1 research outputs found
Scalable Approximate Inference and Some Applications
Approximate inference in probability models is a fundamental task in machine
learning. Approximate inference provides powerful tools to Bayesian reasoning,
decision making, and Bayesian deep learning. The main goal is to estimate the
expectation of interested functions w.r.t. a target distribution. When it comes
to high dimensional probability models and large datasets, efficient
approximate inference becomes critically important. In this thesis, we propose
a new framework for approximate inference, which combines the advantages of
these three frameworks and overcomes their limitations. Our proposed four
algorithms are motivated by the recent computational progress of Stein's
method. Our proposed algorithms are applied to continuous and discrete
distributions under the setting when the gradient information of the target
distribution is available or unavailable. Theoretical analysis is provided to
prove the convergence of our proposed algorithms. Our adaptive IS algorithm
iteratively improves the importance proposal by functionally decreasing the KL
divergence between the updated proposal and the target. When the gradient of
the target is unavailable, our proposed sampling algorithm leverages the
gradient of a surrogate model and corrects induced bias with importance
weights, which significantly outperforms other gradient-free sampling
algorithms. In addition, our theoretical results enable us to perform the
goodness-of-fit test on discrete distributions. At the end of the thesis, we
propose an importance-weighted method to efficiently aggregate local models in
distributed learning with one-shot communication. Results on simulated and real
datasets indicate the statistical efficiency and wide applicability of our
algorithm.Comment: PhD thesis, Dartmouth College (2019