Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

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The categories of this paper are: math
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph