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On Constructing Confidence Region for Model Parameters in Stochastic Gradient Descent via Batch Means
Machine Learning · Submitted 4 Nov 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In this paper, we study a simple algorithm to construct asymptotically valid confidence regions for model parameters using the batch means method.
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The abstract, sentence by sentence
In this paper, we study a simple algorithm to construct asymptotically valid confidence regions for model parameters using the batch means method. The main idea is to cancel out the covariance matrix which is hard/costly to estimate. In the process of developing the algorithm, we establish process-level functional central limit theorem for Polyak-Ruppert averaging based stochastic gradient descent estimators. We also extend the batch means method to accommodate more general batch size specifications.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this paper, we study a simple algorithm to construct asymptotically valid confidence regions for model parameters using the batch means method. | contribution 1.00 | 0.89 | 0.36 | asserted 0.94 |
| s1 | The main idea is to cancel out the covariance matrix which is hard/costly to estimate. | method 0.88 | 0.53 | 0.25 | asserted 1.00 |
| s2 | In the process of developing the algorithm, we establish process-level functional central limit theorem for Polyak-Ruppert averaging based stochastic gradient descent estimators. | contribution 0.82 | 0.95 | 0.11 | asserted 1.00 |
| s3 | We also extend the batch means method to accommodate more general batch size specifications. | contribution 0.98 | 0.93 | 0.08 | asserted 1.00 |
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The paper
Original abstract
In this paper, we study a simple algorithm to construct asymptotically valid confidence regions for model parameters using the batch means method. The main idea is to cancel out the covariance matrix which is hard/costly to estimate. In the process of developing the algorithm, we establish process-level functional central limit theorem for Polyak-Ruppert averaging based stochastic gradient descent estimators. We also extend the batch means method to accommodate more general batch size specifications.
Human review
How the literature uses it
2 arXiv papers cite this in 4 sentences
Papers citing it · 2 sentences without a confident label
Compares with it 1 paper
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[ref] appears closer than the others to our FCLT for the partial sums, although the set of sufficient conditions is not the same as ours.
Fast and Robust Online Inference with Stochastic Gradient Descent via Random Scaling · Functional central limit theorem for online SGD · 1.00
Cites it as background 1 paper
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Not for but for the standard optimizer and closely related methods there are also a number of works in the literature that establish error analyses and for averages of the considered optimizer; cf., , [ref] , [ref] , [ref] , [ref] , [ref] , [ref] , and [ref] .
Central limit theorem for the averaged Adam optimizer · Context discussion and literature review · 0.94
What it cites · 2 sentences without a confident label
Uses the method or tool of 1 paper
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To understand the correlation between $Ξ_i$ and $Ξ_i+1$, we follow the arguments in [ref] .
Statistical Inference for Model Parameters in Stochastic Gradient Descent · Batch size · 0.80
Compares with 2 papers
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The main difference between our method and the one in [ref] is that the method in [ref] requires sending $m$ to infinity as $T$ goes to infinity, while our method holds $m$ fixed.
Statistical Inference for Model Parameters in Stochastic Gradient Descent · Batch size · 1.00
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Specifically, the methods are developed in [ref] and [ref] , which we refer to as batch means with an increasing number of batches (BMI) and hierarchical incremental gradient descent (HiGrad), respectively.
HiGrad: Uncertainty Quantification for Online Learning and Stochastic Approximation · Comparison to other methods · 1.00
Cites as background 3 papers
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Before we present the theorem, we first introduce a few assumptions, which are standard for the convergence analysis of Polyak-Ruppert averaging, e.g., [ref] .
Statistical Inference for Model Parameters in Stochastic Gradient Descent · Batch means method · 0.86
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While there is a rich literature studying convergence rate of the objective function or the parameter estimation errors based on stochastic gradient descent, e.g., [ref] , much less is known about the statistical inference for true model parameters [ref] .
On Scalable Inference with Stochastic Gradient Descent · Introduction · 0.90
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While there is a rich literature studying convergence rate of the objective function or the parameter estimation errors based on stochastic gradient descent, e.g., [ref] , much less is known about the statistical inference for true model parameters [ref] .
HiGrad: Uncertainty Quantification for Online Learning and Stochastic Approximation · Introduction · 0.90
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