimetry
We study the Proximal Langevin Algorithm (PLA) for sampling from a probability distribution
$\nu= e^{-f} $ on $\mathbb {R}^ n $ under isoperimetry. We prove a convergence guarantee …
$\nu= e^{-f} $ on $\mathbb {R}^ n $ under isoperimetry. We prove a convergence guarantee …
Gaussian interpolation flows
Gaussian denoising has emerged as a powerful principle for constructing simulation-free
continuous normalizing flows for generative modeling. Despite their empirical successes …
continuous normalizing flows for generative modeling. Despite their empirical successes …
Information geometry of dynamics on graphs and hypergraphs
We introduce a new information-geometric structure associated with the dynamics on
discrete objects such as graphs and hypergraphs. The presented setup consists of two …
discrete objects such as graphs and hypergraphs. The presented setup consists of two …
Convexity of mutual information along the Fokker-Planck flow
We study the convexity of mutual information as a function of time along the Fokker-Planck
flow. The results are generalizations of that along heat flow and Ornstein-Ulenbeck flow …
flow. The results are generalizations of that along heat flow and Ornstein-Ulenbeck flow …
Mixing Time of the Proximal Sampler in Relative Fisher Information via Strong Data Processing Inequality
We study the mixing time guarantee for sampling in relative Fisher information via the
Proximal Sampler algorithm, which is an approximate proximal discretization of the …
Proximal Sampler algorithm, which is an approximate proximal discretization of the …
McKean's conjecture under the log-concavity assumption
McKean conjectured that Gaussian random variables are optimal for the nth order derivative
of differential entropy along the heat flow, and verified this for n=1,2. Recently, Zhang …
of differential entropy along the heat flow, and verified this for n=1,2. Recently, Zhang …
On Independent Samples Along the Langevin Diffusion and the Unadjusted Langevin Algorithm
We study the rate at which the initial and current random variables become independent
along a Markov chain, focusing on the Langevin diffusion in continuous time and the …
along a Markov chain, focusing on the Langevin diffusion in continuous time and the …
Differential Properties of Information in Jump-diffusion Channels
We propose a channel modeling using jump-diffusion processes, and study the differential
properties of entropy and mutual information. By utilizing the Kramers-Moyal and …
properties of entropy and mutual information. By utilizing the Kramers-Moyal and …
[كتاب][B] Information-based methods and models for particle flow filtering
KC Ward - 2021 - search.proquest.com
Recursive estimation methodologies, such as Kalman and Bayesian filters, typically require
models of some kind to perform the estimation. This filtering process seeks to improve …
models of some kind to perform the estimation. This filtering process seeks to improve …