Research map / Learning theory and algorithms / Sample complexity
Sample Complexity of Probability Divergences under Group Symmetry
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Restrict the variational test functions to group-invariant functions | Wasserstein-1 estimation between finite-group-invariant distributions · Wasserstein-1 | estimation error bound: ((1/(|Σ|m))^(1/(d+s)) + (1/(|Σ|n))^(1/(d+s))) | Helped |
| Restrict the variational test functions to group-invariant functions | Wasserstein-1 estimation with an infinite group · Wasserstein-1 | estimation error bound: ((vol(X₀)/m)^(1/(d*+s)) + (vol(X₀)/n)^(1/(d*+s))) | Helped |
| Restrict the variational test functions to group-invariant functions | Lipschitz-regularized α-divergence estimation between finite-group-invariant distributions · Lipschitz-regularized α-divergence | estimation error bound: ((1/(|Σ|m))^(1/(d+s)) + (1/(|Σ|n))^(1/(d+s))) | Helped |
| Restrict the variational test functions to group-invariant functions | Lipschitz-regularized α-divergence estimation with an infinite group · Lipschitz-regularized α-divergence | estimation error bound: ((vol(X₀)/m)^(1/(d*+s)) + (vol(X₀)/n)^(1/(d*+s))) | Helped |
| Use group-invariant test functions with a kernel satisfying the orbit-decay condition | MMD estimation between finite-group-invariant distributions · MMD | estimation error bound: C_{Σ,k}=√((1+c_{Σ,k}(|Σ|-1))/|Σ|) | Helped |
| Increase group size while keeping the kernel fixed | MMD estimation · MMD | sample-complexity improvement | Mixed |
| Adapt the Gaussian-kernel bandwidth inversely with group size | MMD estimation · MMD | sample-complexity improvement: C_{Σ,k}≈1/√|Σ| | Helped |
| Increase the assumed group size from 1 to 4, 16, 64, and 256 | W^Σ empirical estimator · Wasserstein-1, [0,1) | adjacent-group-size error ratio: 4 | Helped |
| Increase the assumed group size from 1 to 2 and 4 | W^Σ empirical estimator · Wasserstein-1, R² | adjacent-group-size error ratio: √2≈1.414 | Helped |
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