@Override
public void updateReward(User user, Article a, boolean clicked) {
String aId = a.getId();
// Collect Variables
RealMatrix xta = MatrixUtils.createColumnRealMatrix(a.getFeatures());
RealMatrix zta = makeZta(MatrixUtils.createColumnRealMatrix(user.getFeatures()), xta);
RealMatrix Aa = AMap.get(aId);
RealMatrix ba = bMap.get(aId);
RealMatrix Ba = BMap.get(aId);
// Find common transpose/inverse to save computation
RealMatrix AaInverse = MatrixUtils.inverse(Aa);
RealMatrix BaTranspose = Ba.transpose();
RealMatrix xtaTranspose = xta.transpose();
RealMatrix ztaTranspose = zta.transpose();
// Update
A0 = A0.add(BaTranspose.multiply(AaInverse).multiply(Ba));
b0 = b0.add(BaTranspose.multiply(AaInverse).multiply(ba));
Aa = Aa.add(xta.multiply(xtaTranspose));
AMap.put(aId, Aa);
Ba = Ba.add(xta.multiply(ztaTranspose));
BMap.put(aId, Ba);
if (clicked) {
ba = ba.add(xta);
bMap.put(aId, ba);
}
// Update A0 and b0 with the new values
A0 =
A0.add(zta.multiply(ztaTranspose))
.subtract(Ba.transpose().multiply(MatrixUtils.inverse(Aa).multiply(Ba)));
b0 = b0.subtract(Ba.transpose().multiply(MatrixUtils.inverse(Aa)).multiply(ba));
if (clicked) {
b0 = b0.add(zta);
}
}
@Override
public Article chooseArm(User user, List<Article> articles) {
Article bestA = null;
double bestArmP = Double.MIN_VALUE;
RealMatrix Aa;
RealMatrix Ba;
RealMatrix ba;
for (Article a : articles) {
String aId = a.getId();
if (!AMap.containsKey(aId)) {
Aa = MatrixUtils.createRealIdentityMatrix(6);
AMap.put(aId, Aa); // set as identity for now and we will update
// in reward
double[] zeros = {0, 0, 0, 0, 0, 0};
ba = MatrixUtils.createColumnRealMatrix(zeros);
bMap.put(aId, ba);
double[][] BMapZeros = new double[6][36];
for (double[] row : BMapZeros) {
Arrays.fill(row, 0.0);
}
Ba = MatrixUtils.createRealMatrix(BMapZeros);
BMap.put(aId, Ba);
} else {
Aa = AMap.get(aId);
ba = bMap.get(aId);
Ba = BMap.get(aId);
}
// Make column vector out of features
RealMatrix xta = MatrixUtils.createColumnRealMatrix(a.getFeatures());
RealMatrix zta = makeZta(MatrixUtils.createColumnRealMatrix(user.getFeatures()), xta);
// Set up common variables
RealMatrix A0Inverse = MatrixUtils.inverse(A0);
RealMatrix AaInverse = MatrixUtils.inverse(Aa);
RealMatrix ztaTranspose = zta.transpose();
RealMatrix BaTranspose = Ba.transpose();
RealMatrix xtaTranspose = xta.transpose();
// Find theta
RealMatrix theta = AaInverse.multiply(ba.subtract(Ba.multiply(BetaHat)));
// Find sta
RealMatrix staMatrix = ztaTranspose.multiply(A0Inverse).multiply(zta);
staMatrix =
staMatrix.subtract(
ztaTranspose
.multiply(A0Inverse)
.multiply(BaTranspose)
.multiply(AaInverse)
.multiply(xta)
.scalarMultiply(2));
staMatrix = staMatrix.add(xtaTranspose.multiply(AaInverse).multiply(xta));
staMatrix =
staMatrix.add(
xtaTranspose
.multiply(AaInverse)
.multiply(Ba)
.multiply(A0Inverse)
.multiply(BaTranspose)
.multiply(AaInverse)
.multiply(xta));
// Find pta for arm
RealMatrix ptaMatrix = ztaTranspose.multiply(BetaHat);
ptaMatrix = ptaMatrix.add(xtaTranspose.multiply(theta));
double ptaVal = ptaMatrix.getData()[0][0];
double staVal = staMatrix.getData()[0][0];
ptaVal = ptaVal + alpha * Math.sqrt(staVal);
// Update argmax
if (ptaVal > bestArmP) {
bestArmP = ptaVal;
bestA = a;
}
}
return bestA;
}
@Override
protected Object execute(Object[] data) {
if (data[0] == null) {
throw new ExecutionPlanRuntimeException(
"Invalid input given to kf:kalmanFilter() "
+ "function. First argument should be a double");
}
if (data[1] == null) {
throw new ExecutionPlanRuntimeException(
"Invalid input given to kf:kalmanFilter() "
+ "function. Second argument should be a double");
}
if (data.length == 2) {
double measuredValue = (Double) data[0]; // to remain as the initial state
if (prevEstimatedValue == 0) {
transition = 1;
variance = 1000;
measurementNoiseSD = (Double) data[1];
prevEstimatedValue = measuredValue;
}
prevEstimatedValue = transition * prevEstimatedValue;
double kalmanGain = variance / (variance + measurementNoiseSD);
prevEstimatedValue = prevEstimatedValue + kalmanGain * (measuredValue - prevEstimatedValue);
variance = (1 - kalmanGain) * variance;
return prevEstimatedValue;
} else {
if (data[2] == null) {
throw new ExecutionPlanRuntimeException(
"Invalid input given to kf:kalmanFilter() "
+ "function. Third argument should be a double");
}
if (data[3] == null) {
throw new ExecutionPlanRuntimeException(
"Invalid input given to kf:kalmanFilter() "
+ "function. Fourth argument should be a long");
}
double measuredXValue = (Double) data[0];
double measuredChangingRate = (Double) data[1];
double measurementNoiseSD = (Double) data[2];
long timestamp = (Long) data[3];
long timestampDiff;
double[][] measuredValues = {{measuredXValue}, {measuredChangingRate}};
if (measurementMatrixH == null) {
timestampDiff = 1;
double[][] varianceValues = {{1000, 0}, {0, 1000}};
double[][] measurementValues = {{1, 0}, {0, 1}};
measurementMatrixH = MatrixUtils.createRealMatrix(measurementValues);
varianceMatrixP = MatrixUtils.createRealMatrix(varianceValues);
prevMeasuredMatrix = MatrixUtils.createRealMatrix(measuredValues);
} else {
timestampDiff = (timestamp - prevTimestamp);
}
double[][] Rvalues = {{measurementNoiseSD, 0}, {0, measurementNoiseSD}};
RealMatrix rMatrix = MatrixUtils.createRealMatrix(Rvalues);
double[][] transitionValues = {{1d, timestampDiff}, {0d, 1d}};
RealMatrix transitionMatrixA = MatrixUtils.createRealMatrix(transitionValues);
RealMatrix measuredMatrixX = MatrixUtils.createRealMatrix(measuredValues);
// Xk = (A * Xk-1)
prevMeasuredMatrix = transitionMatrixA.multiply(prevMeasuredMatrix);
// Pk = (A * P * AT) + Q
varianceMatrixP =
(transitionMatrixA.multiply(varianceMatrixP)).multiply(transitionMatrixA.transpose());
// S = (H * P * HT) + R
RealMatrix S =
((measurementMatrixH.multiply(varianceMatrixP)).multiply(measurementMatrixH.transpose()))
.add(rMatrix);
RealMatrix S_1 = new LUDecomposition(S).getSolver().getInverse();
// P * HT * S-1
RealMatrix kalmanGainMatrix =
(varianceMatrixP.multiply(measurementMatrixH.transpose())).multiply(S_1);
// Xk = Xk + kalmanGainMatrix (Zk - HkXk )
prevMeasuredMatrix =
prevMeasuredMatrix.add(
kalmanGainMatrix.multiply(
(measuredMatrixX.subtract(measurementMatrixH.multiply(prevMeasuredMatrix)))));
// Pk = Pk - K.Hk.Pk
varianceMatrixP =
varianceMatrixP.subtract(
(kalmanGainMatrix.multiply(measurementMatrixH)).multiply(varianceMatrixP));
prevTimestamp = timestamp;
return prevMeasuredMatrix.getRow(0)[0];
}
}
private double generalizedCorrelationRatio(SampleIterator it, int inputDim, int out) {
Map<Double, Integer> n_y = new HashMap<>();
Map<Double, MultivariateSummaryStatistics> stat_y = new HashMap<>();
List<RealMatrix> x = new ArrayList<>();
MultivariateSummaryStatistics stat = new MultivariateSummaryStatistics(inputDim, unbiased);
for (int i = 0; i < maxSamples && it.hasNext(); i++) {
Sample sample = it.next();
double[] input = sample.getEncodedInput().toArray();
double output = sample.getEncodedOutput().getEntry(out);
if (!n_y.containsKey(output)) {
n_y.put(output, 0);
stat_y.put(output, new MultivariateSummaryStatistics(inputDim, unbiased));
}
injectNoise(input);
n_y.put(output, n_y.get(output) + 1);
stat_y.get(output).addValue(input);
x.add(new Array2DRowRealMatrix(input));
stat.addValue(input);
}
RealMatrix x_sum = new Array2DRowRealMatrix(stat.getSum());
Map<Double, RealMatrix> x_y_sum = new HashMap<>();
for (Entry<Double, MultivariateSummaryStatistics> entry : stat_y.entrySet()) {
x_y_sum.put(entry.getKey(), new Array2DRowRealMatrix(entry.getValue().getSum()));
}
RealMatrix H = new Array2DRowRealMatrix(inputDim, inputDim);
RealMatrix temp = new Array2DRowRealMatrix(inputDim, inputDim);
for (double key : n_y.keySet()) {
temp =
temp.add(
x_y_sum
.get(key)
.multiply(x_y_sum.get(key).transpose())
.scalarMultiply(1.0 / n_y.get(key)));
}
H = temp.subtract(x_sum.multiply(x_sum.transpose()).scalarMultiply(1.0 / x.size()));
RealMatrix E = new Array2DRowRealMatrix(inputDim, inputDim);
for (RealMatrix m : x) {
E = E.add(m.multiply(m.transpose()));
}
E = E.subtract(temp);
List<Integer> zeroColumns = findZeroColumns(E);
E = removeZeroColumns(E, zeroColumns);
H = removeZeroColumns(H, zeroColumns);
Matrix JE = new Matrix(E.getData());
Matrix JH = new Matrix(H.getData());
if (JE.rank() < JE.getRowDimension()) {
Log.write(this, "Some error occurred (E matrix is singular)");
return -1;
} else {
double lambda;
if (useEigenvalues) {
Matrix L = JE.inverse().times(JH);
double[] eigs = L.eig().getRealEigenvalues();
Arrays.sort(eigs);
lambda = 1;
int nonNullEigs = n_y.keySet().size() - 1;
for (int i = eigs.length - nonNullEigs; i < eigs.length; i++) {
if (Math.abs(eigs[i]) < zeroThreshold) {
Log.write(this, "Some error occurred (E matrix has too many null eigenvalues)");
return -1;
}
lambda *= 1.0 / (1.0 + eigs[i]);
}
} else {
Matrix sum = JE.plus(JH);
if (sum.rank() < sum.getRowDimension()) {
Log.write(this, "Some error occourred (E+H is singular");
return -1;
}
lambda = JE.det() / sum.det();
}
return Math.sqrt(1 - lambda);
}
}