mirror of https://github.com/jlizier/jidt
412 lines
14 KiB
Java
Executable File
412 lines
14 KiB
Java
Executable File
package infodynamics.measures.continuous.kraskov;
|
|
|
|
import infodynamics.utils.FirstIndexComparatorDouble;
|
|
import infodynamics.utils.MathsUtils;
|
|
import infodynamics.utils.MatrixUtils;
|
|
|
|
/**
|
|
* <p>Compute the Mutual Info using the Kraskov estimation method.
|
|
* Uses the second algorithm (defined at start of p.3 of the paper)</p>
|
|
* <p>Computes this directly looking at the marginal space for each variable, rather than
|
|
* using the multi-info (or integration) in the marginal spaces.
|
|
* </p>
|
|
* @see "Estimating mutual information", Kraskov, A., Stogbauer, H., Grassberger, P., Physical Review E 69, (2004) 066138
|
|
* @see http://dx.doi.org/10.1103/PhysRevE.69.066138
|
|
*
|
|
* @author Joseph Lizier
|
|
*
|
|
*/
|
|
public class MutualInfoCalculatorMultiVariateKraskov2
|
|
extends MutualInfoCalculatorMultiVariateKraskov {
|
|
|
|
protected static final int JOINT_NORM_VAL_COLUMN = 0;
|
|
protected static final int JOINT_NORM_TIMESTEP_COLUMN = 1;
|
|
|
|
// Multiplier used in hueristic for determining whether to use a linear search
|
|
// for min kth element or a binary search.
|
|
protected static final double CUTOFF_MULTIPLIER = 1.5;
|
|
|
|
/**
|
|
* Compute what the average MI would look like were the second time series reordered
|
|
* as per the array of time indices in reordering.
|
|
* The user should ensure that all values 0..N-1 are represented exactly once in the
|
|
* array reordering and that no other values are included here.
|
|
*
|
|
* @param reordering
|
|
* @return
|
|
* @throws Exception
|
|
*/
|
|
public double computeAverageLocalOfObservations(int[] reordering) throws Exception {
|
|
if (!tryKeepAllPairsNorms || (data1.length > MAX_DATA_SIZE_FOR_KEEP_ALL_PAIRS_NORM)) {
|
|
double[][] originalData2 = data2;
|
|
// Generate a new re-ordered data2
|
|
data2 = MatrixUtils.extractSelectedTimePointsReusingArrays(originalData2, reordering);
|
|
// Compute the MI
|
|
double newMI = computeAverageLocalOfObservationsWhileComputingDistances();
|
|
// restore data2
|
|
data2 = originalData2;
|
|
return newMI;
|
|
}
|
|
|
|
// Otherwise we will use the norms we've already computed, and use a "virtual"
|
|
// reordered data2.
|
|
|
|
if (xNorms == null) {
|
|
computeNorms();
|
|
}
|
|
int N = data1.length; // number of observations
|
|
int cutoffForKthMinLinear = (int) (CUTOFF_MULTIPLIER * Math.log(N) / Math.log(2.0));
|
|
|
|
// Count the average number of points within eps_x and eps_y
|
|
double averageDiGammas = 0;
|
|
double avNx = 0;
|
|
double avNy = 0;
|
|
|
|
for (int t = 0; t < N; t++) {
|
|
// Compute eps_x and eps_y for this time step:
|
|
// First get x and y norms to all neighbours
|
|
// (note that norm of point t to itself will be set to infinity).
|
|
|
|
int tForY = reordering[t];
|
|
|
|
double[][] jointNorm = new double[N][2];
|
|
for (int t2 = 0; t2 < N; t2++) {
|
|
int t2ForY = reordering[t2];
|
|
jointNorm[t2][JOINT_NORM_VAL_COLUMN] = Math.max(xNorms[t][t2], yNorms[tForY][t2ForY]);
|
|
// And store the time step for back reference after the
|
|
// array is sorted.
|
|
jointNorm[t2][JOINT_NORM_TIMESTEP_COLUMN] = t2;
|
|
}
|
|
// Then find the k closest neighbours:
|
|
double eps_x = 0.0;
|
|
double eps_y = 0.0;
|
|
int[] timeStepsOfKthMins = null;
|
|
if (k <= cutoffForKthMinLinear) {
|
|
// just do a linear search for the minimum epsilon value
|
|
timeStepsOfKthMins = MatrixUtils.kMinIndices(jointNorm, JOINT_NORM_VAL_COLUMN, k);
|
|
} else {
|
|
// Sort the array of joint norms
|
|
java.util.Arrays.sort(jointNorm, FirstIndexComparatorDouble.getInstance());
|
|
// and now we have the closest k points.
|
|
timeStepsOfKthMins = new int[k];
|
|
for (int j = 0; j < k; j++) {
|
|
timeStepsOfKthMins[j] = (int) jointNorm[j][JOINT_NORM_TIMESTEP_COLUMN];
|
|
}
|
|
}
|
|
// and now we have the closest k points.
|
|
// Find eps_{x,y} as the maximum x and y norms amongst this set:
|
|
for (int j = 0; j < k; j++) {
|
|
int timeStepOfJthPoint = timeStepsOfKthMins[j];
|
|
if (xNorms[t][timeStepOfJthPoint] > eps_x) {
|
|
eps_x = xNorms[t][timeStepOfJthPoint];
|
|
}
|
|
if (yNorms[tForY][reordering[timeStepOfJthPoint]] > eps_y) {
|
|
eps_y = yNorms[tForY][reordering[timeStepOfJthPoint]];
|
|
}
|
|
}
|
|
|
|
// Count the number of points whose x distance is less
|
|
// than or equal to eps_x, and whose y distance is less
|
|
// than or equal to eps_y
|
|
int n_x = 0;
|
|
int n_y = 0;
|
|
for (int t2 = 0; t2 < N; t2++) {
|
|
if (xNorms[t][t2] <= eps_x) {
|
|
n_x++;
|
|
}
|
|
if (yNorms[tForY][reordering[t2]] <= eps_y) {
|
|
n_y++;
|
|
}
|
|
}
|
|
avNx += n_x;
|
|
avNy += n_y;
|
|
// And take the digamma before adding into the
|
|
// average:
|
|
averageDiGammas += MathsUtils.digamma(n_x) + MathsUtils.digamma(n_y);
|
|
}
|
|
averageDiGammas /= (double) N;
|
|
if (debug) {
|
|
avNx /= (double)N;
|
|
avNy /= (double)N;
|
|
System.out.println(String.format("Average n_x=%.3f, Average n_y=%.3f", avNx, avNy));
|
|
}
|
|
|
|
mi = MathsUtils.digamma(k) - 1.0/(double)k - averageDiGammas + MathsUtils.digamma(N);
|
|
miComputed = true;
|
|
return mi;
|
|
}
|
|
|
|
public double computeAverageLocalOfObservations() throws Exception {
|
|
if (!tryKeepAllPairsNorms || (data1.length > MAX_DATA_SIZE_FOR_KEEP_ALL_PAIRS_NORM)) {
|
|
return computeAverageLocalOfObservationsWhileComputingDistances();
|
|
}
|
|
|
|
if (xNorms == null) {
|
|
computeNorms();
|
|
}
|
|
int N = data1.length; // number of observations
|
|
int cutoffForKthMinLinear = (int) (CUTOFF_MULTIPLIER * Math.log(N) / Math.log(2.0));
|
|
|
|
// Count the average number of points within eps_x and eps_y
|
|
double averageDiGammas = 0;
|
|
double avNx = 0;
|
|
double avNy = 0;
|
|
|
|
for (int t = 0; t < N; t++) {
|
|
// Compute eps_x and eps_y for this time step:
|
|
// using x and y norms to all neighbours
|
|
// (note that norm of point t to itself will be set to infinity).
|
|
|
|
double[][] jointNorm = new double[N][2];
|
|
for (int t2 = 0; t2 < N; t2++) {
|
|
jointNorm[t2][JOINT_NORM_VAL_COLUMN] = Math.max(xNorms[t][t2], yNorms[t][t2]);
|
|
// And store the time step for back reference after the
|
|
// array is sorted.
|
|
jointNorm[t2][JOINT_NORM_TIMESTEP_COLUMN] = t2;
|
|
}
|
|
// Then find the k closest neighbours:
|
|
double eps_x = 0.0;
|
|
double eps_y = 0.0;
|
|
int[] timeStepsOfKthMins = null;
|
|
if (k <= cutoffForKthMinLinear) {
|
|
// just do a linear search for the minimum epsilon value
|
|
timeStepsOfKthMins = MatrixUtils.kMinIndices(jointNorm, JOINT_NORM_VAL_COLUMN, k);
|
|
} else {
|
|
// Sort the array of joint norms
|
|
java.util.Arrays.sort(jointNorm, FirstIndexComparatorDouble.getInstance());
|
|
// and now we have the closest k points.
|
|
timeStepsOfKthMins = new int[k];
|
|
for (int j = 0; j < k; j++) {
|
|
timeStepsOfKthMins[j] = (int) jointNorm[j][JOINT_NORM_TIMESTEP_COLUMN];
|
|
}
|
|
}
|
|
// and now we have the closest k points.
|
|
// Find eps_{x,y} as the maximum x and y norms amongst this set:
|
|
for (int j = 0; j < k; j++) {
|
|
int timeStepOfJthPoint = timeStepsOfKthMins[j];
|
|
if (xNorms[t][timeStepOfJthPoint] > eps_x) {
|
|
eps_x = xNorms[t][timeStepOfJthPoint];
|
|
}
|
|
if (yNorms[t][timeStepOfJthPoint] > eps_y) {
|
|
eps_y = yNorms[t][timeStepOfJthPoint];
|
|
}
|
|
}
|
|
|
|
// Count the number of points whose x distance is less
|
|
// than or equal to eps_x, and whose y distance is less
|
|
// than or equal to eps_y
|
|
int n_x = 0;
|
|
int n_y = 0;
|
|
for (int t2 = 0; t2 < N; t2++) {
|
|
if (xNorms[t][t2] <= eps_x) {
|
|
n_x++;
|
|
}
|
|
if (yNorms[t][t2] <= eps_y) {
|
|
n_y++;
|
|
}
|
|
}
|
|
avNx += n_x;
|
|
avNy += n_y;
|
|
// And take the digamma before adding into the
|
|
// average:
|
|
averageDiGammas += MathsUtils.digamma(n_x) + MathsUtils.digamma(n_y);
|
|
}
|
|
averageDiGammas /= (double) N;
|
|
if (debug) {
|
|
avNx /= (double)N;
|
|
avNy /= (double)N;
|
|
System.out.println(String.format("Average n_x=%.3f, Average n_y=%.3f", avNx, avNy));
|
|
}
|
|
|
|
mi = MathsUtils.digamma(k) - 1.0/(double)k - averageDiGammas + MathsUtils.digamma(N);
|
|
miComputed = true;
|
|
return mi;
|
|
}
|
|
|
|
/**
|
|
* This method correctly computes the average local MI, but recomputes the x and y
|
|
* distances between all tuples in time.
|
|
* Kept here for cases where we have too many observations
|
|
* to keep the norm between all pairs, and for testing purposes.
|
|
*
|
|
* @return
|
|
* @throws Exception
|
|
*/
|
|
public double computeAverageLocalOfObservationsWhileComputingDistances() throws Exception {
|
|
int N = data1.length; // number of observations
|
|
int cutoffForKthMinLinear = (int) (CUTOFF_MULTIPLIER * Math.log(N) / Math.log(2.0));
|
|
|
|
// Count the average number of points within eps_x and eps_y
|
|
double averageDiGammas = 0;
|
|
double avNx = 0;
|
|
double avNy = 0;
|
|
|
|
for (int t = 0; t < N; t++) {
|
|
// Compute eps_x and eps_y for this time step:
|
|
// First get x and y norms to all neighbours
|
|
// (note that norm of point t to itself will be set to infinity).
|
|
double[][] xyNorms = normCalculator.computeNorms(data1, data2, t);
|
|
double[][] jointNorm = new double[N][2];
|
|
for (int t2 = 0; t2 < N; t2++) {
|
|
jointNorm[t2][JOINT_NORM_VAL_COLUMN] = Math.max(xyNorms[t2][0], xyNorms[t2][1]);
|
|
// And store the time step for back reference after the
|
|
// array is sorted.
|
|
jointNorm[t2][JOINT_NORM_TIMESTEP_COLUMN] = t2;
|
|
}
|
|
// Then find the k closest neighbours:
|
|
double eps_x = 0.0;
|
|
double eps_y = 0.0;
|
|
int[] timeStepsOfKthMins = null;
|
|
if (k <= cutoffForKthMinLinear) {
|
|
// just do a linear search for the minimum epsilon value
|
|
timeStepsOfKthMins = MatrixUtils.kMinIndices(jointNorm, JOINT_NORM_VAL_COLUMN, k);
|
|
} else {
|
|
// Sort the array of joint norms
|
|
java.util.Arrays.sort(jointNorm, FirstIndexComparatorDouble.getInstance());
|
|
// and now we have the closest k points.
|
|
timeStepsOfKthMins = new int[k];
|
|
for (int j = 0; j < k; j++) {
|
|
timeStepsOfKthMins[j] = (int) jointNorm[j][JOINT_NORM_TIMESTEP_COLUMN];
|
|
}
|
|
}
|
|
// and now we have the closest k points.
|
|
// Find eps_{x,y} as the maximum x and y norms amongst this set:
|
|
for (int j = 0; j < k; j++) {
|
|
int timeStepOfJthPoint = timeStepsOfKthMins[j];
|
|
if (xyNorms[timeStepOfJthPoint][0] > eps_x) {
|
|
eps_x = xyNorms[timeStepOfJthPoint][0];
|
|
}
|
|
if (xyNorms[timeStepOfJthPoint][1] > eps_y) {
|
|
eps_y = xyNorms[timeStepOfJthPoint][1];
|
|
}
|
|
}
|
|
|
|
// Count the number of points whose x distance is less
|
|
// than or equal to eps_x, and whose y distance is less
|
|
// than or equal to eps_y
|
|
int n_x = 0;
|
|
int n_y = 0;
|
|
for (int t2 = 0; t2 < N; t2++) {
|
|
if (xyNorms[t2][0] <= eps_x) {
|
|
n_x++;
|
|
}
|
|
if (xyNorms[t2][1] <= eps_y) {
|
|
n_y++;
|
|
}
|
|
}
|
|
avNx += n_x;
|
|
avNy += n_y;
|
|
// And take the digamma before adding into the
|
|
// average:
|
|
averageDiGammas += MathsUtils.digamma(n_x) + MathsUtils.digamma(n_y);
|
|
}
|
|
averageDiGammas /= (double) N;
|
|
if (debug) {
|
|
avNx /= (double)N;
|
|
avNy /= (double)N;
|
|
System.out.println(String.format("Average n_x=%.3f, Average n_y=%.3f", avNx, avNy));
|
|
}
|
|
|
|
mi = MathsUtils.digamma(k) - 1.0/(double)k - averageDiGammas + MathsUtils.digamma(N);
|
|
miComputed = true;
|
|
return mi;
|
|
}
|
|
|
|
public double[] computeLocalOfPreviousObservations() throws Exception {
|
|
int N = data1.length; // number of observations
|
|
int cutoffForKthMinLinear = (int) (CUTOFF_MULTIPLIER * Math.log(N) / Math.log(2.0));
|
|
double[] localMi = new double[N];
|
|
|
|
// Constants:
|
|
double digammaK = MathsUtils.digamma(k);
|
|
double invK = 1.0 / (double)k;
|
|
double digammaN = MathsUtils.digamma(N);
|
|
|
|
// Count the average number of points within eps_x and eps_y
|
|
double averageDiGammas = 0;
|
|
double avNx = 0;
|
|
double avNy = 0;
|
|
|
|
for (int t = 0; t < N; t++) {
|
|
// Compute eps_x and eps_y for this time step:
|
|
// First get x and y norms to all neighbours
|
|
// (note that norm of point t to itself will be set to infinity).
|
|
double[][] xyNorms = normCalculator.computeNorms(data1, data2, t);
|
|
double[][] jointNorm = new double[N][2];
|
|
for (int t2 = 0; t2 < N; t2++) {
|
|
jointNorm[t2][JOINT_NORM_VAL_COLUMN] = Math.max(xyNorms[t2][0], xyNorms[t2][1]);
|
|
// And store the time step for back reference after the
|
|
// array is sorted.
|
|
jointNorm[t2][JOINT_NORM_TIMESTEP_COLUMN] = t2;
|
|
}
|
|
// Then find the k closest neighbours:
|
|
double eps_x = 0.0;
|
|
double eps_y = 0.0;
|
|
int[] timeStepsOfKthMins = null;
|
|
if (k <= cutoffForKthMinLinear) {
|
|
// just do a linear search for the minimum epsilon value
|
|
timeStepsOfKthMins = MatrixUtils.kMinIndices(jointNorm, JOINT_NORM_VAL_COLUMN, k);
|
|
} else {
|
|
// Sort the array of joint norms
|
|
java.util.Arrays.sort(jointNorm, FirstIndexComparatorDouble.getInstance());
|
|
// and now we have the closest k points.
|
|
timeStepsOfKthMins = new int[k];
|
|
for (int j = 0; j < k; j++) {
|
|
timeStepsOfKthMins[j] = (int) jointNorm[j][JOINT_NORM_TIMESTEP_COLUMN];
|
|
}
|
|
}
|
|
// and now we have the closest k points.
|
|
// Find eps_{x,y} as the maximum x and y norms amongst this set:
|
|
for (int j = 0; j < k; j++) {
|
|
int timeStepOfJthPoint = timeStepsOfKthMins[j];
|
|
if (xyNorms[timeStepOfJthPoint][0] > eps_x) {
|
|
eps_x = xyNorms[timeStepOfJthPoint][0];
|
|
}
|
|
if (xyNorms[timeStepOfJthPoint][1] > eps_y) {
|
|
eps_y = xyNorms[timeStepOfJthPoint][1];
|
|
}
|
|
}
|
|
|
|
// Count the number of points whose x distance is less
|
|
// than or equal to eps_x, and whose y distance is less
|
|
// than or equal to eps_y
|
|
int n_x = 0;
|
|
int n_y = 0;
|
|
for (int t2 = 0; t2 < N; t2++) {
|
|
if (xyNorms[t2][0] <= eps_x) {
|
|
n_x++;
|
|
}
|
|
if (xyNorms[t2][1] <= eps_y) {
|
|
n_y++;
|
|
}
|
|
}
|
|
avNx += n_x;
|
|
avNy += n_y;
|
|
// And take the digamma:
|
|
double digammaNx = MathsUtils.digamma(n_x);
|
|
double digammaNy = MathsUtils.digamma(n_y);
|
|
|
|
localMi[t] = digammaK - invK - digammaNx - digammaNy + digammaN;
|
|
|
|
averageDiGammas += digammaNx + digammaNy;
|
|
}
|
|
averageDiGammas /= (double) N;
|
|
if (debug) {
|
|
avNx /= (double)N;
|
|
avNy /= (double)N;
|
|
System.out.println(String.format("Average n_x=%.3f, Average n_y=%.3f", avNx, avNy));
|
|
}
|
|
|
|
mi = digammaK - invK - averageDiGammas + digammaN;
|
|
miComputed = true;
|
|
return localMi;
|
|
}
|
|
|
|
public String printConstants(int N) throws Exception {
|
|
String constants = String.format("digamma(k=%d)=%.3e - 1/k=%.3e + digamma(N=%d)=%.3e => %.3e",
|
|
k, MathsUtils.digamma(k), 1.0/(double)k, N, MathsUtils.digamma(N),
|
|
(MathsUtils.digamma(k) - 1.0/(double)k + MathsUtils.digamma(N)));
|
|
return constants;
|
|
}
|
|
}
|