27 citations · 93 across the 14 of their papers we have counts for
14 papers
Training Latent Diffusion Models with Interacting Particle Algorithms
Tim Y. J. Wang, Juan Kuntz, O. Deniz Akyildiz
We introduce a novel particle-based algorithm for end-to-end training of latent diffusion models. We reformulate the training task as minimizing a free energy functional and obtain…
Error bounds for particle gradient descent, and extensions of the log-Sobolev and Talagrand inequalities
Rocco Caprio, Juan Kuntz, Samuel Power +1
We prove non-asymptotic error bounds for particle gradient descent (PGD, Kuntz et al., 2023), a recently introduced algorithm for maximum likelihood estimation of large latent vari…
Momentum Particle Maximum Likelihood
Jen Ning Lim, Juan Kuntz, Samuel Power +1
Maximum likelihood estimation (MLE) of latent variable models is often recast as the minimization of a free energy functional over an extended space of parameters and probability d…
Particle algorithms for maximum likelihood training of latent variable models
Juan Kuntz, Jen Ning Lim, Adam M. Johansen
(Neal and Hinton, 1998) recast maximum likelihood estimation of any given latent variable model as the minimization of a free energy functional , and the EM algorithm as coordin…
The divide-and-conquer sequential Monte Carlo algorithm: theoretical properties and limit theorems
Juan Kuntz, Francesca R. Crucinio, Adam M. Johansen
We provide a comprehensive characterisation of the theoretical properties of the divide-and-conquer sequential Monte Carlo (DaC-SMC) algorithm. We firmly establish it as a well-fou…
Product-form estimators: exploiting independence to scale up Monte Carlo
Juan Kuntz, Francesca R. Crucinio, Adam M. Johansen
We introduce a class of Monte Carlo estimators that aim to overcome the rapid growth of variance with dimension often observed for standard estimators by exploiting the target's in…
Markov chains revisited
Juan Kuntz
A rigorous and largely self-contained account of (a) the bread-and-butter concepts and techniques in Markov chain theory and (b) the long-term behaviour of chains. As much as possi…
Stationary distributions of continuous-time Markov chains: a review of theory and truncation-based approximations
Juan Kuntz, Philipp Thomas, Guy-Bart Stan +1
Computing the stationary distributions of a continuous-time Markov chain (CTMC) involves solving a set of linear equations. In most cases of interest, the number of equations is in…
Approximations of countably-infinite linear programs over bounded measure spaces
Juan Kuntz, Philipp Thomas, Guy-Bart Stan +1
We study a class of countably-infinite-dimensional linear programs (CILPs) whose feasible sets are bounded subsets of appropriately defined spaces of measures. The optimal value, o…
The exit time finite state projection scheme: bounding exit distributions and occupation measures of continuous-time Markov chains
Juan Kuntz, Philipp Thomas, Guy-Bart Stan +1
We introduce the exit time finite state projection (ETFSP) scheme, a truncation-based method that yields approximations to the exit distribution and occupation measure associated w…
Rigorous bounds on the stationary distributions of the chemical master equation via mathematical programming
Juan Kuntz, Philipp Thomas, Guy-Bart Stan +1
The stochastic dynamics of biochemical networks are usually modelled with the chemical master equation (CME). The stationary distributions of CMEs are seldom solvable analytically,…
Non-stationary phase of the MALA algorithm
J. Kuntz, M. Ottobre, A. M. Stuart
The Metropolis-Adjusted Langevin Algorithm (MALA) is a Markov Chain Monte Carlo method which creates a Markov chain reversible with respect to a given target distribution, pi^N, wi…
Bounding stationary averages of polynomial diffusions via semidefinite programming
Juan Kuntz, Michela Ottobre, Guy-Bart Stan +1
We introduce an algorithm based on semidefinite programming that yields increasing (resp. decreasing) sequences of lower (resp. upper) bounds on polynomial stationary averages of d…
Diffusion Limit For The Random Walk Metropolis Algorithm Out Of stationarity
J. Kuntz, M. Ottobre, A. M. Stuart
The Random Walk Metropolis (RWM) algorithm is a Metropolis- Hastings MCMC algorithm designed to sample from a given target distribution πwith Lebesgue density on R^N. RWM construct…