Summary of Minimax Optimality Of Deep Neural Networks on Dependent Data Via Pac-bayes Bounds, by Pierre Alquier and William Kengne
Minimax optimality of deep neural networks on dependent data via PAC-Bayes bounds
by Pierre Alquier, William Kengne
First submitted to arxiv on: 29 Oct 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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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 builds upon previous work by Schmidt-Hieber (2020), which established the optimality of deep neural networks with ReLu activation for least-square regression estimation. The authors extend these results to more general machine learning problems, including logistic regression. They relax the assumption of independent and identically distributed observations, instead allowing for time dependence modeled as a Markov chain. Using PAC-Bayes oracle inequalities and a version of Bernstein’s inequality due to Paulin (2015), the authors derive upper bounds on the estimation risk for a generalized Bayesian estimator. In the case of least-square regression, this bound matches the lower bound from Schmidt-Hieber (2020) up to a logarithmic factor. The authors also establish a similar lower bound for classification with logistic loss and prove that their DNN estimator is minimax optimal. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper makes some big discoveries about how computers can learn from data. It’s like solving a puzzle, but instead of pieces fitting together, it’s all about finding the best way to make predictions. The researchers started with something called ReLu activation and least-square regression, which is important for things like image recognition. Then, they made it more complicated by allowing some time dependence in the data. They also looked at other types of problems, like predicting what someone will say or do next. The results show that a special kind of computer model, called a deep neural network, can be really good at solving these problems. |
Keywords
» Artificial intelligence » Classification » Logistic regression » Machine learning » Neural network » Regression » Relu
