Research map / Learning theory and algorithms / Sample complexity
Nonparametric Density Estimation under Adversarial Losses
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a truncated orthogonal series estimator with smoothness-aware tuning | Density estimation under adversarial losses · Sobolev density estimation | minimax adversarial risk rate: n^{-\min \left\{ \frac{1}{2}, \frac{s + t}{2t + d} \right\}} | Helped |
| Restrict the generator class to distributions with greater smoothness | Density estimation under a Sobolev discriminator loss · Sobolev density estimation | minimax adversarial risk rate: n^{-\min \left\{ \frac{1}{2}, \frac{s + t}{2t + d} \right\}} | Helped |
| Use a translation-invariant RKHS discriminator loss | Density estimation over any distribution class · Translation-invariant RKHS/MMD | minimax adversarial risk rate: n^{-1/2} | Helped |
| Adapt the truncation parameter using a data-dependent choice independent of smoothness | Orthogonal series density estimation · Sobolev density estimation | adversarial risk | Helped |
| Use a perfectly optimized ReLU GAN with architecture sizes tied to smoothness | GAN density estimation · Sobolev density estimation | expected adversarial risk upper bound: C \left( \epsilon + n^{-\min \left\{ \frac{1}{2}, \frac{s + t}{2t + d} \right\}} \right) | Helped |
| Estimate the implicit distribution of a sampler from generated samples | Implicit generative models satisfying the theorem's conditions · Minimax sampling versus density estimation | minimax risk: M_D(\mathcal{F}_G,\ell,n) \leq C_\triangle M_I(\mathcal{F}_G,\ell,n) | No clear effect |
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