Journal ArticleVol. · September 27, 2021
We study the mixing time of the Metropolis-adjusted Langevin algorithm (MALA)
for sampling from a log-smooth and strongly log-concave distribution. We
establish its optimal minimax mixing time under a warm start. Our main
contribution is two-fold. First, f ...
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Journal Article · November 27, 2020
We prove an almost constant lower bound of the isoperimetric coefficient in
the KLS conjecture. The lower bound has the dimension dependency $d^{-o_d(1)}$.
When the dimension is large enough, our lower bound is tighter than the
previous best bound which ha ...
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Journal Article · October 29, 2020
Domain adaptation (DA) arises as an important problem in statistical machine
learning when the source data used to train a model is different from the
target data used to test the model. Recent advances in DA have mainly been
application-driven and have la ...
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Journal ArticleProceedings of the National Academy of Sciences of the United States of America · October 2019
Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical understanding of the relati ...
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Journal Article · May 29, 2019
Hamiltonian Monte Carlo (HMC) is a state-of-the-art Markov chain Monte Carlo
sampling algorithm for drawing samples from smooth probability densities over
continuous spaces. We study the variant most widely used in practice,
Metropolized HMC with the St\"{ ...
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Journal Article · November 9, 2018
AbstractDeep neural network models have recently been shown to be effective in predicting single neuron responses in primate visual cortex areas V4. Despite their high predictive accuracy, these models are generally difficu ...
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Journal Article · April 4, 2018
The overall performance or expected excess risk of an iterative machine
learning algorithm can be decomposed into training error and generalization
error. While the former is controlled by its convergence analysis, the latter
can be tightly handled by algo ...
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Journal ArticleJournal of Machine Learning Research, 2019 · January 8, 2018
We consider the problem of sampling from a strongly log-concave density in
$\mathbb{R}^d$, and prove a non-asymptotic upper bound on the mixing time of
the Metropolis-adjusted Langevin algorithm (MALA). The method draws samples by
simulating a Markov chain ...
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Journal ArticleThe Journal of Machine Learning Research · October 23, 2017
We propose and analyze two new MCMC sampling algorithms, the Vaidya walk and
the John walk, for generating samples from the uniform distribution over a
polytope. Both random walks are sampling algorithms derived from interior point
methods. The former is b ...
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