506 research outputs found
High-Order Stochastic Gradient Thermostats for Bayesian Learning of Deep Models
Learning in deep models using Bayesian methods has generated significant
attention recently. This is largely because of the feasibility of modern
Bayesian methods to yield scalable learning and inference, while maintaining a
measure of uncertainty in the model parameters. Stochastic gradient MCMC
algorithms (SG-MCMC) are a family of diffusion-based sampling methods for
large-scale Bayesian learning. In SG-MCMC, multivariate stochastic gradient
thermostats (mSGNHT) augment each parameter of interest, with a momentum and a
thermostat variable to maintain stationary distributions as target posterior
distributions. As the number of variables in a continuous-time diffusion
increases, its numerical approximation error becomes a practical bottleneck, so
better use of a numerical integrator is desirable. To this end, we propose use
of an efficient symmetric splitting integrator in mSGNHT, instead of the
traditional Euler integrator. We demonstrate that the proposed scheme is more
accurate, robust, and converges faster. These properties are demonstrated to be
desirable in Bayesian deep learning. Extensive experiments on two canonical
models and their deep extensions demonstrate that the proposed scheme improves
general Bayesian posterior sampling, particularly for deep models.Comment: AAAI 201
Implicit Langevin Algorithms for Sampling From Log-concave Densities
For sampling from a log-concave density, we study implicit integrators
resulting from -method discretization of the overdamped Langevin
diffusion stochastic differential equation. Theoretical and algorithmic
properties of the resulting sampling methods for and a
range of step sizes are established. Our results generalize and extend prior
works in several directions. In particular, for , we prove
geometric ergodicity and stability of the resulting methods for all step sizes.
We show that obtaining subsequent samples amounts to solving a strongly-convex
optimization problem, which is readily achievable using one of numerous
existing methods. Numerical examples supporting our theoretical analysis are
also presented
Self-Adversarially Learned Bayesian Sampling
Scalable Bayesian sampling is playing an important role in modern machine
learning, especially in the fast-developed unsupervised-(deep)-learning models.
While tremendous progresses have been achieved via scalable Bayesian sampling
such as stochastic gradient MCMC (SG-MCMC) and Stein variational gradient
descent (SVGD), the generated samples are typically highly correlated.
Moreover, their sample-generation processes are often criticized to be
inefficient. In this paper, we propose a novel self-adversarial learning
framework that automatically learns a conditional generator to mimic the
behavior of a Markov kernel (transition kernel). High-quality samples can be
efficiently generated by direct forward passes though a learned generator. Most
importantly, the learning process adopts a self-learning paradigm, requiring no
information on existing Markov kernels, e.g., knowledge of how to draw samples
from them. Specifically, our framework learns to use current samples, either
from the generator or pre-provided training data, to update the generator such
that the generated samples progressively approach a target distribution, thus
it is called self-learning. Experiments on both synthetic and real datasets
verify advantages of our framework, outperforming related methods in terms of
both sampling efficiency and sample quality.Comment: AAAI 201
- …