1,140 research outputs found
Stochastic Gradient Hamiltonian Monte Carlo
Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for
defining distant proposals with high acceptance probabilities in a
Metropolis-Hastings framework, enabling more efficient exploration of the state
space than standard random-walk proposals. The popularity of such methods has
grown significantly in recent years. However, a limitation of HMC methods is
the required gradient computation for simulation of the Hamiltonian dynamical
system-such computation is infeasible in problems involving a large sample size
or streaming data. Instead, we must rely on a noisy gradient estimate computed
from a subset of the data. In this paper, we explore the properties of such a
stochastic gradient HMC approach. Surprisingly, the natural implementation of
the stochastic approximation can be arbitrarily bad. To address this problem we
introduce a variant that uses second-order Langevin dynamics with a friction
term that counteracts the effects of the noisy gradient, maintaining the
desired target distribution as the invariant distribution. Results on simulated
data validate our theory. We also provide an application of our methods to a
classification task using neural networks and to online Bayesian matrix
factorization.Comment: ICML 2014 versio
Sparse Gaussian Processes Revisited: Bayesian Approaches to Inducing-Variable Approximations
Variational inference techniques based on inducing variables provide an
elegant framework for scalable posterior estimation in Gaussian process (GP)
models. Besides enabling scalability, one of their main advantages over sparse
approximations using direct marginal likelihood maximization is that they
provide a robust alternative for point estimation of the inducing inputs, i.e.
the location of the inducing variables. In this work we challenge the common
wisdom that optimizing the inducing inputs in the variational framework yields
optimal performance. We show that, by revisiting old model approximations such
as the fully-independent training conditionals endowed with powerful
sampling-based inference methods, treating both inducing locations and GP
hyper-parameters in a Bayesian way can improve performance significantly. Based
on stochastic gradient Hamiltonian Monte Carlo, we develop a fully Bayesian
approach to scalable GP and deep GP models, and demonstrate its
state-of-the-art performance through an extensive experimental campaign across
several regression and classification problems
Variational Sequential Monte Carlo
Many recent advances in large scale probabilistic inference rely on
variational methods. The success of variational approaches depends on (i)
formulating a flexible parametric family of distributions, and (ii) optimizing
the parameters to find the member of this family that most closely approximates
the exact posterior. In this paper we present a new approximating family of
distributions, the variational sequential Monte Carlo (VSMC) family, and show
how to optimize it in variational inference. VSMC melds variational inference
(VI) and sequential Monte Carlo (SMC), providing practitioners with flexible,
accurate, and powerful Bayesian inference. The VSMC family is a variational
family that can approximate the posterior arbitrarily well, while still
allowing for efficient optimization of its parameters. We demonstrate its
utility on state space models, stochastic volatility models for financial data,
and deep Markov models of brain neural circuits
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