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dmitrip authored Oct 14, 2017
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Expand Up @@ -34,11 +34,11 @@ Root mean squared error (RMSE) in estimating entropy (unknown support set size)
+ `WY` is Wu and Yang, "Minimax rates of entropy estimation on large alphabets via best polynomial approximation" 2014 [link](https://arxiv.org/abs/1407.0381). This estimator requires the support set size as an input.
+ `approx. PML` is the method implemented here.

<p align="center"><img src="https://github.com/dmitrip/PML/blob/master/.github/approx_PML_performance_github.png" alt="performance of PML approximate distribution plug-in estimator" width="100%"/></p>
<p align="center"><img src="https://github.com/dmitrip/PML/blob/master/.github/approx_PML_performance_github.png" alt="performance of PML approximate distribution plug-in estimator" width="80%"/></p>

RMSE in estimating the L₁ distance between distributions `p` and `q`. `Zipf(α)` is the distribution `p[i] ~ i^α` up to normalization with finite support 10^4.
RMSE in estimating the L₁ distance between distributions `p` (constant in each row below) and `q` (constant in each column below). `Zipf(α)` is the distribution `p[i] ~ i^α` up to normalization with finite support 10^4.

<p align="center"><img src="https://github.com/dmitrip/PML/blob/master/.github/approx_PML_performance_L1_distance_github.png" alt="performance of PML approximate distribution plug-in estimator" width="100%"/></p>
<p align="center"><img src="https://github.com/dmitrip/PML/blob/master/.github/approx_PML_performance_L1_distance_github.png" alt="performance of PML approximate distribution plug-in estimator" width="80%"/></p>

## Usage

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