OLS/SVD example
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@ -28,6 +28,7 @@ dependencies {
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implementation(project(":kmath-dimensions"))
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implementation(project(":kmath-ejml"))
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implementation(project(":kmath-nd4j"))
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implementation(project(":kmath-tensors"))
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implementation(project(":kmath-for-real"))
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@ -0,0 +1,68 @@
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/*
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* Copyright 2018-2021 KMath contributors.
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* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
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*/
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package space.kscience.kmath.tensors
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import space.kscience.kmath.tensors.core.DoubleTensor
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import space.kscience.kmath.tensors.core.algebras.DoubleAnalyticTensorAlgebra
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import space.kscience.kmath.tensors.core.algebras.DoubleLinearOpsTensorAlgebra
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// OLS estimator using SVD
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fun main() {
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//seed for random
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val randSeed = 100500L
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// work in context with linear operations
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DoubleLinearOpsTensorAlgebra {
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// take coefficient vector from normal distribution
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val alpha = randNormal(
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intArrayOf(5),
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randSeed
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) + fromArray(
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intArrayOf(5),
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doubleArrayOf(1.0, 2.5, 3.4, 5.0, 10.1)
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)
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println("Real alpha:\n" +
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"$alpha")
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// also take sample of size 20 from normal distribution for x TODO rename
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val x = randNormal(
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intArrayOf(20, 5),
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randSeed
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)
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// calculate y and add gaussian noise (N(0, 0.05)) TODO rename
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val y = x dot alpha
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y += y.randNormalLike(randSeed) * 0.05
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// now restore the coefficient vector with OSL estimator with SVD
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val (u, singValues, v) = x.svd()
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// we have to make sure the singular values of the matrix are not close to zero
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println("Singular values:\n" +
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"$singValues")
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// TODO something with Boolean tensors
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// inverse Sigma matrix can be restored from singular values with diagonalEmbedding function
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val sigma = diagonalEmbedding(1.0/singValues)
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val alphaOLS = v dot sigma dot u.transpose() dot y
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println("Estimated alpha:\n" +
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"$alphaOLS")
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// figure out MSE of approximation
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fun mse(yTrue: DoubleTensor, yPred: DoubleTensor): Double = DoubleAnalyticTensorAlgebra{
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require(yTrue.shape.size == 1)
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require(yTrue.shape contentEquals yPred.shape)
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val diff = yTrue - yPred
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diff.dot(diff).sqrt().value()
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}
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println("MSE: ${mse(alpha, alphaOLS)}")
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}
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}
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