Examples with Covariance org.apache.commons.math3.stat.correlation.Covariance used on opensource projects

Example 1 with Covariance

use of org.apache.commons.math3.stat.correlation.Covariance in project jstructure by JonStargaryen.

the class SVDSuperimposer method align.

@Override
public StructureAlignmentResult align(AtomContainer reference, AtomContainer query) {
    AtomContainer originalReference = reference;
    AtomContainer originalCandidate = query;
    Pair<GroupContainer, GroupContainer> atomContainerPair = AbstractAlignmentAlgorithm.comparableGroupContainerPair(reference, query, minimalSetOfAtomNames, maximalSetOfAtomNames);
    reference = atomContainerPair.getLeft();
    query = atomContainerPair.getRight();
    // calculate centroids
    double[] centroid1 = reference.calculate().centroid().getValue();
    double[] centroid2 = query.calculate().centroid().getValue();
    // center atoms
    reference.calculate().center();
    query.calculate().center();
    // compose covariance matrix and calculate SVD
    RealMatrix matrix1 = convertToMatrix(reference);
    RealMatrix matrix2 = convertToMatrix(query);
    RealMatrix covariance = matrix2.transpose().multiply(matrix1);
    SingularValueDecomposition svd = new SingularValueDecomposition(covariance);
    // R = (V * U')'
    RealMatrix ut = svd.getU().transpose();
    RealMatrix rotationMatrix = svd.getV().multiply(ut).transpose();
    // check if reflection
    if (new LUDecomposition(rotationMatrix).getDeterminant() < 0) {
        RealMatrix v = svd.getV().transpose();
        v.setEntry(2, 0, (0 - v.getEntry(2, 0)));
        v.setEntry(2, 1, (0 - v.getEntry(2, 1)));
        v.setEntry(2, 2, (0 - v.getEntry(2, 2)));
        rotationMatrix = v.transpose().multiply(ut).transpose();
    }
    double[][] rotation = rotationMatrix.getData();
    // calculate translation
    double[] translation = LinearAlgebra.on(centroid1).subtract(LinearAlgebra.on(centroid2).multiply(rotation)).getValue();
    logger.trace("rotation matrix\n{}\ntranslation vector\n{}", Arrays.deepToString(rotationMatrix.getData()), Arrays.toString(translation));
    /* transform 2nd atom select - employ neutral translation (3D vector of zeros), because the atoms are already
        * centered and calculate RMSD */
    query.calculate().transform(new Transformation(rotation));
    double rmsd = calculateRmsd(reference, query);
    // return alignment
    return new StructureAlignmentResult(originalReference, originalCandidate, query, rmsd, translation, rotation);
}

Example 2 with Covariance

use of org.apache.commons.math3.stat.correlation.Covariance in project GDSC-SMLM by aherbert.

the class MaximumLikelihoodFitter method computeFit.

/*
	 * (non-Javadoc)
	 * 
	 * @see gdsc.smlm.fitting.nonlinear.BaseFunctionSolver#computeFit(double[], double[], double[], double[])
	 */
public FitStatus computeFit(double[] y, double[] y_fit, double[] a, double[] a_dev) {
    final int n = y.length;
    LikelihoodWrapper maximumLikelihoodFunction = createLikelihoodWrapper((NonLinearFunction) f, n, y, a);
    @SuppressWarnings("rawtypes") BaseOptimizer baseOptimiser = null;
    try {
        double[] startPoint = getInitialSolution(a);
        PointValuePair optimum = null;
        if (searchMethod == SearchMethod.POWELL || searchMethod == SearchMethod.POWELL_BOUNDED || searchMethod == SearchMethod.POWELL_ADAPTER) {
            // Non-differentiable version using Powell Optimiser
            // This is as per the method in Numerical Recipes 10.5 (Direction Set (Powell's) method)
            // I could extend the optimiser and implement bounds on the directions moved. However the mapping
            // adapter seems to work OK.
            final boolean basisConvergence = false;
            // Perhaps these thresholds should be tighter?
            // The default is to use the sqrt() of the overall tolerance
            //final double lineRel = FastMath.sqrt(relativeThreshold);
            //final double lineAbs = FastMath.sqrt(absoluteThreshold);
            //final double lineRel = relativeThreshold * 1e2;
            //final double lineAbs = absoluteThreshold * 1e2;
            // Since we are fitting only a small number of parameters then just use the same tolerance 
            // for each search direction
            final double lineRel = relativeThreshold;
            final double lineAbs = absoluteThreshold;
            CustomPowellOptimizer o = new CustomPowellOptimizer(relativeThreshold, absoluteThreshold, lineRel, lineAbs, null, basisConvergence);
            baseOptimiser = o;
            OptimizationData maxIterationData = null;
            if (getMaxIterations() > 0)
                maxIterationData = new MaxIter(getMaxIterations());
            if (searchMethod == SearchMethod.POWELL_ADAPTER) {
                // Try using the mapping adapter for a bounded Powell search
                MultivariateFunctionMappingAdapter adapter = new MultivariateFunctionMappingAdapter(new MultivariateLikelihood(maximumLikelihoodFunction), lower, upper);
                optimum = o.optimize(maxIterationData, new MaxEval(getMaxEvaluations()), new ObjectiveFunction(adapter), GoalType.MINIMIZE, new InitialGuess(adapter.boundedToUnbounded(startPoint)));
                double[] solution = adapter.unboundedToBounded(optimum.getPointRef());
                optimum = new PointValuePair(solution, optimum.getValue());
            } else {
                if (powellFunction == null) {
                    // Python code by using the sqrt of the number of photons and background.
                    if (mapGaussian) {
                        Gaussian2DFunction gf = (Gaussian2DFunction) f;
                        // Re-map signal and background using the sqrt
                        int[] indices = gf.gradientIndices();
                        int[] map = new int[indices.length];
                        int count = 0;
                        // Background is always first
                        if (indices[0] == Gaussian2DFunction.BACKGROUND) {
                            map[count++] = 0;
                        }
                        // Look for the Signal in multiple peak 2D Gaussians
                        for (int i = 1; i < indices.length; i++) if (indices[i] % 6 == Gaussian2DFunction.SIGNAL) {
                            map[count++] = i;
                        }
                        if (count > 0) {
                            powellFunction = new MappedMultivariateLikelihood(maximumLikelihoodFunction, Arrays.copyOf(map, count));
                        }
                    }
                    if (powellFunction == null) {
                        powellFunction = new MultivariateLikelihood(maximumLikelihoodFunction);
                    }
                }
                // Update the maximum likelihood function in the Powell function wrapper
                powellFunction.fun = maximumLikelihoodFunction;
                OptimizationData positionChecker = null;
                // new org.apache.commons.math3.optim.PositionChecker(relativeThreshold, absoluteThreshold);
                SimpleBounds simpleBounds = null;
                if (powellFunction.isMapped()) {
                    MappedMultivariateLikelihood adapter = (MappedMultivariateLikelihood) powellFunction;
                    if (searchMethod == SearchMethod.POWELL_BOUNDED)
                        simpleBounds = new SimpleBounds(adapter.map(lower), adapter.map(upper));
                    optimum = o.optimize(maxIterationData, new MaxEval(getMaxEvaluations()), new ObjectiveFunction(powellFunction), GoalType.MINIMIZE, new InitialGuess(adapter.map(startPoint)), positionChecker, simpleBounds);
                    double[] solution = adapter.unmap(optimum.getPointRef());
                    optimum = new PointValuePair(solution, optimum.getValue());
                } else {
                    if (searchMethod == SearchMethod.POWELL_BOUNDED)
                        simpleBounds = new SimpleBounds(lower, upper);
                    optimum = o.optimize(maxIterationData, new MaxEval(getMaxEvaluations()), new ObjectiveFunction(powellFunction), GoalType.MINIMIZE, new InitialGuess(startPoint), positionChecker, simpleBounds);
                }
            }
        } else if (searchMethod == SearchMethod.BOBYQA) {
            // Differentiable approximation using Powell's BOBYQA algorithm.
            // This is slower than the Powell optimiser and requires a high number of evaluations.
            int numberOfInterpolationPoints = this.getNumberOfFittedParameters() + 2;
            BOBYQAOptimizer o = new BOBYQAOptimizer(numberOfInterpolationPoints);
            baseOptimiser = o;
            optimum = o.optimize(new MaxEval(getMaxEvaluations()), new ObjectiveFunction(new MultivariateLikelihood(maximumLikelihoodFunction)), GoalType.MINIMIZE, new InitialGuess(startPoint), new SimpleBounds(lower, upper));
        } else if (searchMethod == SearchMethod.CMAES) {
            // TODO - Understand why the CMAES optimiser does not fit very well on test data. It appears 
            // to converge too early and the likelihood scores are not as low as the other optimisers.
            // CMAESOptimiser based on Matlab code:
            // https://www.lri.fr/~hansen/cmaes.m
            // Take the defaults from the Matlab documentation
            //Double.NEGATIVE_INFINITY;
            double stopFitness = 0;
            boolean isActiveCMA = true;
            int diagonalOnly = 0;
            int checkFeasableCount = 1;
            RandomGenerator random = new Well19937c();
            boolean generateStatistics = false;
            // The sigma determines the search range for the variables. It should be 1/3 of the initial search region.
            double[] sigma = new double[lower.length];
            for (int i = 0; i < sigma.length; i++) sigma[i] = (upper[i] - lower[i]) / 3;
            int popSize = (int) (4 + Math.floor(3 * Math.log(sigma.length)));
            // The CMAES optimiser is random and restarting can overcome problems with quick convergence.
            // The Apache commons documentations states that convergence should occur between 30N and 300N^2
            // function evaluations
            final int n30 = FastMath.min(sigma.length * sigma.length * 30, getMaxEvaluations() / 2);
            evaluations = 0;
            OptimizationData[] data = new OptimizationData[] { new InitialGuess(startPoint), new CMAESOptimizer.PopulationSize(popSize), new MaxEval(getMaxEvaluations()), new CMAESOptimizer.Sigma(sigma), new ObjectiveFunction(new MultivariateLikelihood(maximumLikelihoodFunction)), GoalType.MINIMIZE, new SimpleBounds(lower, upper) };
            // Iterate to prevent early convergence
            int repeat = 0;
            while (evaluations < n30) {
                if (repeat++ > 1) {
                    // Update the start point and population size
                    data[0] = new InitialGuess(optimum.getPointRef());
                    popSize *= 2;
                    data[1] = new CMAESOptimizer.PopulationSize(popSize);
                }
                CMAESOptimizer o = new CMAESOptimizer(getMaxIterations(), stopFitness, isActiveCMA, diagonalOnly, checkFeasableCount, random, generateStatistics, new SimpleValueChecker(relativeThreshold, absoluteThreshold));
                baseOptimiser = o;
                PointValuePair result = o.optimize(data);
                iterations += o.getIterations();
                evaluations += o.getEvaluations();
                //		o.getEvaluations(), totalEvaluations);
                if (optimum == null || result.getValue() < optimum.getValue()) {
                    optimum = result;
                }
            }
            // Prevent incrementing the iterations again
            baseOptimiser = null;
        } else if (searchMethod == SearchMethod.BFGS) {
            // BFGS can use an approximate line search minimisation where as Powell and conjugate gradient
            // methods require a more accurate line minimisation. The BFGS search does not do a full 
            // minimisation but takes appropriate steps in the direction of the current gradient.
            // Do not use the convergence checker on the value of the function. Use the convergence on the 
            // point coordinate and gradient
            //BFGSOptimizer o = new BFGSOptimizer(new SimpleValueChecker(rel, abs));
            BFGSOptimizer o = new BFGSOptimizer();
            baseOptimiser = o;
            // Configure maximum step length for each dimension using the bounds
            double[] stepLength = new double[lower.length];
            for (int i = 0; i < stepLength.length; i++) {
                stepLength[i] = (upper[i] - lower[i]) * 0.3333333;
                if (stepLength[i] <= 0)
                    stepLength[i] = Double.POSITIVE_INFINITY;
            }
            // The GoalType is always minimise so no need to pass this in
            OptimizationData positionChecker = null;
            //new org.apache.commons.math3.optim.PositionChecker(relativeThreshold, absoluteThreshold);
            optimum = o.optimize(new MaxEval(getMaxEvaluations()), new ObjectiveFunctionGradient(new MultivariateVectorLikelihood(maximumLikelihoodFunction)), new ObjectiveFunction(new MultivariateLikelihood(maximumLikelihoodFunction)), new InitialGuess(startPoint), new SimpleBounds(lowerConstraint, upperConstraint), new BFGSOptimizer.GradientTolerance(relativeThreshold), positionChecker, new BFGSOptimizer.StepLength(stepLength));
        } else {
            // The line search algorithm often fails. This is due to searching into a region where the 
            // function evaluates to a negative so has been clipped. This means the upper bound of the line
            // cannot be found.
            // Note that running it on an easy problem (200 photons with fixed fitting (no background)) the algorithm
            // does sometimes produces results better than the Powell algorithm but it is slower.
            BoundedNonLinearConjugateGradientOptimizer o = new BoundedNonLinearConjugateGradientOptimizer((searchMethod == SearchMethod.CONJUGATE_GRADIENT_FR) ? Formula.FLETCHER_REEVES : Formula.POLAK_RIBIERE, new SimpleValueChecker(relativeThreshold, absoluteThreshold));
            baseOptimiser = o;
            // Note: The gradients may become unstable at the edge of the bounds. Or they will not change 
            // direction if the true solution is on the bounds since the gradient will always continue 
            // towards the bounds. This is key to the conjugate gradient method. It searches along a vector 
            // until the direction of the gradient is in the opposite direction (using dot products, i.e. 
            // cosine of angle between them)
            // NR 10.7 states there is no advantage of the variable metric DFP or BFGS methods over
            // conjugate gradient methods. So I will try these first.
            // Try this:
            // Adapt the conjugate gradient optimiser to use the gradient to pick the search direction
            // and then for the line minimisation. However if the function is out of bounds then clip the 
            // variables at the bounds and continue. 
            // If the current point is at the bounds and the gradient is to continue out of bounds then 
            // clip the gradient too.
            // Or: just use the gradient for the search direction then use the line minimisation/rest
            // as per the Powell optimiser. The bounds should limit the search.
            // I tried a Bounded conjugate gradient optimiser with clipped variables:
            // This sometimes works. However when the variables go a long way out of the expected range the gradients
            // can have vastly different magnitudes. This results in the algorithm stalling since the gradients
            // can be close to zero and the some of the parameters are no longer adjusted.
            // Perhaps this can be looked for and the algorithm then gives up and resorts to a Powell optimiser from 
            // the current point.
            // Changed the bracketing step to very small (default is 1, changed to 0.001). This improves the 
            // performance. The gradient direction is very sensitive to small changes in the coordinates so a 
            // tighter bracketing of the line search helps.
            // Tried using a non-gradient method for the line search copied from the Powell optimiser:
            // This also works when the bracketing step is small but the number of iterations is higher.
            // 24.10.2014: I have tried to get conjugate gradient to work but the gradient function 
            // must not behave suitably for the optimiser. In the current state both methods of using a 
            // Bounded Conjugate Gradient Optimiser perform poorly relative to other optimisers:
            // Simulated : n=1000, signal=200, x=0.53, y=0.47
            // LVM : n=1000, signal=171, x=0.537, y=0.471 (1.003s)
            // Powell : n=1000, signal=187, x=0.537, y=0.48 (1.238s)
            // Gradient based PR (constrained): n=858, signal=161, x=0.533, y=0.474 (2.54s)
            // Gradient based PR (bounded): n=948, signal=161, x=0.533, y=0.473 (2.67s)
            // Non-gradient based : n=1000, signal=151.47, x=0.535, y=0.474 (1.626s)
            // The conjugate optimisers are slower, under predict the signal by the most and in the case of 
            // the gradient based optimiser, fail to converge on some problems. This is worse when constrained
            // fitting is used and not tightly bounded fitting.
            // I will leave the code in as an option but would not recommend using it. I may remove it in the 
            // future.
            // Note: It is strange that the non-gradient based line minimisation is more successful.
            // It may be that the gradient function is not accurate (due to round off error) or that it is
            // simply wrong when far from the optimum. My JUnit tests only evaluate the function within the 
            // expected range of the answer.
            // Note the default step size on the Powell optimiser is 1 but the initial directions are unit vectors.
            // So our bracketing step should be a minimum of 1 / average length of the first gradient vector to prevent
            // the first step being too large when bracketing.
            final double[] gradient = new double[startPoint.length];
            maximumLikelihoodFunction.likelihood(startPoint, gradient);
            double l = 0;
            for (double d : gradient) l += d * d;
            final double bracketingStep = FastMath.min(0.001, ((l > 1) ? 1.0 / l : 1));
            //System.out.printf("Bracketing step = %f (length=%f)\n", bracketingStep, l);
            o.setUseGradientLineSearch(gradientLineMinimisation);
            optimum = o.optimize(new MaxEval(getMaxEvaluations()), new ObjectiveFunctionGradient(new MultivariateVectorLikelihood(maximumLikelihoodFunction)), new ObjectiveFunction(new MultivariateLikelihood(maximumLikelihoodFunction)), GoalType.MINIMIZE, new InitialGuess(startPoint), new SimpleBounds(lowerConstraint, upperConstraint), new BoundedNonLinearConjugateGradientOptimizer.BracketingStep(bracketingStep));
        //maximumLikelihoodFunction.value(solution, gradient);
        //System.out.printf("Iter = %d, %g @ %s : %s\n", iterations, ll, Arrays.toString(solution),
        //		Arrays.toString(gradient));
        }
        final double[] solution = optimum.getPointRef();
        setSolution(a, solution);
        if (a_dev != null) {
            // Assume the Maximum Likelihood estimator returns the optimum fit (achieves the Cramer Roa
            // lower bounds) and so the covariance can be obtained from the Fisher Information Matrix.
            FisherInformationMatrix m = new FisherInformationMatrix(maximumLikelihoodFunction.fisherInformation(a));
            setDeviations(a_dev, m.crlb(true));
        }
        // Reverse negative log likelihood for maximum likelihood score
        value = -optimum.getValue();
    } catch (TooManyIterationsException e) {
        //e.printStackTrace();
        return FitStatus.TOO_MANY_ITERATIONS;
    } catch (TooManyEvaluationsException e) {
        //e.printStackTrace();
        return FitStatus.TOO_MANY_EVALUATIONS;
    } catch (ConvergenceException e) {
        //System.out.printf("Singular non linear model = %s\n", e.getMessage());
        return FitStatus.SINGULAR_NON_LINEAR_MODEL;
    } catch (BFGSOptimizer.LineSearchRoundoffException e) {
        //e.printStackTrace();
        return FitStatus.FAILED_TO_CONVERGE;
    } catch (Exception e) {
        //System.out.printf("Unknown error = %s\n", e.getMessage());
        e.printStackTrace();
        return FitStatus.UNKNOWN;
    } finally {
        if (baseOptimiser != null) {
            iterations += baseOptimiser.getIterations();
            evaluations += baseOptimiser.getEvaluations();
        }
    }
    // Check this as likelihood functions can go wrong
    if (Double.isInfinite(value) || Double.isNaN(value))
        return FitStatus.INVALID_LIKELIHOOD;
    return FitStatus.OK;
}

Example 3 with Covariance

use of org.apache.commons.math3.stat.correlation.Covariance in project gatk by broadinstitute.

the class CoverageModelEMWorkspace method initializeWorkersWithPCA.

/**
     * Initialize model parameters by performing PCA.
     */
@EvaluatesRDD
@UpdatesRDD
@CachesRDD
private void initializeWorkersWithPCA() {
    logger.info("Initializing model parameters using PCA...");
    /* initially, set m_t, Psi_t and W_tl to zero to get an estimate of the read depth */
    final int numLatents = config.getNumLatents();
    mapWorkers(cb -> cb.cloneWithUpdatedPrimitive(CoverageModelEMComputeBlock.CoverageModelICGCacheNode.m_t, Nd4j.zeros(new int[] { 1, cb.getTargetSpaceBlock().getNumElements() })).cloneWithUpdatedPrimitive(CoverageModelEMComputeBlock.CoverageModelICGCacheNode.Psi_t, Nd4j.zeros(new int[] { 1, cb.getTargetSpaceBlock().getNumElements() })));
    if (biasCovariatesEnabled) {
        mapWorkers(cb -> cb.cloneWithUpdatedPrimitive(CoverageModelEMComputeBlock.CoverageModelICGCacheNode.W_tl, Nd4j.zeros(new int[] { cb.getTargetSpaceBlock().getNumElements(), numLatents })));
    }
    /* update read depth without taking into account correction from bias covariates */
    updateReadDepthPosteriorExpectations(1.0, true);
    /* fetch sample covariance matrix */
    final int minPCAInitializationReadCount = config.getMinPCAInitializationReadCount();
    mapWorkers(cb -> cb.cloneWithPCAInitializationData(minPCAInitializationReadCount, Integer.MAX_VALUE));
    cacheWorkers("PCA initialization");
    final INDArray targetCovarianceMatrix = mapWorkersAndReduce(CoverageModelEMComputeBlock::calculateTargetCovarianceMatrixForPCAInitialization, INDArray::add);
    /* perform eigen-decomposition on the target covariance matrix */
    final ImmutablePair<INDArray, INDArray> targetCovarianceEigensystem = CoverageModelEMWorkspaceMathUtils.eig(targetCovarianceMatrix, false, logger);
    /* the eigenvalues of sample covariance matrix can be immediately inferred by scaling */
    final INDArray sampleCovarianceEigenvalues = targetCovarianceEigensystem.getLeft().div(numSamples);
    /* estimate the isotropic unexplained variance -- see Bishop 12.46 */
    final int residualDim = numTargets - numLatents;
    final double isotropicVariance = sampleCovarianceEigenvalues.get(NDArrayIndex.interval(numLatents, numSamples)).sumNumber().doubleValue() / residualDim;
    logger.info(String.format("PCA estimate of isotropic unexplained variance: %f", isotropicVariance));
    /* estimate bias factors -- see Bishop 12.45 */
    final INDArray scaleFactors = Transforms.sqrt(sampleCovarianceEigenvalues.get(NDArrayIndex.interval(0, numLatents)).sub(isotropicVariance), false);
    final INDArray biasCovariatesPCA = Nd4j.create(new int[] { numTargets, numLatents });
    for (int li = 0; li < numLatents; li++) {
        final INDArray v = targetCovarianceEigensystem.getRight().getColumn(li);
        /* calculate [Delta_PCA_st]^T v */
        /* note: we do not need to broadcast vec since it is small and lambda capture is just fine */
        final INDArray unnormedBiasCovariate = CoverageModelSparkUtils.assembleINDArrayBlocksFromCollection(mapWorkersAndCollect(cb -> ImmutablePair.of(cb.getTargetSpaceBlock(), cb.getINDArrayFromCache(CoverageModelEMComputeBlock.CoverageModelICGCacheNode.Delta_PCA_st).transpose().mmul(v))), 0);
        final double norm = unnormedBiasCovariate.norm1Number().doubleValue();
        final INDArray normedBiasCovariate = unnormedBiasCovariate.divi(norm).muli(scaleFactors.getDouble(li));
        biasCovariatesPCA.getColumn(li).assign(normedBiasCovariate);
    }
    if (ardEnabled) {
        /* a better estimate of ARD coefficients */
        biasCovariatesARDCoefficients.assign(Nd4j.zeros(new int[] { 1, numLatents }).addi(config.getInitialARDPrecisionRelativeToNoise() / isotropicVariance));
    }
    final CoverageModelParameters modelParamsFromPCA = new CoverageModelParameters(processedTargetList, Nd4j.zeros(new int[] { 1, numTargets }), Nd4j.zeros(new int[] { 1, numTargets }).addi(isotropicVariance), biasCovariatesPCA, biasCovariatesARDCoefficients);
    /* clear PCA initialization data from workers */
    mapWorkers(CoverageModelEMComputeBlock::cloneWithRemovedPCAInitializationData);
    /* push model parameters to workers */
    initializeWorkersWithGivenModel(modelParamsFromPCA);
    /* update bias latent posterior expectations without admixing */
    updateBiasLatentPosteriorExpectations(1.0);
}

Example 4 with Covariance

use of org.apache.commons.math3.stat.correlation.Covariance in project gatk by broadinstitute.

the class CoverageModelParameters method write.

/**
     * Writes the model to disk.
     *
     * @param outputPath model output path
     */
public static void write(@Nonnull CoverageModelParameters model, @Nonnull final String outputPath) {
    /* create output directory if it doesn't exist */
    createOutputPath(Utils.nonNull(outputPath, "The output path string must be non-null"));
    /* write targets list */
    final File targetListFile = new File(outputPath, CoverageModelGlobalConstants.TARGET_LIST_OUTPUT_FILE);
    TargetWriter.writeTargetsToFile(targetListFile, model.getTargetList());
    final List<String> targetNames = model.getTargetList().stream().map(Target::getName).collect(Collectors.toList());
    /* write target mean bias to file */
    final File targetMeanBiasFile = new File(outputPath, CoverageModelGlobalConstants.TARGET_MEAN_LOG_BIAS_OUTPUT_FILE);
    Nd4jIOUtils.writeNDArrayMatrixToTextFile(model.getTargetMeanLogBias().transpose(), targetMeanBiasFile, MEAN_LOG_BIAS_MATRIX_NAME, targetNames, null);
    /* write target unexplained variance to file */
    final File targetUnexplainedVarianceFile = new File(outputPath, CoverageModelGlobalConstants.TARGET_UNEXPLAINED_VARIANCE_OUTPUT_FILE);
    Nd4jIOUtils.writeNDArrayMatrixToTextFile(model.getTargetUnexplainedVariance().transpose(), targetUnexplainedVarianceFile, TARGET_UNEXPLAINED_VARIANCE_MATRIX_NAME, targetNames, null);
    if (model.isBiasCovariatesEnabled()) {
        /* write mean bias covariates to file */
        final List<String> meanBiasCovariatesNames = IntStream.range(0, model.getNumLatents()).mapToObj(li -> String.format(BIAS_COVARIATE_COLUMN_NAME_FORMAT, li)).collect(Collectors.toList());
        final File meanBiasCovariatesFile = new File(outputPath, CoverageModelGlobalConstants.MEAN_BIAS_COVARIATES_OUTPUT_FILE);
        Nd4jIOUtils.writeNDArrayMatrixToTextFile(model.getMeanBiasCovariates(), meanBiasCovariatesFile, MEAN_BIAS_COVARIATES_MATRIX_NAME, targetNames, meanBiasCovariatesNames);
        /* write norm_2 of mean bias covariates to file */
        final INDArray WTW = model.getMeanBiasCovariates().transpose().mmul(model.getMeanBiasCovariates());
        final double[] biasCovariatesNorm2 = IntStream.range(0, model.getNumLatents()).mapToDouble(li -> WTW.getDouble(li, li)).toArray();
        final File biasCovariatesNorm2File = new File(outputPath, CoverageModelGlobalConstants.MEAN_BIAS_COVARIATES_NORM2_OUTPUT_FILE);
        Nd4jIOUtils.writeNDArrayMatrixToTextFile(Nd4j.create(biasCovariatesNorm2, new int[] { 1, model.getNumLatents() }), biasCovariatesNorm2File, MEAN_BIAS_COVARIATES_NORM_2_MATRIX_NAME, null, meanBiasCovariatesNames);
        /* if ARD is enabled, write the ARD coefficients and covariance of W as well */
        if (model.isARDEnabled()) {
            final File biasCovariatesARDCoefficientsFile = new File(outputPath, CoverageModelGlobalConstants.BIAS_COVARIATES_ARD_COEFFICIENTS_OUTPUT_FILE);
            Nd4jIOUtils.writeNDArrayMatrixToTextFile(model.getBiasCovariateARDCoefficients(), biasCovariatesARDCoefficientsFile, BIAS_COVARIATES_ARD_COEFFICIENTS_MATRIX_NAME, null, meanBiasCovariatesNames);
        }
    }
}

Example 5 with Covariance

use of org.apache.commons.math3.stat.correlation.Covariance in project gatk-protected by broadinstitute.

the class CoverageModelEMWorkspace method initializeWorkersWithPCA.

/**
     * Initialize model parameters by performing PCA.
     */
@EvaluatesRDD
@UpdatesRDD
@CachesRDD
private void initializeWorkersWithPCA() {
    logger.info("Initializing model parameters using PCA...");
    /* initially, set m_t, Psi_t and W_tl to zero to get an estimate of the read depth */
    final int numLatents = config.getNumLatents();
    mapWorkers(cb -> cb.cloneWithUpdatedPrimitive(CoverageModelEMComputeBlock.CoverageModelICGCacheNode.m_t, Nd4j.zeros(new int[] { 1, cb.getTargetSpaceBlock().getNumElements() })).cloneWithUpdatedPrimitive(CoverageModelEMComputeBlock.CoverageModelICGCacheNode.Psi_t, Nd4j.zeros(new int[] { 1, cb.getTargetSpaceBlock().getNumElements() })));
    if (biasCovariatesEnabled) {
        mapWorkers(cb -> cb.cloneWithUpdatedPrimitive(CoverageModelEMComputeBlock.CoverageModelICGCacheNode.W_tl, Nd4j.zeros(new int[] { cb.getTargetSpaceBlock().getNumElements(), numLatents })));
    }
    /* update read depth without taking into account correction from bias covariates */
    updateReadDepthPosteriorExpectations(1.0, true);
    /* fetch sample covariance matrix */
    final int minPCAInitializationReadCount = config.getMinPCAInitializationReadCount();
    mapWorkers(cb -> cb.cloneWithPCAInitializationData(minPCAInitializationReadCount, Integer.MAX_VALUE));
    cacheWorkers("PCA initialization");
    final INDArray targetCovarianceMatrix = mapWorkersAndReduce(CoverageModelEMComputeBlock::calculateTargetCovarianceMatrixForPCAInitialization, INDArray::add);
    /* perform eigen-decomposition on the target covariance matrix */
    final ImmutablePair<INDArray, INDArray> targetCovarianceEigensystem = CoverageModelEMWorkspaceMathUtils.eig(targetCovarianceMatrix, false, logger);
    /* the eigenvalues of sample covariance matrix can be immediately inferred by scaling */
    final INDArray sampleCovarianceEigenvalues = targetCovarianceEigensystem.getLeft().div(numSamples);
    /* estimate the isotropic unexplained variance -- see Bishop 12.46 */
    final int residualDim = numTargets - numLatents;
    final double isotropicVariance = sampleCovarianceEigenvalues.get(NDArrayIndex.interval(numLatents, numSamples)).sumNumber().doubleValue() / residualDim;
    logger.info(String.format("PCA estimate of isotropic unexplained variance: %f", isotropicVariance));
    /* estimate bias factors -- see Bishop 12.45 */
    final INDArray scaleFactors = Transforms.sqrt(sampleCovarianceEigenvalues.get(NDArrayIndex.interval(0, numLatents)).sub(isotropicVariance), false);
    final INDArray biasCovariatesPCA = Nd4j.create(new int[] { numTargets, numLatents });
    for (int li = 0; li < numLatents; li++) {
        final INDArray v = targetCovarianceEigensystem.getRight().getColumn(li);
        /* calculate [Delta_PCA_st]^T v */
        /* note: we do not need to broadcast vec since it is small and lambda capture is just fine */
        final INDArray unnormedBiasCovariate = CoverageModelSparkUtils.assembleINDArrayBlocksFromCollection(mapWorkersAndCollect(cb -> ImmutablePair.of(cb.getTargetSpaceBlock(), cb.getINDArrayFromCache(CoverageModelEMComputeBlock.CoverageModelICGCacheNode.Delta_PCA_st).transpose().mmul(v))), 0);
        final double norm = unnormedBiasCovariate.norm1Number().doubleValue();
        final INDArray normedBiasCovariate = unnormedBiasCovariate.divi(norm).muli(scaleFactors.getDouble(li));
        biasCovariatesPCA.getColumn(li).assign(normedBiasCovariate);
    }
    if (ardEnabled) {
        /* a better estimate of ARD coefficients */
        biasCovariatesARDCoefficients.assign(Nd4j.zeros(new int[] { 1, numLatents }).addi(config.getInitialARDPrecisionRelativeToNoise() / isotropicVariance));
    }
    final CoverageModelParameters modelParamsFromPCA = new CoverageModelParameters(processedTargetList, Nd4j.zeros(new int[] { 1, numTargets }), Nd4j.zeros(new int[] { 1, numTargets }).addi(isotropicVariance), biasCovariatesPCA, biasCovariatesARDCoefficients);
    /* clear PCA initialization data from workers */
    mapWorkers(CoverageModelEMComputeBlock::cloneWithRemovedPCAInitializationData);
    /* push model parameters to workers */
    initializeWorkersWithGivenModel(modelParamsFromPCA);
    /* update bias latent posterior expectations without admixing */
    updateBiasLatentPosteriorExpectations(1.0);
}