// <copyright file="LocallyWeightedRegression.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2013 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System;
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using System.Collections.Generic;
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using IStation.Numerics.LinearAlgebra;
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namespace IStation.Numerics.LinearRegression
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{
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public static class WeightedRegression
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{
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/// <summary>
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/// Weighted Linear Regression using normal equations.
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/// </summary>
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/// <param name="x">Predictor matrix X</param>
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/// <param name="y">Response vector Y</param>
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/// <param name="w">Weight matrix W, usually diagonal with an entry for each predictor (row).</param>
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public static Vector<T> Weighted<T>(Matrix<T> x, Vector<T> y, Matrix<T> w) where T : struct, IEquatable<T>, IFormattable
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{
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return x.TransposeThisAndMultiply(w*x).Cholesky().Solve(x.TransposeThisAndMultiply(w*y));
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}
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/// <summary>
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/// Weighted Linear Regression using normal equations.
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/// </summary>
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/// <param name="x">Predictor matrix X</param>
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/// <param name="y">Response matrix Y</param>
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/// <param name="w">Weight matrix W, usually diagonal with an entry for each predictor (row).</param>
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public static Matrix<T> Weighted<T>(Matrix<T> x, Matrix<T> y, Matrix<T> w) where T : struct, IEquatable<T>, IFormattable
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{
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return x.TransposeThisAndMultiply(w*x).Cholesky().Solve(x.TransposeThisAndMultiply(w*y));
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}
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/// <summary>
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/// Weighted Linear Regression using normal equations.
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/// </summary>
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/// <param name="x">Predictor matrix X</param>
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/// <param name="y">Response vector Y</param>
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/// <param name="w">Weight matrix W, usually diagonal with an entry for each predictor (row).</param>
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/// <param name="intercept">True if an intercept should be added as first artificial predictor value. Default = false.</param>
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public static T[] Weighted<T>(T[][] x, T[] y, T[] w, bool intercept = false) where T : struct, IEquatable<T>, IFormattable
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{
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var predictor = Matrix<T>.Build.DenseOfRowArrays(x);
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if (intercept)
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{
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predictor = predictor.InsertColumn(0, Vector<T>.Build.Dense(predictor.RowCount, Vector<T>.One));
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}
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var response = Vector<T>.Build.Dense(y);
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var weights = Matrix<T>.Build.Diagonal(w);
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return predictor.TransposeThisAndMultiply(weights*predictor).Cholesky().Solve(predictor.TransposeThisAndMultiply(weights*response)).ToArray();
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}
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/// <summary>
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/// Weighted Linear Regression using normal equations.
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/// </summary>
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/// <param name="samples">List of sample vectors (predictor) together with their response.</param>
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/// <param name="weights">List of weights, one for each sample.</param>
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/// <param name="intercept">True if an intercept should be added as first artificial predictor value. Default = false.</param>
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public static T[] Weighted<T>(IEnumerable<Tuple<T[], T>> samples, T[] weights, bool intercept = false) where T : struct, IEquatable<T>, IFormattable
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{
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var xy = samples.UnpackSinglePass();
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return Weighted(xy.Item1, xy.Item2, weights, intercept);
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}
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/// <summary>
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/// Locally-Weighted Linear Regression using normal equations.
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/// </summary>
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[Obsolete("Warning: This function is here to stay but its signature will likely change. Opting out from semantic versioning.")]
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public static Vector<T> Local<T>(Matrix<T> x, Vector<T> y, Vector<T> t, double radius, Func<double, T> kernel) where T : struct, IEquatable<T>, IFormattable
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{
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// TODO: Weird kernel definition
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var w = Matrix<T>.Build.Dense(x.RowCount, x.RowCount);
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for (int i = 0; i < x.RowCount; i++)
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{
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w.At(i, i, kernel(Distance.Euclidean(t, x.Row(i))/radius));
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}
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return Weighted(x, y, w);
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}
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/// <summary>
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/// Locally-Weighted Linear Regression using normal equations.
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/// </summary>
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[Obsolete("Warning: This function is here to stay but its signature will likely change. Opting out from semantic versioning.")]
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public static Matrix<T> Local<T>(Matrix<T> x, Matrix<T> y, Vector<T> t, double radius, Func<double, T> kernel) where T : struct, IEquatable<T>, IFormattable
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{
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// TODO: Weird kernel definition
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var w = Matrix<T>.Build.Dense(x.RowCount, x.RowCount);
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for (int i = 0; i < x.RowCount; i++)
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{
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w.At(i, i, kernel(Distance.Euclidean(t, x.Row(i))/radius));
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}
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return Weighted(x, y, w);
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}
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[Obsolete("Warning: This function is here to stay but will likely be refactored and/or moved to another place. Opting out from semantic versioning.")]
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public static double GaussianKernel(double normalizedDistance)
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{
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return Math.Exp(-0.5*normalizedDistance*normalizedDistance);
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}
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}
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}
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