Summary of Asymptotics Of Stochastic Gradient Descent with Dropout Regularization in Linear Models, by Jiaqi Li et al.
Asymptotics of Stochastic Gradient Descent with Dropout Regularization in Linear Models
by Jiaqi Li, Johannes Schmidt-Hieber, Wei Biao Wu
First submitted to arxiv on: 11 Sep 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Statistics Theory (math.ST)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The proposed asymptotic theory provides an online inference framework for stochastic gradient descent (SGD) iterates with dropout regularization in linear regression. By establishing geometric-moment contraction and quenched central limit theorems, the paper shows the existence of a unique stationary distribution of the dropout recursive function. This leads to online estimators for long-run covariance matrices, facilitating recursive inference with improved computational efficiency. The results are demonstrated through numerical experiments, achieving near-nominal coverage probabilities for sufficiently large samples. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us understand how computers can learn from data by using a special type of algorithm called stochastic gradient descent (SGD). The authors want to know what happens when we add something called dropout regularization to this process. They develop a new theory that explains how the computer’s calculations change over time, which is important for making predictions and drawing conclusions about the data. By doing this, they can create more efficient ways to analyze big datasets and make better decisions. |
Keywords
» Artificial intelligence » Dropout » Inference » Linear regression » Regularization » Stochastic gradient descent
