TY - GEN
T1 - Stochastic Fista Algorithms
T2 - 20th IEEE Statistical Signal Processing Workshop, SSP 2018
AU - Fort, G.
AU - Risser, L.
AU - Atchade, Y.
AU - Moulines, E.
N1 - Publisher Copyright:
© 2018 IEEE.
PY - 2018/8/29
Y1 - 2018/8/29
N2 - Motivated by challenges in Computational Statistics such as Penalized Maximum Likelihood inference in statistical models with intractable likelihoods, we analyze the convergence of a stochastic perturbation of the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), when the stochastic approximation relies on a biased Monte Carlo estimation as it happens when the points are drawn from a Markov chain Monte Carlo (MCMC) sampler. We first motivate this general framework and then show a convergence result for the perturbed FISTA algorithm. We discuss the convergence rate of this algorithm and the computational cost of the Monte Carlo approximation to reach a given precision. Finally, through a numerical example, we explore new directions for a better understanding of these Proximal-Gradient based stochastic optimization algorithms.
AB - Motivated by challenges in Computational Statistics such as Penalized Maximum Likelihood inference in statistical models with intractable likelihoods, we analyze the convergence of a stochastic perturbation of the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), when the stochastic approximation relies on a biased Monte Carlo estimation as it happens when the points are drawn from a Markov chain Monte Carlo (MCMC) sampler. We first motivate this general framework and then show a convergence result for the perturbed FISTA algorithm. We discuss the convergence rate of this algorithm and the computational cost of the Monte Carlo approximation to reach a given precision. Finally, through a numerical example, we explore new directions for a better understanding of these Proximal-Gradient based stochastic optimization algorithms.
KW - Computational Statistics
KW - Markov chain Monte Carlo
KW - Nesterov acceleration
KW - Proximal-Gradient algorithms
KW - Stochastic Approximation
U2 - 10.1109/SSP.2018.8450740
DO - 10.1109/SSP.2018.8450740
M3 - Conference contribution
AN - SCOPUS:85053847768
SN - 9781538615706
T3 - 2018 IEEE Statistical Signal Processing Workshop, SSP 2018
SP - 388
EP - 392
BT - 2018 IEEE Statistical Signal Processing Workshop, SSP 2018
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 10 June 2018 through 13 June 2018
ER -