Research map / Learning theory and algorithms / Sample complexity
Robust Density Estimation under Besov IPM Losses
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use scaled wavelet thresholding under arbitrary contamination | Besov IPM density estimation · Unstructured contamination, sparse regime | minimax risk rate: R(n, B_{p_g,q_g}^{σ_g}, B_{p_d,q_d}^{σ_d}) + ε + ε^{(σ_g+σ_d+D/p_d'-D/p_g)/(σ_g-D/p_g+D)} | Helped |
| Use a linear wavelet estimator instead of nonlinear thresholding | Besov IPM density estimation · Unstructured contamination, sparse regime | dependence of minimax rate on contamination ε: ε + ε^{(σ_g+σ_d+D/p_d'-D/p_g)/(σ_g-D/p_g+D)} | No clear effect |
| Assume the contamination density is bounded | Besov IPM density estimation · Structured versus unstructured contamination | contamination-dependent risk rate: ε | Helped |
| Assume additional smoothness of an already bounded contamination density | Besov IPM density estimation · Structured contamination | minimax risk rate | No clear effect |
| Use a ReLU GAN architecture with approximation error at most the wavelet estimator's convergence rate | Besov density estimation · Contaminated training data | risk rate: δ + R(n, B_{p_g,q_g}^{σ_g}, B_{p_d,q_d}^{σ_d}) + ε | Helped |
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