Summary of Statistical Properties Of Deep Neural Networks with Dependent Data, by Chad Brown
Statistical Properties of Deep Neural Networks with Dependent Data
by Chad Brown
First submitted to arxiv on: 14 Oct 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Econometrics (econ.EM)
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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 This paper explores the statistical properties of deep neural network (DNN) estimators under dependent data. It presents two general results for nonparametric sieve estimators applicable to DNN estimators, including rates for convergence in probability under nonstationary data and non-asymptotic probability bounds on L2-errors under stationary beta-mixing data. The paper then applies these results to DNN estimators in regression and classification contexts, assuming only a standard Hölder smoothness assumption. The considered DNN architectures are common in applications, featuring fully connected feedforward networks with any continuous piecewise linear activation function, unbounded weights, and growing width and depth with sample size. This framework has potential for research into other DNN architectures and time-series applications. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how deep neural networks (DNNs) work when the data isn’t independent. It finds two important facts about DNNs: one says that they get better and better as the data gets bigger, even if the data isn’t constant; and the other says that they make mistakes less often under certain conditions. The paper then uses these findings to understand how DNNs work in different situations, like when we’re trying to predict a number or classifying something. The kinds of DNNs studied are the kind used in many real-world applications. |
Keywords
» Artificial intelligence » Classification » Neural network » Probability » Regression » Time series
