2 research outputs found
Convergence Rates of Biased Stochastic Optimization for Learning Sparse Ising Models
We study the convergence rate of stochastic optimization of exact (NP-hard)
objectives, for which only biased estimates of the gradient are available. We
motivate this problem in the context of learning the structure and parameters
of Ising models. We first provide a convergence-rate analysis of deterministic
errors for forward-backward splitting (FBS). We then extend our analysis to
biased stochastic errors, by first characterizing a family of samplers and
providing a high probability bound that allows understanding not only FBS, but
also proximal gradient (PG) methods. We derive some interesting conclusions:
FBS requires only a logarithmically increasing number of random samples in
order to converge (although at a very low rate); the required number of random
samples is the same for the deterministic and the biased stochastic setting for
FBS and basic PG; accelerated PG is not guaranteed to converge in the biased
stochastic setting.Comment: ICML201
Stochastic Learning for Sparse Discrete Markov Random Fields with Controlled Gradient Approximation Error
We study the -regularized maximum likelihood estimator/estimation (MLE)
problem for discrete Markov random fields (MRFs), where efficient and scalable
learning requires both sparse regularization and approximate inference. To
address these challenges, we consider a stochastic learning framework called
stochastic proximal gradient (SPG; Honorio 2012a, Atchade et al.
2014,Miasojedow and Rejchel 2016). SPG is an inexact proximal gradient
algorithm [Schmidtet al., 2011], whose inexactness stems from the stochastic
oracle (Gibbs sampling) for gradient approximation - exact gradient evaluation
is infeasible in general due to the NP-hard inference problem for discrete MRFs
[Koller and Friedman, 2009]. Theoretically, we provide novel verifiable bounds
to inspect and control the quality of gradient approximation. Empirically, we
propose the tighten asymptotically (TAY) learning strategy based on the
verifiable bounds to boost the performance of SPG