Theoretical analysis of the denoising autoencoder using Tweedie's formula.
1Graduate school of Science and Technology, Information Science, Nara Institute of Science and Technology, 8916-5, Takayama-cho, Ikoma, 630-0192, Nara, Japan.
Summary
Denoising autoencoders can now be analyzed beyond Gaussian noise. This study extends their analysis to exponential families, revealing they capture essential data statistics and corrupted data scores.
Area of Science:
- Machine Learning
- Statistical Inference
- Information Theory
Background:
- Denoising autoencoders (DAEs) are powerful generative models.
- Classical analysis of DAEs is limited to Gaussian corruption processes.
- Non-Gaussian corruption is prevalent in real-world data.
Purpose of the Study:
- Extend the theoretical analysis of DAEs to non-Gaussian corruption.
- Introduce a new formulation of DAEs using Tweedie's formula.
- Elucidate the theoretical underpinnings of DAEs in broader settings.
Main Methods:
- Leveraging Tweedie's formula for exponential families.
- Developing an empirical Bayes estimator for DAEs.
- Analyzing the conditional expectation of sufficient statistics.
Main Results:
- DAEs capture the conditional expectation of the sufficient statistic under exponential family corruption.
- This captured quantity estimates an information-theoretically compressed representation.
- The DAE implicitly captures the score of the corrupted data distribution.
Conclusions:
- The generalized DAE formulation handles exponential family corruption.
- DAEs simultaneously estimate sufficient statistics and corrupted data scores.
- Theoretical findings are supported by numerical experiments.
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