Online Statistical Inference for Gradient-free Stochastic Optimization

02/05/2021
by   Xi Chen, et al.
0

As gradient-free stochastic optimization gains emerging attention for a wide range of applications recently, the demand for uncertainty quantification of parameters obtained from such approaches arises. In this paper, we investigate the problem of statistical inference for model parameters based on gradient-free stochastic optimization methods that use only function values rather than gradients. We first present central limit theorem results for Polyak-Ruppert-averaging type gradient-free estimators. The asymptotic distribution reflects the trade-off between the rate of convergence and function query complexity. We next construct valid confidence intervals for model parameters through the estimation of the covariance matrix in a fully online fashion. We further give a general gradient-free framework for covariance estimation and analyze the role of function query complexity in the convergence rate of the covariance estimator. This provides a one-pass computationally efficient procedure for simultaneously obtaining an estimator of model parameters and conducting statistical inference. Finally, we provide numerical experiments to verify our theoretical results and illustrate some extensions of our method for various machine learning and deep learning applications.

READ FULL TEXT

page 1

page 2

page 3

page 4

02/10/2021

Statistical Inference for Polyak-Ruppert Averaged Zeroth-order Stochastic Gradient Algorithm

As machine learning models are deployed in critical applications, it bec...
05/27/2022

Asymptotic Convergence Rate and Statistical Inference for Stochastic Sequential Quadratic Programming

We apply a stochastic sequential quadratic programming (StoSQP) algorith...
12/20/2017

Statistical Inference for the Population Landscape via Moment Adjusted Stochastic Gradients

Modern statistical inference tasks often require iterative optimization ...
06/16/2020

Efficient nonparametric statistical inference on population feature importance using Shapley values

The true population-level importance of a variable in a prediction task ...
10/27/2016

Statistical Inference for Model Parameters in Stochastic Gradient Descent

The stochastic gradient descent (SGD) algorithm has been widely used in ...
03/26/2020

Quantifying deviations from separability in space-time functional processes

The estimation of covariance operators of spatio-temporal data is in man...
05/22/2022

Nonparametric likelihood-free inference with Jensen-Shannon divergence for simulator-based models with categorical output

Likelihood-free inference for simulator-based statistical models has rec...