Abstract | ||
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We consider a linear autoencoder in which the latent variables are quantized, or corrupted by noise, and the constraint is Schur-concave in the set of latent variances. Although finding the optimal encoder/decoder pair for this setup is a nonconvex optimization problem, we show that decomposing the source into its principal components is optimal. If the constraint is strictly Schur-concave and the empirical covariance matrix has only simple eigenvalues, then any optimal encoder/decoder must decompose the source in this way. As one application, we consider a strictly Schur-concave constraint that estimates the number of bits needed to represent the latent variables under fixed-rate encoding, a setup that we call Principal Bit Analysis (PBA). This yields a practical, general-purpose, fixed-rate compressor that outperforms existing algorithms. As a second application, we show that a prototypical autoencoder-based variable-rate compressor is guaranteed to decompose the source into its principal components. |
Year | Venue | DocType |
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2021 | INTERNATIONAL CONFERENCE ON MACHINE LEARNING, VOL 139 | Conference |
Volume | ISSN | Citations |
139 | 2640-3498 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
---|---|---|---|
Sourbh Bhadane | 1 | 0 | 0.34 |
Aaron B. Wagner | 2 | 322 | 37.39 |
Jayadev Acharya | 3 | 209 | 26.37 |