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Neural networks efficiently learn low-dimensional representations with sgd
We study the problem of training a two-layer neural network (NN) of arbitrary width using
stochastic gradient descent (SGD) where the input $\boldsymbol {x}\in\mathbb {R}^ d $ is …
stochastic gradient descent (SGD) where the input $\boldsymbol {x}\in\mathbb {R}^ d $ is …
A selective review on statistical methods for massive data computation: distributed computing, subsampling, and minibatch techniques
This paper presents a selective review of statistical computation methods for massive data
analysis. A huge amount of statistical methods for massive data computation have been …
analysis. A huge amount of statistical methods for massive data computation have been …
Towards a complete analysis of langevin monte carlo: Beyond poincaré inequality
Langevin diffusions are rapidly convergent under appropriate functional inequality
assumptions. Hence, it is natural to expect that with additional smoothness conditions to …
assumptions. Hence, it is natural to expect that with additional smoothness conditions to …
On the convergence of langevin monte carlo: The interplay between tail growth and smoothness
We study sampling from a target distribution $\nu_*= e^{-f} $ using the unadjusted Langevin
Monte Carlo (LMC) algorithm. For any potential function $ f $ whose tails behave like …
Monte Carlo (LMC) algorithm. For any potential function $ f $ whose tails behave like …
Convergence rates of stochastic gradient descent under infinite noise variance
Recent studies have provided both empirical and theoretical evidence illustrating that heavy
tails can emerge in stochastic gradient descent (SGD) in various scenarios. Such heavy tails …
tails can emerge in stochastic gradient descent (SGD) in various scenarios. Such heavy tails …
Bias and extrapolation in Markovian linear stochastic approximation with constant stepsizes
We consider Linear Stochastic Approximation (LSA) with constant stepsize and Markovian
data. Viewing the joint process of the data and LSA iterate as a time-homogeneous Markov …
data. Viewing the joint process of the data and LSA iterate as a time-homogeneous Markov …
Stochastic multilevel composition optimization algorithms with level-independent convergence rates
In this paper, we study smooth stochastic multilevel composition optimization problems,
where the objective function is a nested composition of T functions. We assume access to …
where the objective function is a nested composition of T functions. We assume access to …
Convergence of Langevin Monte Carlo in chi-squared and Rényi divergence
We study sampling from a target distribution $\nu_*= e^{-f} $ using the unadjusted Langevin
Monte Carlo (LMC) algorithm when the potential $ f $ satisfies a strong dissipativity condition …
Monte Carlo (LMC) algorithm when the potential $ f $ satisfies a strong dissipativity condition …
Fractal structure and generalization properties of stochastic optimization algorithms
Understanding generalization in deep learning has been one of the major challenges in
statistical learning theory over the last decade. While recent work has illustrated that the …
statistical learning theory over the last decade. While recent work has illustrated that the …
Computing the bias of constant-step stochastic approximation with markovian noise
We study stochastic approximation algorithms with Markovian noise and constant step-size
$\alpha $. We develop a method based on infinitesimal generator comparisons to study the …
$\alpha $. We develop a method based on infinitesimal generator comparisons to study the …