Implemented closed form of Ridge regression

src/Numerics.Tests/LinearRegressionTests/LinearRegressionTests.cs

@@ -0,0 +1,99 @@
+using System;
+using System.Collections.Generic;
+using System.IO;
+using System.Linq;
+using System.Reflection;
+using MathNet.Numerics.LinearAlgebra;
+using MathNet.Numerics.LinearAlgebra.Double;
+using NUnit.Framework;
+
+namespace MathNet.Numerics.Tests.LinearRegressionTests
+{
+    [TestFixture, Category("Linear Regression Tests")]
+    public class LinearRegressionTests
+    {
+        [Test]
+        public void LinearRegressionsTest()
+        {
+            /*
+                x1 = 3;
+                x2 = 8;
+                x3 = 39;
+
+                Test solving of system of linear equations:
+
+                x1 + x2 + x3 = 50
+                x1 - x2 + x3 = 34
+                x1 + x2 - x3 = -23
+
+            */
+
+            Matrix<double> input = DenseMatrix.OfArray(new double[,] {
+                {1,1,1},
+                {1,-1,1},
+                {1,1,-1}});
+
+            var y = Vector<double>.Build.DenseOfArray(new double[] { 50, 34, -23 });
+            var weights = LinearRegression.MultipleRegression.DirectMethod(input, y);
+            var diff = new double[3];
+            diff[0] = 5.499999;
+            diff[1] = 8.000000;
+            diff[2] = 36.50000;
+            Assert.AreEqual(diff[0] - weights[0] < 0.0001, true);
+            Assert.AreEqual(diff[1] - weights[1] < 0.0001, true);
+            Assert.AreEqual(diff[2] - weights[2] < 0.0001, true);
+        }
+
+        private static double[][] GetInputsOutputsAll(out double[] outputs)
+        {
+            var fileName = Path.GetDirectoryName(typeof(LinearRegressionTests).GetTypeInfo().Assembly.Location) + @"\LinearRegressionTests\bikes_rent.csv";
+            var data = File.ReadAllLines(fileName);
+            var dataStrings = new List<string>(data.Skip(1));
+
+            var dataFragmentedStrigns = dataStrings.Select(a => a.Split(',')).ToList();
+            double[][] inputs = new double[dataFragmentedStrigns.Count][];
+            outputs = new double[dataFragmentedStrigns.Count];
+
+            for (int i = 0; i < dataFragmentedStrigns.Count(); i++)
+            {
+                inputs[i] = new double[dataFragmentedStrigns[0].Length - 1];
+            }
+
+            for (int i = 0; i < dataFragmentedStrigns.Count; i++)
+            {
+                int j;
+                for (j = 0; j < dataFragmentedStrigns[0].Length - 1; j++)
+                {
+                    inputs[i][j] = double.Parse(dataFragmentedStrigns[i][j]);
+                }
+
+                outputs[i] = double.Parse(dataFragmentedStrigns[i][j]);
+            }
+
+            return inputs;
+        }
+
+        [Test]
+        public void LinearRegressionsTestRidge()
+        {
+
+            var inputs = GetInputsOutputsAll(out var outputs);
+            var result0 = LinearRegression.MultipleRegression.RidgeRegression(inputs, outputs, 0);
+            var result1 = LinearRegression.MultipleRegression.RidgeRegression(inputs, outputs);
+            var result2 = LinearRegression.MultipleRegression.RidgeRegression(inputs, outputs, 10);
+
+            Assert.AreEqual(result0.Length, 13);
+            Assert.AreEqual(result1.Length, 13);
+            Assert.AreEqual(result2.Length, 13);
+
+            var avg0 = result0.Select(a => Math.Abs(a)).Average();
+            var avg1 = result1.Select(a => Math.Abs(a)).Average();
+            var avg2 = result2.Select(a => Math.Abs(a)).Average();
+
+            Assert.Greater(avg1, avg2); // The greater is the value of lambda, the smaller weights should be
+            Assert.Greater(avg0, avg1); // The greater is the value of lambda, the smaller weights should be
+
+        }
+
+    }
+}

src/Numerics.Tests/LinearRegressionTests/bikes_rent.csv

@@ -0,0 +1,732 @@
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src/Numerics.Tests/Numerics.Tests.csproj

@@ -29,5 +29,10 @@
   <ItemGroup>
     <Service Include="{82a7f48d-3b50-4b1e-b82e-3ada8210c358}" />
   </ItemGroup>
+  <ItemGroup>
+    <None Update="LinearRegressionTests\bikes_rent.csv">
+      <CopyToOutputDirectory>Always</CopyToOutputDirectory>
+    </None>
+  </ItemGroup>
   <Import Project="..\..\.paket\Paket.Restore.targets" />
 </Project>

src/Numerics/LinearRegression/MultipleRegression.cs

@@ -148,6 +148,34 @@ namespace MathNet.Numerics.LinearRegression
             return x.TransposeThisAndMultiply(x).Cholesky().Solve(x.TransposeThisAndMultiply(y));
         }
 
+        /// <summary>
+        /// Returns closed form solution for ridge regression calculation according to the following formula:
+        /// weights = (X' * X + lambda * I ) * X' * Y . Where X' stands for X' transposed
+        /// </summary>
+        /// <param name="xTrain">Training inputs</param>
+        /// <param name="yTrain">Training outputs</param>
+        /// <param name="lambda">Learning parameter. Will be used for decreasing weights. Default is set to 1</param>
+        /// <returns></returns>
+        public static double[] RidgeRegression(double[][] xTrain, double[] yTrain, double lambda = 1)
+        {
+            var M = Matrix<double>.Build;
+            var x = M.DenseOfRowArrays(xTrain);
+
+            var ones = Vector<double>.Build.Dense(x.RowCount, 1);
+            x = x.InsertColumn(0, ones);
+            var y = Vector<double>.Build.DenseOfArray(yTrain);
+
+            var xt = x.Transpose();
+
+            var lambdaIdentity = lambda * M.DenseIdentity(x.ColumnCount);
+            var sumDot = xt.Multiply(x) + lambdaIdentity;
+            var theInverse = sumDot.Inverse();
+            var inverseXt = theInverse * xt;
+            var w = inverseXt * y;
+
+            return w.ToArray();
+        }
+
         /// <summary>
         /// Find the model parameters β such that X*β with predictor X becomes as close to response Y as possible, with least squares residuals.
         /// Uses the cholesky decomposition of the normal equations.