Research map / Learning theory and algorithms / Sample complexity
The Broad Optimality of Profile Maximum Likelihood
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PML for sorted distribution estimation | Distribution estimation · Sorted ℓ1 distribution estimation | sample complexity: Θ(k/(ε^2 log k)) | Helped |
| Use a PML plug-in estimator for additive symmetric 1-Lipschitz properties | Property estimation · Additive symmetric 1-Lipschitz properties | sample size: 4n; (2+o(1)) ε | Helped |
| Use PML for integer-order Rényi entropy estimation | Rényi entropy estimation · Integer α>1 | sample complexity: k^{1-1/α} | Helped |
| Use PML for non-integer Rényi entropy estimation | Rényi entropy estimation · Non-integer α>1 | sample complexity: k/(ε^{1/α} log k) | Helped |
| Use PML for Rényi entropy estimation | Rényi entropy estimation · α∈(3/4, 1) | sample complexity: k^{1/α}/(ε^{1/α} log k) | Helped |
| Use a PML-based tester | Identity testing · Uniformity testing | sample complexity: √k/ε^2 | Helped |
| Use the PML-based distribution estimator instead of improved Good-Turing | Unsorted ℓ1 distribution estimation · Six tested distributions | ℓ1 distance | Helped |
| Use the PML estimator instead of VV-LP | Sorted ℓ1 distribution estimation · Non-uniform tested distributions | sorted ℓ1 distance | Helped |
| Use VV-LP instead of PML | Sorted ℓ1 distribution estimation · Uniform distribution | sorted ℓ1 distance | Hurt |
| Use the PML-based estimator rather than the empirical and state-of-the-art estimators | Shannon entropy estimation · Shannon entropy | absolute error | No clear effect |
| Use the PML-based estimator instead of JVHW | Rényi entropy estimation · α=0.5 and α=1.5 | absolute error | Helped |
| Replace PML with truncated PML | Additive symmetric properties · Shannon entropy, support coverage, and support size | lower bound on ε: n^{-0.49} | Helped |
Closest papers by meaning
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