Estimation of mutual information using kernel density estimators

Moon, Young‐Il; Rajagopalan, Balaji; Lall, Upmanu

doi:10.1103/physreve.52.2318

Cited by 399 publications

(294 citation statements)

References 16 publications

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“…However, where stimuli and responses are both continuous (an example might be local field potential responses to a white noise sensory stimulus), it may be advantageous to take advantages of techniques better suited to continuous signals, such as kernel density estimators (Moon et al, 1995), nearest neighbor estimators (Kraskov et al, 2004) or binless metric space methods (Victor, 2002). We refer to the entry "Bin--Less Estimators for Information Quantities" for an in--depth discussion of these techniques.…”

Section: Binless Methods For Estimating Informationmentioning

confidence: 99%

Estimating Information-Theoretic Quantities

Ince¹,

Schultz²,

Panzeri

2015

Encyclopedia of Computational Neuroscience

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(Tn) Italy16 pages 5724 words. DefinitionInformation theory is a practical and theoretical framework developed for the study of communication over noisy channels. Its probabilistic basis and capacity to relate statistical structure to function make it ideally suited for studying information flow in the nervous system. It has a number of useful properties: it is a general measure sensitive to any relationship, not only linear effects; it has meaningful units which in many cases allow direct comparison between different experiments; and it can be used to study how much information can be gained by observing neural responses in single trials, rather than in averages over multiple trials. A variety of information theoretic quantities are in common use in neuroscience -(see entry "Summary of Information--Theoretic Quantities"). Estimating these quantities in an accurate and unbiased way from real neurophysiological data frequently presents challenges, which are explained in this entry.

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Section: Binless Methods For Estimating Informationmentioning

confidence: 99%

Estimating Information-Theoretic Quantities

Ince¹,

Schultz²,

Panzeri

2015

Encyclopedia of Computational Neuroscience

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“…An MI value equal to 0 indicates complete independence between x and y, while a higher MI value indicates stronger dependence between x and y (Fraser and Swinney, 1986;Moon et al, 1995).…”

Section: Determination Of Input Variablesmentioning

confidence: 99%

Multi-objective optimization of typhoon inundation forecast models with cross-site structures for a water-level gauging network by integrating ARMAX with a genetic algorithm

Ouyang

2016

Nat. Hazards Earth Syst. Sci.

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Abstract. The forecasting of inundation levels during typhoons requires that multiple objectives be taken into account, including the forecasting capacity with regard to variations in water level throughout the entire weather event, the accuracy that can be attained in forecasting peak water levels, and the time at which peak water levels are likely to occur. This paper proposed a means of forecasting inundation levels in real time using monitoring data from a water-level gauging network. ARMAX was used to construct water-level forecast models for each gauging station using input variables including cumulative rainfall and water-level data from other gauging stations in the network. Analysis of the correlation between cumulative rainfall and water-level data makes it possible to obtain the appropriate accumulation duration of rainfall and the time lags associated with each gauging station. Analyses on cross-site water levels as well as on cumulative rainfall enable the identification of associate sites pertaining to each gauging station that share high correlations with regard to water level and low mutual information with regard to cumulative rainfall. Water-level data from the identified associate sites are used as a second input variable for the water-level forecast model of the target site. Three indices were considered in the selection of an optimal model: the coefficient of efficiency (CE), error in the stage of peak water level (ESP), and relative time shift (RTS). A multiobjective genetic algorithm was employed to derive an optimal Pareto set of models capable of performing well in the three objectives. A case study was conducted on the Xinnan area of Yilan County, Taiwan, in which optimal water-level forecast models were established for each of the four waterlevel gauging stations in the area. Test results demonstrate that the model best able to satisfy ESP exhibited significant time shift, whereas the models best able to satisfy CE and RTS provide accurate forecasts of inundations when variations in water level are less extreme.

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“…If we have two kinds of time series data sets such as (s 1 , s 2 , s 3 , · · ·, s n , q 1 , q 2 , q 3 , · · ·, q n ), where n is the observed periods, then the MI value between observation s i and q j is defined by Moon et al (1995) as follows: MI s,q s i , q j = log 2 P s, q s i , q j P s (s i ) P q q j .…”

Section: Mutual Information Techniquesmentioning

confidence: 99%

Investigation of hydrological variability in the Korean Peninsula with the ENSO teleconnections

Yoon

Lee

2016

Proc. IAHS

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Abstract. This study analyzes nonlinear behavior links with atmospheric teleconnections between hydrologic variables and climate indices using statistical models during warm season (June to September) over the Korean Peninsula (KP). The ocean-related major climate factor, which is the El Niño-Southern Oscillation (ENSO) was used to analyze the atmospheric teleconnections by principal component analysis (PCA) and a singular spectrum analysis (SSA). The nonlinear lag time correlations between climate indices and hydrologic variables are calculated by Mutual Information (MI) technique. The nonlinear correlation coefficients (CCs) by MI were higher than linear CCs, and ENSO shows a few months of lag time correlation. The warm season hydrologic variables in KP shows a significant increasing tendency during the warm pool (WP), and the cold tongue (CT) El Niño decaying years shows a significant decreasing tendency, while the La Niña year shows slightly above normal conditions, respectively. A better understanding of the relationship between climate indices and streamflow, and their local impacts can help to prepare for the river discharge management by water managers and scientists. Furthermore, these results provide useful data for policy makers and end-users to support long-range water resources prediction and water-related policy.

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Estimation of mutual information using kernel density estimators

Cited by 399 publications

References 16 publications

Estimating Information-Theoretic Quantities

Estimating Information-Theoretic Quantities

Multi-objective optimization of typhoon inundation forecast models with cross-site structures for a water-level gauging network by integrating ARMAX with a genetic algorithm

Investigation of hydrological variability in the Korean Peninsula with the ENSO teleconnections

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