OLS/SVD example

examples/build.gradle.kts

@@ -28,6 +28,7 @@ dependencies {
     implementation(project(":kmath-dimensions"))
     implementation(project(":kmath-ejml"))
     implementation(project(":kmath-nd4j"))
+    implementation(project(":kmath-tensors"))
 
     implementation(project(":kmath-for-real"))
 

examples/src/main/kotlin/space/kscience/kmath/tensors/OLSWithSVD.kt

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