Research map / Learning theory and algorithms / Sample complexity
Non-asymptotic Error Bounds for Bidirectional GANs
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Specify generator, encoder, and discriminator network sizes as in the bounded-support theorem | BiGAN · Bounded-support BiGAN | expected Dudley distance: C_0 \sqrt{d} n^{-\frac{1}{d+1}}(\log n)^{\frac{1}{d+1}} | Helped |
| Allow the reference and target distributions to have different dimensions | BiGAN · Reference distribution on R^k and target distribution on R^d | expected Dudley distance: \min\big\{C_0 \sqrt{d} n^{-\frac{1}{d+k}}(\log n)^{1+\frac{1}{d+k}}, C_d n^{-\frac{1}{d+k}}\log n\big\} | Helped |
| Permit unbounded support under the stated tail conditions | BiGAN · Unbounded-support target and reference distributions | expected Dudley distance: \min\big\{C_0 \sqrt{d} n^{-\frac{1}{d+1}}(\log n)^{1+\frac{1}{d+1}}, C_d n^{-\frac{1}{d+1}}\log n\big\} | Helped |
| Use a bound with an explicit dimension-dependent prefactor | BiGAN stochastic error analysis · Unbounded-support BiGAN | expected Dudley distance: \sqrt{d} n^{-\frac{1}{d+1}}(\log n)^{1+\frac{1}{d+1}}; C_d n^{-\frac{1}{d+1}}\log n | Mixed |
| Construct generator and encoder networks to map empirical samples between dimensions | BiGAN · Empirical distributions with the same number of sample points | empirical approximation error: 0 | Helped |
| Use the novel four-term error decomposition | BiGAN estimation analysis · Latent joint distribution versus data joint distribution | Dudley distance upper bound: 2\mathcal{E}_1+\mathcal{E}_2+\mathcal{E}_3+\mathcal{E}_4 | Helped |
| Use a reference dimension k that differs from the data dimension d | BiGAN · Reference distribution on R^k, target distribution on R^d | rate exponent in expected Dudley distance: n^{-\frac{1}{d+1}}; n^{-\frac{1}{d+k}} | Mixed |
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