Summary of A Statistical Analysis For Supervised Deep Learning with Exponential Families For Intrinsically Low-dimensional Data, by Saptarshi Chakraborty and Peter L. Bartlett
A Statistical Analysis for Supervised Deep Learning with Exponential Families for Intrinsically Low-dimensional Data
by Saptarshi Chakraborty, Peter L. Bartlett
First submitted to arxiv on: 13 Dec 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 A recent study revealed that the convergence rate of deep supervised learning is influenced by the intrinsic dimension rather than the input space’s dimension. Existing methods define intrinsic dimension as Minkowski or manifold dimension, leading to suboptimal rates and unrealistic assumptions. This paper proposes an entropic notion of intrinsic data-dimension and shows that test error scales as (n^{-}) with n samples, improving the best-known rates. The study also characterizes the rate of convergence under upper-bounded densities and establishes that dependence on d is at most polynomial rather than exponential. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Deep learning has made great progress recently! But have you ever wondered how fast it can learn from data? This paper helps us understand this by looking at a special kind of dimension called the “intrinsic dimension”. It turns out that this dimension affects how quickly deep learning algorithms improve, not just the number of data points. The researchers also find that if we assume some nice properties about the data, we can even get nearly-optimal results for learning complex relationships between variables. |
Keywords
* Artificial intelligence * Deep learning * Supervised
