Summary of On the Statistical Representation Properties Of the Perturb-softmax and the Perturb-argmax Probability Distributions, by Hedda Cohen Indelman et al.
On The Statistical Representation Properties Of The Perturb-Softmax And The Perturb-Argmax Probability Distributions
by Hedda Cohen Indelman, Tamir Hazan
First submitted to arxiv on: 4 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Machine Learning (stat.ML)
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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 Gumbel-Softmax and Gumbel-Argmax probability distributions are used in generative and discriminative learning, respectively. Despite efforts to optimize them, their statistical properties remain under-explored. This paper investigates the representation properties of these distributions, determining which families of parameters make them complete (able to represent any probability distribution) or minimal (able to represent a probability distribution uniquely). The authors rely on convexity and differentiability to determine these conditions and extend the framework to general probability models like Gaussian-Softmax and Gaussian-Argmax. Experimental validation shows that these extensions enjoy a faster convergence rate. The paper concludes by identifying two sets of parameters that satisfy the assumptions, allowing for complete and minimal representation. This theoretical work is supported by practical evaluation. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The researchers studied special kinds of probability distributions used in machine learning. They wanted to know how well these distributions could represent different possibilities. To do this, they looked at what happens when you change certain numbers that are part of the distribution. They found some patterns and rules that help us understand how well these distributions work. This is important because it can make machine learning algorithms more efficient and effective. The researchers also tested their ideas to see if they really worked. |
Keywords
» Artificial intelligence » Machine learning » Probability » Softmax
