Summary of Enhanced Feature Learning Via Regularisation: Integrating Neural Networks and Kernel Methods, by Bertille Follain and Francis Bach
Enhanced Feature Learning via Regularisation: Integrating Neural Networks and Kernel Methods
by Bertille Follain, Francis Bach
First submitted to arxiv on: 24 Jul 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 proposes a novel approach for feature learning and function estimation in supervised learning using regularized empirical risk minimization. The method views functions as expectations of Sobolev functions over all possible one-dimensional projections of the data, similar to kernel ridge regression with a Brownian kernel. This framework can be seen as an infinite-width one-hidden layer neural network optimizing the first layer’s weights through gradient descent and adjusting the non-linearity and weights of the second layer explicitly. The paper introduces an efficient computation method called Brownian Kernel Neural Network (BKerNN) using particles to approximate the expectation. The optimization is principled due to the positive homogeneity of the Brownian kernel. The expected risk of BKerNN converges to the minimal risk with high-probability rates, and numerical experiments confirm the optimisation intuitions, outperforming kernel ridge regression and favourably comparing to a one-hidden layer neural network with ReLU activations in various settings and real datasets. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about finding new ways to learn patterns from data. It’s like training a model on how to recognize certain features or shapes. The researchers came up with a new method that works by looking at all possible ways to project the data onto one-dimensional lines, kind of like how we might look at different angles when trying to understand something. This approach is similar to another popular way to do this called kernel ridge regression, but it uses a special type of mathematical function called the Brownian kernel. The new method is like a super-powerful neural network that can learn and adapt really well. It’s been tested on real-world data and has performed better than some other methods. |
Keywords
» Artificial intelligence » Gradient descent » Neural network » Optimization » Probability » Regression » Relu » Supervised
