/**Return a D x N matrix*/
public static Matrix ToInputMatrix(RandomFeatureMap fm, List <IKEPDist[]> inputs)
{
Vector[] features = inputs.Select(msgs => fm.MapToVector(msgs)).ToArray();
Matrix m = MatrixUtils.StackColumns(features);
return(m);
}
public override RandomFeatureMap Regenerate(int[] numFeatures)
{
RandomFeatureMap[] newMaps = new RandomFeatureMap[maps.Length];
for (int i = 0; i < maps.Length; i++)
{
newMaps[i] = maps[i].Regenerate(numFeatures);
}
return(new StackFeatureMap(newMaps));
}
/**
* Evaluate the feature map with a leave-one-out cross validation.
* Return a vector of squared loss values, each corresponding to a regularization
* parameter in regList.
* This implementation follows cond_fm_finiteout.m
*/
public static double[] EvaluateFeatureMap(RandomFeatureMap fm,
double[] regList, List <IKEPDist[]> inputs, List <double> outputs)
{
// see http://numerics.mathdotnet.com/Matrix.html for how to use MathNet Matrix
Matrix xtemp = ToInputMatrix(fm, inputs);
MNMatrix x = MatrixUtils.ToMathNetMatrix(xtemp);
double[] errs = new double[regList.Length];
for (int i = 0; i < regList.Length; i++)
{
double lambda = regList[i];
}
throw new NotImplementedException();
}
public static new BayesLinRegFM FromMatlabStruct(MatlabStruct s)
{
// s.className=class(this);
// s.featureMap=this.featureMap.toStruct();
// %s.regParam=this.regParam;
// s.mapMatrix=this.mapMatrix;
// s.posteriorCov = this.posteriorCov;
// s.noise_var = this.noise_var;
string className = s.GetString("className");
if (!className.Equals(MATLAB_CLASS))
{
throw new ArgumentException("The input does not represent a " + MATLAB_CLASS);
}
MatlabStruct fmStruct = s.GetStruct("featureMap");
RandomFeatureMap featureMap = RandomFeatureMap.FromMatlabStruct(fmStruct);
// This is the same as a posterior mean
Vector mapMatrix = s.Get1DVector("mapMatrix");
if (mapMatrix.Count != featureMap.GetOutputDimension())
{
throw new ArgumentException("mapMatrix and featureMap's dimenions are incompatible.");
}
Matrix postCov = s.GetMatrix("posteriorCov");
if (postCov.Cols != featureMap.GetOutputDimension())
{
throw new ArgumentException("posterior covariance and featureMap's dimenions are incompatible.");
}
double noise_var = s.GetDouble("noise_var");
Vector crossCorr = s.Get1DVector("crossCorrelation");
var bayes = new BayesLinRegFM();
bayes.featureMap = featureMap;
bayes.posteriorMean = mapMatrix;
bayes.posteriorCov = postCov;
bayes.noiseVar = noise_var;
bayes.crossCorr = crossCorr;
// No need to do the initial batch train because we loaded the result
// from .mat.
bayes.WillNeedInitialTrain = false;
return(bayes);
}
/**
* Initialize an empty Bayesian linear regressor suitable for online
* learning from scratch.
*/
public BayesLinRegFM(RandomFeatureMap featureMap)
{
// if(noiseVar < 0){
// throw new ArgumentException("Require noise variance >= 0");
// }
// this.noiseVar = noiseVar;
// if(uThreshold < 0){
// throw new ArgumentException("Require uncertainty threshold >= 0");
// }
// this.uThreshold = uThreshold;
int D = featureMap.GetOutputDimension();
this.featureMap = featureMap;
// this.noiseVar = noiseVar;
// this.uThreshold = uThreshold;
this.posteriorMean = Vector.Zero(D);
// assume that the prior for W is N(0, 1)
this.posteriorCov = Matrix.IdentityScaledBy(D, 1.0);
this.crossCorr = Vector.Zero(D);
}
public static RandomFeatureMap FromMatlabStruct(MatlabStruct s)
{
string className = s.GetString("className");
RandomFeatureMap map = null;
if (className.Equals(RFGJointKGG.MATLAB_CLASS))
{
map = RFGJointKGG.FromMatlabStruct(s);
}
else
{
throw new ArgumentException("Unknown className: " + className);
}
// else if(className.Equals("RFGSumEProdMap")){
//
// }else if(className.Equals("RFGEProdMap")){
//
// }else if(className.Equals("RFGJointEProdMap")){
//
// }else if(className.Equals("RFGProductEProdMap")){
//
// }
return(map);
}
private void BatchLearn()
{
// Batch learning uses the collected messages. This will reset many
// properties of the object.
// TODO: full cross validation later.
// For now, we will use median heuristic to set the parameter.
// int[] inOutNumFeatures = { this.MinibatchInnerFeatures, this.MinibatchOuterFeatures };
int[] inOutNumFeatures = { this.InnerFeatures, this.OuterFeatures };
// int[] inOutNumFeatures = { 200, 400 };
// int[] inOutNumFeatures = {400, 700};
// int[] inOutNumFeatures = {50, 50};
double[] medianFactors = { 0.5 };
Random rng = new Random(1);
List <IKEPDist[]> inputs = this.batchInputs;
List <RandomFeatureMap> candidates = featureMap.GenCandidates(
inputs, inOutNumFeatures, medianFactors, rng);
/*
* unfinished cross validation implementation
* double[] noiseVarCandidates = new double[]{1e-4, 1e-3, 1e-2};
* var M = MNMatrix.Build;
* int n = inputs.Count;
* MNVector Y = MNVector.Build.Dense(batchOutputs.ToArray());
* double[][] looMSErrs = new double[candidates.Count][];
* // TODO: Improve this with parallel for-loop ?
* Console.WriteLine("#### Performing initial batch learning ####");
* Console.WriteLine();
*
* for(int i=0; i<candidates.Count; i++){
* RandomFeatureMap fm = candidates[i];
* int d = fm.GetOutputDimension();
* MNMatrix Idd = M.SparseIdentity(d);
* // D x N matrix
* MNMatrix phi = fm.GenFeaturesMNMat(inputs);
* MNMatrix ppt = phi.TransposeAndMultiply(phi);
* looMSErrs[i] = new double[noiseVarCandidates.Length];
* for(int nj=0; nj<noiseVarCandidates.Length; nj++){
* double noiseVariance = noiseVarCandidates[nj];
* MNMatrix regI = M.SparseDiagonal(d, noiseVariance);
* MNMatrix A = ppt + regI;
* MNMatrix X = A.Solve(phi);
* Debug.Assert(X.RowCount == d);
* Debug.Assert(X.ColumnCount == n);
* // TODO: H does not need to be formed explicitly.
* // This is efficient if n > d. Later.
* MNMatrix H = Idd - phi.TransposeThisAndMultiply(X);
* MNVector HDiagInv = H.Diagonal();
* HDiagInv.MapInplace(delegate(double v){
* return 1.0/v;
* });
* double errSqrt = H.LeftMultiply(Y).PointwiseMultiply(HDiagInv).L2Norm();
* looMSErrs[i][nj] = errSqrt*errSqrt/n;
*
* Console.WriteLine("");
* }
* }
*/
this.featureMap = candidates[0];
this.noiseVar = 1e-4;
const double priorVariance = 1.0;
// this.featureMap = fm;
// threshold on log predict variance
// Used -8.5 for the logistic regression problem
// this.uThreshold = -8.5;
Vector[] features = inputs.Select(msgs => featureMap.MapToVector(msgs)).ToArray();
Matrix x = MatrixUtils.StackColumns(features);
Vector y = Vector.FromList(batchOutputs);
int Dout = x.Rows;
// Matrix x is d x n
Matrix xxt = x * x.Transpose();
crossCorr = x * y;
Matrix postPrec = xxt * (1.0 / noiseVar) + Matrix.IdentityScaledBy(Dout, 1.0 / priorVariance);
this.posteriorCov = MatrixUtils.Inverse(postPrec);
this.posteriorMean = this.posteriorCov * crossCorr * (1.0 / this.noiseVar);
if (double.IsNaN(uThreshold))
{
uThreshold = -8.5;
}
// throw new NotImplementedException();
}
