Extended fix to local cond MI values for handling linear redundancies amongst variables properly in ConditionalMICalculatorMultivariateGaussian - this resolves Issue 16

java/source/infodynamics/measures/continuous/gaussian/ConditionalMutualInfoCalculatorMultiVariateGaussian.java

@@ -577,13 +577,31 @@ public class ConditionalMutualInfoCalculatorMultiVariateGaussian
 			// Simple way:
 			// detCovariance = MatrixUtils.determinantSymmPosDefMatrix(covariance);
 			// Using cached Cholesky decomposition:
-			detCovariance = MatrixUtils.determinantViaCholeskyResult(L);
-			if (detCovariance == 0) {
-				throw new Exception("Covariance matrix is not positive definite");
-			}
-			det1cCovariance = MatrixUtils.determinantViaCholeskyResult(L_1c);
-			det2cCovariance = MatrixUtils.determinantViaCholeskyResult(L_2c);
+
+			// Should always have a valid L_cc (since we can reduce it down to one variable:
 			detccCovariance = MatrixUtils.determinantViaCholeskyResult(L_cc);
+			if (L_1c == null) {
+				// Variable 1 is fully linearly redundant with conditional, so
+				//  we will have zero conditional MI:
+				return MatrixUtils.constantArray(newVar2Obs.length, 0);
+			} else {
+				det1cCovariance = MatrixUtils.determinantViaCholeskyResult(L_1c);
+				if (L_2c == null) {
+					// Variable 2 is fully linearly redundant with conditional, so
+					//  we will have zero conditional MI:
+					return MatrixUtils.constantArray(newVar2Obs.length, 0);
+				} else {
+					det2cCovariance = MatrixUtils.determinantViaCholeskyResult(L_2c);
+					if (L == null) {
+						// There is a linear dependence amongst variables 1 and 2 given the
+						//  conditional which did not exist for either with the conditional alone,
+						//  so conditional MI diverges:
+						return MatrixUtils.constantArray(newVar2Obs.length, Double.POSITIVE_INFINITY);
+					} else {
+						detCovariance = MatrixUtils.determinantViaCholeskyResult(L);
+					}
+				}
+			}
 		}
 
 		// Now we are clear to take the matrix inverse (via Cholesky decomposition,
@@ -597,23 +615,34 @@ public class ConditionalMutualInfoCalculatorMultiVariateGaussian
 		double[][] invCondCovariance = MatrixUtils.solveViaCholeskyResult(L_cc,
 				MatrixUtils.identityMatrix(L_cc.length));
 			
-		double[] var1Means = MatrixUtils.select(means, 0, dimensionsVar1);
-		double[] var2Means = MatrixUtils.select(means, dimensionsVar1, dimensionsVar2);
-		double[] condMeans = MatrixUtils.select(means, dimensionsVar1 + dimensionsVar2, dimensionsCond);
+		// Now, only use the means from the subsets of linearly independent variables:
+		// double[] var1Means = MatrixUtils.select(means, 0, dimensionsVar1);
+		double[] var1Means = MatrixUtils.select(means, var1IndicesInCovariance);
+		// double[] var2Means = MatrixUtils.select(means, dimensionsVar1, dimensionsVar2);
+		double[] var2Means = MatrixUtils.select(means, var2IndicesInCovariance);
+		// double[] condMeans = MatrixUtils.select(means, dimensionsVar1 + dimensionsVar2, dimensionsCond);
+		double[] condMeans = MatrixUtils.select(means, condIndicesInCovariance);
 		
 		int lengthOfReturnArray;
 		lengthOfReturnArray = newVar2Obs.length;
 
 		double[] localValues = new double[lengthOfReturnArray];
+		int[] var2IndicesSelected = MatrixUtils.subtract(var2IndicesInCovariance, dimensionsVar1);
+		int[] condIndicesSelected = MatrixUtils.subtract(condIndicesInCovariance, dimensionsVar1 + dimensionsVar2);
 		for (int t = 0; t < newVar2Obs.length; t++) {
 			
 			double[] var1DeviationsFromMean =
-					MatrixUtils.subtract(newVar1Obs[t],
+					MatrixUtils.subtract(
+							MatrixUtils.select(newVar1Obs[t], var1IndicesInCovariance),
 							var1Means);
 			double[] var2DeviationsFromMean =
-					MatrixUtils.subtract(newVar2Obs[t], var2Means);
+					MatrixUtils.subtract(
+							MatrixUtils.select(newVar2Obs[t], var2IndicesSelected),
+							var2Means);
 			double[] condDeviationsFromMean =
-					MatrixUtils.subtract(newCondObs[t], condMeans);
+					MatrixUtils.subtract(
+							MatrixUtils.select(newCondObs[t], condIndicesSelected),
+							condMeans);
 			double[] var1CondDeviationsFromMean =
 					MatrixUtils.append(var1DeviationsFromMean,
 							condDeviationsFromMean);

java/source/infodynamics/utils/MatrixUtils.java

@@ -44,6 +44,19 @@ public class MatrixUtils {
 		return array;
 	}
 	
+	/**
+	 * Return an array with the given value at every index
+	 * 
+	 * @param length length of array
+	 * @param value value for every element of the arry
+	 * @return
+	 */
+	public static double[] constantArray(int length, double value) {
+		double[] array = new double[length];
+		Arrays.fill(array, value);
+		return array;
+	}
+	
 	public static double sum(double[] input) {
 		double total = 0;
 		for (int i = 0; i < input.length; i++) {
@@ -599,6 +612,21 @@ public class MatrixUtils {
 		return returnValues;
 	}
 
+	/**
+	 * Subtracts a constant value from all items in an array
+	 * 
+	 * @param array
+	 * @param value
+	 * @return array - constant value
+	 */
+	public static double[] subtract(double[] array, double value) throws Exception {
+		double[] returnValues = new double[array.length];
+		for (int i = 0; i < returnValues.length; i++) {
+			returnValues[i] = array[i] - value;
+		}
+		return returnValues;
+	}
+
 	/**
 	 * Subtracts second array from the first, overwriting the
 	 *  values in first
@@ -641,6 +669,21 @@ public class MatrixUtils {
 		return returnValues;
 	}
 
+	/**
+	 * Subtracts a constant value from all items in an array
+	 * 
+	 * @param array
+	 * @param value
+	 * @return array - constant value
+	 */
+	public static int[] subtract(int[] array, int value) throws Exception {
+		int[] returnValues = new int[array.length];
+		for (int i = 0; i < returnValues.length; i++) {
+			returnValues[i] = array[i] - value;
+		}
+		return returnValues;
+	}
+
 	/**
 	 * Return the matrix product A x B
 	 * 
@@ -1150,6 +1193,21 @@ public class MatrixUtils {
 		return returnData;
 	}
 	
+	/**
+	 * Select out part of an array.
+	 * 
+	 * @param data
+	 * @param indices which array indices to pull out
+	 * @return
+	 */
+	public static double[] select(double[] data, int[] indices) {
+		double[] returnData = new double[indices.length];
+		for (int i = 0; i < indices.length; i++) {
+			returnData[i] = data[indices[i]];
+		}
+		return returnData;
+	}
+	
 	/**
 	 * Select out part of an array.
 	 * 
@@ -1164,6 +1222,21 @@ public class MatrixUtils {
 		return returnData;
 	}
 	
+	/**
+	 * Select out part of an array.
+	 * 
+	 * @param data
+	 * @param indices which array indices to pull out
+	 * @return
+	 */
+	public static int[] select(int[] data, int[] indices) {
+		int[] returnData = new int[indices.length];
+		for (int i = 0; i < indices.length; i++) {
+			returnData[i] = data[indices[i]];
+		}
+		return returnData;
+	}
+
 	public static int[] selectColumn(int matrix[][], int columnNo) {
 		int[] column = new int[matrix.length];
 		for (int r = 0; r < matrix.length; r++) {