jube-fork/Accord.Statistics/Distributions/Multivariate/Independent`3.cs

// Accord Statistics Library
// The Accord.NET Framework
// http://accord-framework.net
//
// Copyright © César Souza, 2009-2017
// cesarsouza at gmail.com
//
//    This library is free software; you can redistribute it and/or
//    modify it under the terms of the GNU Lesser General Public
//    License as published by the Free Software Foundation; either
//    version 2.1 of the License, or (at your option) any later version.
//
//    This library is distributed in the hope that it will be useful,
//    but WITHOUT ANY WARRANTY; without even the implied warranty of
//    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
//    Lesser General Public License for more details.
//
//    You should have received a copy of the GNU Lesser General Public
//    License along with this library; if not, write to the Free Software
//    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
//

namespace Accord.Statistics.Distributions.Multivariate
{
    using System;
    using Accord.Math;
    using Accord.Statistics.Distributions.Fitting;
    using Accord.Math.Random;
    using Accord.Compat;

    /// <summary>
    ///   Joint distribution assuming independence between vector components.
    /// </summary>
    /// 
    /// <typeparam name="TDistribution">The type of the underlying distributions.</typeparam>
    /// <typeparam name="TObservation">The type for the observations being modeled by the distribution (i.e. double).</typeparam>
    /// <typeparam name="TOptions">The options for fitting the distribution to the observations.</typeparam>
    /// 
    /// <remarks>
    /// <para>
    ///   In probability and statistics, given at least two random variables <c>X</c>, 
    ///   <c>Y</c>, ..., that are defined on a probability space, the joint probability 
    ///   distribution for <c>X</c>, <c>Y</c>, ... is a probability distribution that 
    ///   gives the probability that each of X, Y, ... falls in any particular range or
    ///   discrete set of values specified for that variable. In the case of only two 
    ///   random variables, this is called a bivariate distribution, but the concept 
    ///   generalizes to any number of random variables, giving a multivariate distribution.
    /// </para>
    /// 
    /// <para>
    ///   References:
    ///   <list type="bullet">
    ///     <item><description><a href="http://en.wikipedia.org/wiki/Joint_probability_distribution">
    ///       Wikipedia, The Free Encyclopedia. Beta distribution. 
    ///       Available from: http://en.wikipedia.org/wiki/Joint_probability_distribution </a></description></item>
    ///   </list></para>
    /// </remarks>
    /// 
    /// <example>
    /// <para>
    ///   The following example shows how to declare and initialize an Independent Joint
    ///   Gaussian Distribution using known means and variances for each component.</para>
    ///   
    /// <code>
    ///   // Declare two normal distributions
    ///   NormalDistribution pa = new NormalDistribution(4.2, 1); // p(a)
    ///   NormalDistribution pb = new NormalDistribution(7.0, 2); // p(b)
    ///  
    ///   // Now, create a joint distribution combining these two:
    ///   var joint = new Independent&lt;NormalDistribution>(pa, pb);
    ///   
    ///   // This distribution assumes the distributions of the two components are independent,
    ///   // i.e. if we have 2D input vectors on the form {a, b}, then p({a,b}) = p(a) * p(b). 
    ///   
    ///   // Lets check a simple example. Consider a 2D input vector x = { 4.2, 7.0 } as
    ///   //
    ///   double[] x = new double[] { 4.2, 7.0 };
    ///   
    ///   // Those two should be completely equivalent:
    ///   double p1 = joint.ProbabilityDensityFunction(x);
    ///   double p2 = pa.ProbabilityDensityFunction(x[0]) * pb.ProbabilityDensityFunction(x[1]);
    ///   
    ///   bool equal = p1 == p2; // at this point, equal should be true.
    /// </code>
    /// 
    /// <para>
    ///   The following example shows how to fit a distribution (estimate
    ///   its parameters) from a given dataset. </para>
    ///   
    /// <code>
    ///   // Let's consider an input dataset of 2D vectors. We would
    ///   // like to estimate an Independent&lt;NormalDistribution>
    ///   // which best models this data.
    ///   
    ///  double[][] data =
    ///  {
    ///                  // x, y
    ///      new double[] { 1, 8 },
    ///      new double[] { 2, 6 },
    ///      new double[] { 5, 7 },
    ///      new double[] { 3, 9 },
    ///  };
    ///  
    ///  // We start by declaring some initial guesses for the
    ///  // distributions of each random variable (x, and y):
    ///  // 
    ///  var distX = new NormalDistribution(0, 1);
    ///  var distY = new NormalDistribution(0, 1);
    ///
    ///  // Next, we declare our initial guess Independent distribution
    ///  var joint = new Independent&lt;NormalDistribution>(distX, distY);
    ///
    ///  // We can now fit the distribution to our data,
    ///  // producing an estimate of its parameters:
    ///  //
    ///  joint.Fit(data);
    ///
    ///  // At this point, we have estimated our distribution. 
    ///  
    ///  double[] mean = joint.Mean;     // should be { 2.75,  7.50  }
    ///  double[] var  = joint.Variance; // should be { 2.917, 1.667 } 
    ///
    ///                                    //        | 2.917,  0.000 |
    ///  double[,] cov = joint.Covariance; //  Cov = |               |
    ///                                    //        | 0.000,  1.667 |
    ///                                    
    /// // The covariance matrix is diagonal, as it would be expected
    /// // if is assumed there are no interactions between components.
    /// </code>
    /// </example>
    /// 
    [Serializable]
    public class Independent<TDistribution, TObservation, TOptions> :
        Independent<TDistribution, TObservation>,
        IFittableDistribution<TObservation[], IndependentOptions<TOptions>>,
        ISampleableDistribution<TObservation[]>
        where TDistribution : IFittableDistribution<TObservation, TOptions>,
                              IUnivariateDistribution<TObservation>,
                              IUnivariateDistribution
        where TOptions : class, IFittingOptions, new()
    {
        /// <summary>
        ///   Initializes a new instance of the <see cref="Independent&lt;TDistribution&gt;"/> class.
        /// </summary>
        /// 
        /// <param name="dimensions">The number of independent component distributions.</param>
        /// <param name="initializer">A function that creates a new distribution for each component index.</param>
        /// 
        public Independent(int dimensions, Func<TDistribution> initializer)
            : base(dimensions, initializer)
        {
        }

        /// <summary>
        ///   Initializes a new instance of the <see cref="Independent&lt;TDistribution&gt;"/> class.
        /// </summary>
        /// 
        /// <param name="dimensions">The number of independent component distributions.</param>
        /// <param name="initializer">A function that creates a new distribution for each component index.</param>
        /// 
        public Independent(int dimensions, Func<int, TDistribution> initializer)
            : base(dimensions, initializer)
        {
        }

        /// <summary>
        ///   Initializes a new instance of the <see cref="Independent&lt;TDistribution&gt;"/> class.
        /// </summary>
        /// 
        /// <param name="dimensions">The number of independent component distributions.</param>
        /// <param name="component">A base component which will be cloned to all dimensions.</param>
        /// 
        public Independent(int dimensions, TDistribution component)
            : base(dimensions, component)
        {
        }

        /// <summary>
        ///   Initializes a new instance of the <see cref="Independent&lt;TDistribution&gt;"/> class.
        /// </summary>
        /// 
        /// <param name="components">The components.</param>
        /// 
        public Independent(params TDistribution[] components)
            : base(components)
        {
        }

        /// <summary>
        ///   Fits the underlying distribution to a given set of observations.
        /// </summary>
        /// 
        /// <param name="observations">The array of observations to fit the model against. The array
        ///   elements can be either of type double (for univariate data) or
        ///   type double[] (for multivariate data).</param>
        /// <param name="weights">The weight vector containing the weight for each of the samples.</param>
        /// <param name="options">Optional arguments which may be used during fitting, such
        ///   as regularization constants and additional parameters.</param>
        ///
        /// <example>
        ///   For an example on how to fit an independent joint distribution, please
        ///   take a look at the examples section for <see cref="Independent{TDistribution}"/>.
        /// </example>
        /// 

        public void Fit(TObservation[][] observations, double[] weights = null,
            IndependentOptions<TOptions> options = null)
        {
           base.Fit(observations, weights, options);
        }
    }

}