jube-fork/Accord.Statistics/Distributions/Multivariate/Independent`1.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 System.Text;
    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>
    /// 
    /// <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> : MultivariateContinuousDistribution,
        ISampleableDistribution<double[]>,
        IFittableDistribution<double[], IndependentOptions>
        where TDistribution : IUnivariateDistribution
    {
        private TDistribution[] components;

        private double[] mean;
        private double[] variance;
        private double[,] covariance;

        /// <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>
        /// 
        public Independent(int dimensions)
            : base(dimensions)
        {
            try
            {
                this.components = new TDistribution[dimensions];
                for (int i = 0; i < components.Length; i++)
                    components[i] = Activator.CreateInstance<TDistribution>();
            }
            catch
            {
                throw new ArgumentException("The component distribution needs specific parameters that need to be" +
                    "given to its constructor. Please specify in the 'initializer' argument of this constructor" +
                    "how the component distributions should be created.");
            }
        }

        /// <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)
        {
            this.components = new TDistribution[dimensions];
            for (int i = 0; i < components.Length; i++)
                components[i] = 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)
        {
            this.components = new TDistribution[dimensions];
            for (int i = 0; i < components.Length; i++)
                components[i] = initializer(i);
        }

        /// <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)
        {
            this.components = new TDistribution[dimensions];
            for (int i = 0; i < this.components.Length; i++)
                this.components[i] = (TDistribution)component.Clone();
        }

        /// <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.Length)
        {
            this.components = components;
        }

        /// <summary>
        ///   Gets or sets the components of this joint distribution.
        /// </summary>
        /// 
        public TDistribution this[int i]
        {
            get { return components[i]; }
            set { components[i] = value; }
        }

        /// <summary>
        ///   Gets the components of this joint distribution.
        /// </summary>
        /// 
        public TDistribution[] Components
        {
            get { return components; }
        }

        /// <summary>
        ///   Gets the mean for this distribution.
        /// </summary>
        /// 
        /// <value>A vector containing the mean values for the distribution.</value>
        /// 
        public override double[] Mean
        {
            get
            {
                if (mean == null)
                {
                    mean = new double[components.Length];
                    for (int i = 0; i < components.Length; i++)
                        mean[i] = components[i].Mean;
                }
                return mean;
            }
        }

        /// <summary>
        ///   Gets the variance for this distribution.
        /// </summary> 
        /// 
        /// <value>A vector containing the variance values for the distribution.</value>
        /// 
        public override double[] Variance
        {
            get
            {
                if (variance == null)
                {
                    variance = new double[components.Length];
                    for (int i = 0; i < components.Length; i++)
                        variance[i] = components[i].Variance;
                }
                return variance;
            }
        }

        /// <summary>
        ///   Gets the variance-covariance matrix for this distribution.
        /// </summary>
        /// 
        /// <value>A matrix containing the covariance values for the distribution.</value>
        /// 
        /// <remarks>
        ///   For an independent distribution, this matrix will always be diagonal.
        /// </remarks>
        /// 
        public override double[,] Covariance
        {
            get
            {
                if (covariance == null)
                    covariance = Matrix.Diagonal(Variance);
                return covariance;
            }
        }

        /// <summary>
        ///   Gets the probability density function (pdf) for
        ///   this distribution evaluated at point <c>x</c>.
        /// </summary>
        /// 
        /// <param name="x">A single point in the distribution range. For a
        ///   univariate distribution, this should be a single
        ///   double value. For a multivariate distribution,
        ///   this should be a double array.</param>
        /// 
        /// <returns>
        ///   The probability of <c>x</c> occurring
        ///   in the current distribution.
        /// </returns>
        /// 
        /// <remarks>
        ///   The Probability Density Function (PDF) describes the
        ///   probability that a given value <c>x</c> will occur.
        /// </remarks>
        /// 
        protected internal override double InnerDistributionFunction(params double[] x)
        {
            double p = 1;
            for (int i = 0; i < components.Length; i++)
                p *= components[i].DistributionFunction(x[i]);
            return p;
        }

        /// <summary>
        ///   Gets the probability density function (pdf) for
        ///   this distribution evaluated at point <c>x</c>.
        /// </summary>
        /// 
        /// <param name="x">A single point in the distribution range. For a
        ///   univariate distribution, this should be a single
        ///   double value. For a multivariate distribution,
        ///   this should be a double array.</param>
        ///   
        /// <returns>
        ///   The probability of <c>x</c> occurring
        ///   in the current distribution.
        /// </returns>
        /// 
        /// <remarks>
        /// The Probability Density Function (PDF) describes the
        /// probability that a given value <c>x</c> will occur.
        /// </remarks>
        /// 
        protected internal override double InnerProbabilityDensityFunction(params double[] x)
        {
            return Math.Exp(LogProbabilityDensityFunction(x));
        }

        /// <summary>
        ///   Gets the log-probability density function (pdf)
        ///   for this distribution evaluated at point <c>x</c>.
        /// </summary>
        /// 
        /// <param name="x">A single point in the distribution range. For a
        /// univariate distribution, this should be a single
        /// double value. For a multivariate distribution,
        /// this should be a double array.</param>
        /// 
        /// <returns>
        ///   The logarithm of the probability of <c>x</c>
        ///   occurring in the current distribution.
        /// </returns>
        /// 
        protected internal override double InnerLogProbabilityDensityFunction(params double[] x)
        {
            double p = 0;
            for (int i = 0; i < components.Length; i++)
                p += components[i].LogProbabilityFunction(x[i]);
            return p;
        }


        /// <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>
        /// 
        /// <remarks>
        ///   Although both double[] and double[][] arrays are supported,
        ///   providing a double[] for a multivariate distribution or a
        ///   double[][] for a univariate distribution may have a negative
        ///   impact in performance.
        /// </remarks>
        /// 
        /// <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 override void Fit(double[][] observations, double[] weights, IFittingOptions options)
        {
            IndependentOptions independentOptions = options as IndependentOptions;
            if (options != null && independentOptions == null)
                throw new ArgumentException("The specified options' type is invalid.", "options");

            Fit(observations, weights, independentOptions);
        }

        /// <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(double[][] observations, double[] weights, IndependentOptions options)
        {
            if (options != null)
            {
                if (!options.Transposed)
                    observations = observations.Transpose();

                if (options.InnerOptions != null)
                {
                    for (int i = 0; i < components.Length; i++)
                        components[i].Fit(observations[i], weights, options.InnerOptions[i]);
                }
                else
                {
                    for (int i = 0; i < components.Length; i++)
                        components[i].Fit(observations[i], weights, options.InnerOption);
                }
            }
            else
            {
                observations = observations.Transpose();
                for (int i = 0; i < components.Length; i++)
                    components[i].Fit(observations[i], weights, null);
            }

            Reset();
        }

        /// <summary>
        ///   Resets cached values (should be called after re-estimation).
        /// </summary>
        /// 
        protected void Reset()
        {
            mean = null;
            variance = null;
            covariance = null;
        }

        /// <summary>
        /// Generates a random vector of observations from the current distribution.
        /// </summary>
        /// 
        /// <param name="samples">The number of samples to generate.</param>
        /// <param name="result">The location where to store the samples.</param>
        /// <param name="source">The random number generator to use as a source of randomness. 
        ///   Default is to use <see cref="Accord.Math.Random.Generator.Random"/>.</param>
        /// 
        /// <returns>
        /// A random vector of observations drawn from this distribution.
        /// </returns>
        /// 
        public override double[][] Generate(int samples, double[][] result, Random source)
        {
            var gen = components.Apply(x => (ISampleableDistribution<double>)x);

            for (int i = 0; i < result.Length; i++)
                for (int j = 0; j < gen.Length; j++)
                    result[i][j] = gen[j].Generate(source);

            return result;
        }

        /// <summary>
        ///   Creates a new object that is a copy of the current instance.
        /// </summary>
        /// 
        /// <returns>
        ///   A new object that is a copy of this instance.
        /// </returns>
        /// 
        public override object Clone()
        {
            TDistribution[] clone = new TDistribution[components.Length];
            for (int i = 0; i < clone.Length; i++)
                clone[i] = (TDistribution)components[i].Clone();

            return new Independent<TDistribution>(clone);
        }

        /// <summary>
        ///   Returns a <see cref="System.String"/> that represents this instance.
        /// </summary>
        /// 
        /// <returns>
        ///   A <see cref="System.String"/> that represents this instance.
        /// </returns>
        /// 
        public override string ToString(string format, IFormatProvider formatProvider)
        {
            StringBuilder sb = new StringBuilder();
            sb.Append("Independent(");
            for (int i = 0; i < components.Length; i++)
            {
                sb.Append("x" + i);

                if (i < components.Length - 1)
                    sb.Append(", ");
            }

            sb.Append("; ");

            for (int i = 0; i < components.Length; i++)
            {
                var fmt = components[i] as IFormattable;

                String componentText = fmt
                    .ToString(format, formatProvider)
                    .Replace("(x", "(x" + i);

                sb.AppendFormat(componentText);

                if (i < components.Length - 1)
                    sb.Append(" + ");
            }
            sb.Append(")");

            return sb.ToString();
        }
    }
}