Clojure code examples

(defprojectme.lizier/jidt-clojure-samples"1.0-SNAPSHOT":description"Java Information Dynamics Toolkit (JIDT) clojure samples":url"https://code.google.com/p/information-dynamics-toolkit/":license    {:name"GNU GPL v3":url"http://www.gnu.org/licenses/gpl.html":distribution:repo    }:dependencies [[org.clojure/clojure"1.6.0"] [me.lizier/jidt"LATEST"] ])

Example 1 - Transfer entropy on binary data

; Import relevant classes:(import infodynamics.measures.discrete.TransferEntropyCalculatorDiscrete)(let; Generate some random binary data.    [sourceArray (int-array (take100 (repeatedly #(rand-int2))))     destArray (int-array (cons0 (butlast sourceArray))); shifts sourceArray by 1     sourceArray2 (int-array (take100 (repeatedly #(rand-int2)))); Create TE calculator     teCalc (TransferEntropyCalculatorDiscrete.21)    ]; Initialise the TE calculator and run it:(.initialise teCalc)(.addObservations teCalc sourceArray destArray)(println"For copied source, result should be close to 1 bit :"(.computeAverageLocalOfObservations teCalc))(.initialise teCalc)(.addObservations teCalc sourceArray2 destArray)(println"For random source, result should be close to 0 bits :"(.computeAverageLocalOfObservations teCalc)))

Example 2 - Transfer entropy on multidimensional binary data

; Import relevant classes:(import infodynamics.measures.discrete.TransferEntropyCalculatorDiscrete)(let; Create many columns in a multidimensional array (2 rows by 100 columns),;  where the next time step (row 2) copies the value of the column on the left;  from the previous time step (row 1):    [row1 (int-array (take100 (repeatedly #(rand-int2))))     row2 (int-array (cons (aget row199) (butlast row1))); shifts row1 by 1     twoDTimeSeriesClojure (into-array (map int-array [row1 row2])); Create TE calculator     teCalc (TransferEntropyCalculatorDiscrete.21)    ]; Initialise the TE calculator and run it:(.initialise teCalc); Add observations of transfer across one cell to the right per time step:(.addObservations teCalc twoDTimeSeriesClojure1)(println"The result should be close to 1 bit here, since we are executing copy operations of what is effectively a random bit to each cell here:"(.computeAverageLocalOfObservations teCalc)))

Example 3 - Transfer entropy on continuous data using kernel estimators

; Import relevant classes:(import infodynamics.measures.continuous.kernel.TransferEntropyCalculatorKernel)(import java.util.Random)(defrg (Random.))(let    [numObservations1000     covariance0.4; Generate some random normalised data.     sourceArray (double-array (take numObservations (repeatedly #(.nextGaussian rg))))     destArray (double-array(cons0    (map +(map (partial * covariance) (butlast sourceArray))(map (partial * (- covariance1)) (double-array (take (- numObservations1) (repeatedly #(.nextGaussian rg))))) )))     sourceArray2 (double-array (take numObservations (repeatedly #(.nextGaussian rg))))     teCalc (TransferEntropyCalculatorKernel. )    ]; Set up the calculator(.setProperty teCalc"NORMALISE""true")(.initialise teCalc10.5); Use history length 1 (Schreiber k=1), kernel width of 0.5 normalised units(.setObservations teCalc sourceArray destArray); For copied source, should give something close to expected value for correlated Gaussians:(println"TE result" (.computeAverageLocalOfObservations teCalc)" expected to be close to" (/ (Math/log (/1 (-1 (* covariance covariance)))) (Math/log2))" for these correlated Gaussians but biased upward")(.initialise teCalc ); Initialise leaving the parameters the same(.setObservations teCalc sourceArray2 destArray); For random source, it should give something close to 0 bits(println"TE result" (.computeAverageLocalOfObservations teCalc)" expected to be close to 0 bits for these uncorrelated Gaussians but will be biased upward"); We can get insight into the bias by examining the null distribution:(defnullDist (.computeSignificance teCalc100))(println"Null distribution for unrelated source and destination""(i.e. the bias) has mean" (.getMeanOfDistribution nullDist)" and standard deviation" (.getStdOfDistribution nullDist)))

Example 4 - Transfer entropy on continuous data using Kraskov estimators

; Import relevant classes:(import infodynamics.measures.continuous.kraskov.TransferEntropyCalculatorKraskov)(import java.util.Random)(defrg (Random.))(let    [numObservations1000     covariance0.4; Generate some random normalised data.     sourceArray (double-array (take numObservations (repeatedly #(.nextGaussian rg))))     destArray (double-array(cons0    (map +(map (partial * covariance) (butlast sourceArray))(map (partial * (- covariance1)) (double-array (take (- numObservations1) (repeatedly #(.nextGaussian rg))))) )))     sourceArray2 (double-array (take numObservations (repeatedly #(.nextGaussian rg))))     teCalc (TransferEntropyCalculatorKraskov. )    ]; Set up the calculator(.setProperty teCalc"k""4"); Use Kraskov parameter K=4 for 4 nearest points(.initialise teCalc1); Use history length 1 (Schreiber k=1); Perform calculation with correlated source:(.setObservations teCalc sourceArray destArray); Note that the calculation is a random variable (because the generated;  data is a set of random variables) - the result will be of the order;  of what we expect, but not exactly equal to it; in fact, there will;  be a large variance around it.(println"TE result" (.computeAverageLocalOfObservations teCalc)" nats expected to be close to" (Math/log (/1 (-1 (* covariance covariance))))" nats for these correlated Gaussians"); Perform calculation with uncorrelated source:(.initialise teCalc ); Initialise leaving the parameters the same(.setObservations teCalc sourceArray2 destArray); For random source, it should give something close to 0 bits(println"TE result" (.computeAverageLocalOfObservations teCalc)" nats expected to be close to 0 nats for these uncorrelated Gaussians"); We can also compute the local TE values for the time-series samples here:;  (See more about utility of local TE in the CA demos)(deflocalTE (.computeLocalOfPreviousObservations teCalc))(println"Notice that the mean of locals,"(/ (reduce + localTE) (- numObservations1))" nats, equals the previous result"))

Acknowledgements