PMID- 17930123
OWN - NLM
STAT- PubMed-not-MEDLINE
DCOM- 20080206
LR  - 20220310
IS  - 1539-3755 (Print)
IS  - 1539-3755 (Linking)
VI  - 76
IP  - 2 Pt 2
DP  - 2007 Aug
TI  - Relative performance of mutual information estimation methods for quantifying the 
      dependence among short and noisy data.
PG  - 026209
AB  - Commonly used dependence measures, such as linear correlation, cross-correlogram, 
      or Kendall's tau , cannot capture the complete dependence structure in data 
      unless the structure is restricted to linear, periodic, or monotonic. Mutual 
      information (MI) has been frequently utilized for capturing the complete 
      dependence structure including nonlinear dependence. Recently, several methods 
      have been proposed for the MI estimation, such as kernel density estimators 
      (KDEs), k -nearest neighbors (KNNs), Edgeworth approximation of differential 
      entropy, and adaptive partitioning of the XY plane. However, outstanding gaps in 
      the current literature have precluded the ability to effectively automate these 
      methods, which, in turn, have caused limited adoptions by the application 
      communities. This study attempts to address a key gap in the 
      literature-specifically, the evaluation of the above methods to choose the best 
      method, particularly in terms of their robustness for short and noisy data, based 
      on comparisons with the theoretical MI estimates, which can be computed 
      analytically, as well with linear correlation and Kendall's tau . Here we 
      consider smaller data sizes, such as 50, 100, and 1000, and within this study we 
      characterize 50 and 100 data points as very short and 1000 as short. We consider 
      a broader class of functions, specifically linear, quadratic, periodic, and 
      chaotic, contaminated with artificial noise with varying noise-to-signal ratios. 
      Our results indicate KDEs as the best choice for very short data at relatively 
      high noise-to-signal levels whereas the performance of KNNs is the best for very 
      short data at relatively low noise levels as well as for short data consistently 
      across noise levels. In addition, the optimal smoothing parameter of a Gaussian 
      kernel appears to be the best choice for KDEs while three nearest neighbors 
      appear optimal for KNNs. Thus, in situations where the approximate data sizes are 
      known in advance and exploratory data analysis and/or domain knowledge can be 
      used to provide a priori insights into the noise-to-signal ratios, the results in 
      the paper point to a way forward for automating the process of MI estimation.
FAU - Khan, Shiraj
AU  - Khan S
AD  - Computational Sciences and Engineering, Oak Ridge National Laboratory, Oak Ridge, 
      Tennessee 37831, USA.
FAU - Bandyopadhyay, Sharba
AU  - Bandyopadhyay S
FAU - Ganguly, Auroop R
AU  - Ganguly AR
FAU - Saigal, Sunil
AU  - Saigal S
FAU - Erickson, David J 3rd
AU  - Erickson DJ 3rd
FAU - Protopopescu, Vladimir
AU  - Protopopescu V
FAU - Ostrouchov, George
AU  - Ostrouchov G
LA  - eng
PT  - Journal Article
DEP - 20070814
PL  - United States
TA  - Phys Rev E Stat Nonlin Soft Matter Phys
JT  - Physical review. E, Statistical, nonlinear, and soft matter physics
JID - 101136452
EDAT- 2007/10/13 09:00
MHDA- 2007/10/13 09:01
CRDT- 2007/10/13 09:00
PHST- 2007/02/06 00:00 [received]
PHST- 2007/05/17 00:00 [revised]
PHST- 2007/10/13 09:00 [pubmed]
PHST- 2007/10/13 09:01 [medline]
PHST- 2007/10/13 09:00 [entrez]
AID - 10.1103/PhysRevE.76.026209 [doi]
PST - ppublish
SO  - Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Aug;76(2 Pt 2):026209. doi: 
      10.1103/PhysRevE.76.026209. Epub 2007 Aug 14.