content_image/327106.jpg content_image/327112.jpg
<img src='content_image/327106.jpg'>

simulated 50 datasets and computed the estimated mutual information using S DDP m × $_{m}$, 

S ADP m × $_{m}$, and the histogram estimator. The Gaussian mixture density was 

<img src='content_image/327112.jpg'>

where f$_{N}$ ( µ, Σ) is the bivariate normal distribution with mean µ and covariance ma- trix Σ. For each partition, we applied the Miller–Madow correction (Paninski, 2003), a simple and well-known modification that estimates the systematic error of the his- togram estimators and improves the finite-sample properties of these estimators. We compared it to the histogram estimator, as well as to the estimator based on the DDP statistic that considers only a subset of all possible partitions. Table 5 shows that the variability and the bias decrease as N increases for all estimators, and that the ADP estimator is the least variable, as is intuitively expected since it is the average over many partitions. In practice, it is difficult to identify the optimal m : it should not be too small so that the local dependence structure is not missed, causing large bias, nor should it be too large so that the grid created is too sparse, causing large variance. 

