/// <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>
///
public override void Fit(double[] observations, double[] weights, IFittingOptions options)
{
Fit(observations, weights, options as EmpiricalHazardOptions);
}
/// <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>
///
public override void Fit(double[] observations, double[] weights, IFittingOptions options)
{
if (observations.Length != weights.Length)
throw new ArgumentException("The weight vector should have the same size as the observations", "weights");
double[] p = new double[probabilities.Length];
for (int i = 0; i < observations.Length; i++)
{
int symbol = (int)observations[i];
p[symbol] += weights[i];
}
initialize(0, p);
}
/// <summary>
/// Initializes a new instance of the <see cref="IndependentOptions"/> class.
/// </summary>
///
/// <param name="innerOptions">The fitting options for the inner
/// component distributions of the independent distributions.</param>
///
public IndependentOptions(IFittingOptions[] innerOptions)
{
InnerOptions = innerOptions;
}
/// <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="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>
///
public virtual void Fit(double[] observations, IFittingOptions options)
{
Fit(observations, null, options);
}
/// <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>
///
void IDistribution.Fit(Array observations, double[] weights, IFittingOptions options)
{
double[][] multivariate = observations as double[][];
if (multivariate != null)
{
Fit(multivariate, weights, options);
return;
}
double[] univariate = observations as double[];
if (univariate != null)
{
Fit(univariate.Split(dimension), weights, options);
return;
}
throw new ArgumentException("Unsupported parameter type.", "observations");
}
/// <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>
///
public override void Fit(double[][] observations, double[] weights, IFittingOptions options)
{
double[] means;
double[,] cov;
NormalOptions opt = options as NormalOptions;
if (weights != null)
{
#if DEBUG
double sum = 0;
for (int i = 0; i < weights.Length; i++)
{
if (Double.IsNaN(weights[i]) || Double.IsInfinity(weights[i]))
{
throw new Exception("Invalid numbers in the weight vector.");
}
sum += weights[i];
}
if (Math.Abs(sum - 1.0) > 1e-10)
{
throw new Exception("Weights do not sum to one.");
}
#endif
// Compute weighted mean vector
means = Statistics.Tools.Mean(observations, weights);
// Compute weighted covariance matrix
if (opt != null && opt.Diagonal)
{
cov = Matrix.Diagonal(Statistics.Tools.WeightedVariance(observations, weights, means));
}
else
{
cov = Statistics.Tools.WeightedCovariance(observations, weights, means);
}
}
else
{
// Compute mean vector
means = Statistics.Tools.Mean(observations);
// Compute covariance matrix
if (opt != null && opt.Diagonal)
{
cov = Matrix.Diagonal(Statistics.Tools.Variance(observations, means));
}
cov = Statistics.Tools.Covariance(observations, means);
}
CholeskyDecomposition chol = new CholeskyDecomposition(cov, false, true);
if (opt != null)
{
// Parse optional estimation options
double regularization = opt.Regularization;
if (regularization > 0)
{
int dimension = observations[0].Length;
while (!chol.PositiveDefinite)
{
for (int i = 0; i < dimension; i++)
{
for (int j = 0; j < dimension; j++)
{
if (Double.IsNaN(cov[i, j]) || Double.IsInfinity(cov[i, j]))
{
cov[i, j] = 0.0;
}
}
cov[i, i] += regularization;
}
chol = new CholeskyDecomposition(cov, false, true);
}
}
}
if (!chol.PositiveDefinite)
{
throw new NonPositiveDefiniteMatrixException("Covariance matrix is not positive "
+ "definite. Try specifying a regularization constant in the fitting options.");
}
// Become the newly fitted distribution.
initialize(means, cov, chol);
}
private void compute(double[] data, double[] weights)
{
bool[] fail = new bool[Distributions.Count];
// Step 1. Fit all candidate distributions to the data.
for (int i = 0; i < Distributions.Count; i++)
{
var distribution = Distributions[i];
IFittingOptions options = null;
Options.TryGetValue(distribution, out options);
try
{
distribution.Fit(data, weights, options);
}
catch
{
// TODO: Maybe revisit the decision to swallow exceptions here.
fail[i] = true;
}
}
// Step 2. Use statistical tests to see how well each
// distribution was able to model the data.
KolmogorovSmirnov = new KolmogorovSmirnovTest[Distributions.Count];
ChiSquare = new ChiSquareTest[Distributions.Count];
AndersonDarling = new AndersonDarlingTest[Distributions.Count];
DistributionNames = new string[Distributions.Count];
double[] ks = new double[Distributions.Count];
double[] cs = new double[Distributions.Count];
double[] ad = new double[Distributions.Count];
var measures = new List <GoodnessOfFit>();
for (int i = 0; i < Distributions.Count; i++)
{
ks[i] = Double.NegativeInfinity;
cs[i] = Double.NegativeInfinity;
ad[i] = Double.NegativeInfinity;
var d = this.Distributions[i] as IUnivariateDistribution <double>;
if (d == null)
{
continue;
}
this.DistributionNames[i] = GetName(d.GetType());
if (fail[i])
{
continue;
}
int ms = 5000;
run(() =>
{
this.KolmogorovSmirnov[i] = new KolmogorovSmirnovTest(data, d);
ks[i] = -KolmogorovSmirnov[i].Statistic;
}, ms);
run(() =>
{
this.ChiSquare[i] = new ChiSquareTest(data, d);
cs[i] = -ChiSquare[i].Statistic;
}, ms);
run(() =>
{
this.AndersonDarling[i] = new AndersonDarlingTest(data, d);
ad[i] = AndersonDarling[i].Statistic;
}, ms);
if (Double.IsNaN(ks[i]))
{
ks[i] = Double.NegativeInfinity;
}
if (Double.IsNaN(cs[i]))
{
cs[i] = Double.NegativeInfinity;
}
if (Double.IsNaN(ad[i]))
{
ad[i] = Double.NegativeInfinity;
}
measures.Add(new GoodnessOfFit(this, i));
}
this.KolmogorovSmirnovRank = getRank(ks);
this.ChiSquareRank = getRank(cs);
this.AndersonDarlingRank = getRank(ad);
measures.Sort();
this.GoodnessOfFit = new GoodnessOfFitCollection(measures);
}
/// <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>
///
void IDistribution.Fit(Array observations, double[] weights, IFittingOptions options)
{
double[] univariate = observations as double[];
if (univariate != null)
{
Fit(univariate, weights, options);
return;
}
double[][] multivariate = observations as double[][];
if (multivariate != null)
{
Fit(Matrix.Concatenate(multivariate), weights, options);
return;
}
throw new ArgumentException("Invalid input type.", "observations");
}
/// <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>
///
public override void Fit(double[] observations, double[] weights, IFittingOptions options)
{
Fit(observations, weights, options as GeneralizedBetaOptions);
}
/// <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>
///
public override void Fit(double[] observations, double[] weights, IFittingOptions options)
{
double mean = Statistics.Tools.WeightedMean(observations, weights);
initialize(mean);
}
/// <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>
///
public override void Fit(double[] observations, double[] weights, IFittingOptions options)
{
double m, k;
if (weights != null)
{
m = Circular.WeightedMean(observations, weights);
k = Circular.WeightedConcentration(observations, weights, m);
}
else
{
m = Circular.Mean(observations);
k = Circular.Concentration(observations, m);
}
if (options != null)
{
// Parse optional estimation options
VonMisesOptions o = (VonMisesOptions)options;
if (o.UseBiasCorrection)
{
double N = observations.Length;
if (k < 2)
{
k = System.Math.Max(k - 1.0 / (2.0 * (N * k)), 0);
}
else
{
double Nm1 = N - 1;
k = (Nm1 * Nm1 * Nm1 * k) / (N * N * N + N);
}
}
}
initialize(m, k);
}
/// <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>
///
public override void Fit(double[] observations, double[] weights, IFittingOptions options)
{
if (options != null)
throw new ArgumentException("This method does not accept fitting options.");
if (weights != null)
throw new ArgumentException("This distribution does not support weighted samples.");
double sum = 0;
for (int i = 0; i < observations.Length; i++)
sum += observations[i] * observations[i];
sigma = Math.Sqrt(1.0 / (2.0 * observations.Length) * sum);
}
/// <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>
///
public override void Fit(double[] observations, double[] weights, IFittingOptions options)
{
throw new NotImplementedException();
}
/// <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="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>
///
void IDistribution.Fit(Array observations, IFittingOptions options)
{
(this as IDistribution).Fit(observations, null, options);
}
/// <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>
///
public override void Fit(double[] observations, double[] weights, IFittingOptions options)
{
Fit(observations, weights, (GammaOptions)options);
}
/// <summary>
/// Initializes a new instance of the <see cref="MixtureOptions"/> class.
/// </summary>
///
/// <param name="threshold">The convergence criterion for the
/// Expectation-Maximization algorithm. Default is 1e-3.</param>
/// <param name="innerOptions">The fitting options for the inner
/// component distributions of the mixture density.</param>
///
public MixtureOptions(double threshold, IFittingOptions innerOptions)
{
Threshold = threshold;
InnerOptions = innerOptions;
}
/// <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>
///
public override void Fit(double[][] observations, double[] weights, IFittingOptions options)
{
if (options != null)
{
throw new ArgumentException("This method does not accept fitting options.");
}
for (int i = 0; i < probabilities.Length; i++)
{
probabilities[i] = 0;
}
if (weights != null)
{
if (observations.Length != weights.Length)
{
throw new DimensionMismatchException("weights",
"The weight vector should have the same size as the observations");
}
for (int i = 0; i < observations.Length; i++)
{
double[] x = observations[i];
int index = 0;
for (int j = 0; j < x.Length; j++)
{
index += (int)x[j] * positions[j];
}
probabilities[index] += weights[i];
}
}
else
{
for (int i = 0; i < observations.Length; i++)
{
double[] x = observations[i];
int index = 0;
for (int j = 0; j < x.Length; j++)
{
index += (int)x[j] * positions[j];
}
probabilities[index]++;
}
}
double sum = 0;
for (int i = 0; i < probabilities.Length; i++)
{
sum += probabilities[i];
}
if (sum != 0 && sum != 1)
{
// TODO: add the following in a JointOption class:
// avoid locking a parameter in zero.
// if (num == 0) num = 1e-10;
// assert that probabilities sum up to 1.
for (int i = 0; i < probabilities.Length; i++)
{
probabilities[i] /= sum;
}
}
}
/// <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>
///
public virtual void Fit(double[] observations, double[] weights, IFittingOptions options)
{
throw new NotSupportedException();
}
/// <summary>
/// Initializes a new instance of the <see cref="MixtureOptions"/> class.
/// </summary>
///
/// <param name="threshold">The convergence criterion for the
/// Expectation-Maximization algorithm. Default is 1e-3.</param>
/// <param name="innerOptions">The fitting options for the inner
/// component distributions of the mixture density.</param>
///
public MixtureOptions(double threshold, IFittingOptions innerOptions)
{
Threshold = threshold;
InnerOptions = innerOptions;
}
/// <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> /// public abstract void Fit(double[][] observations, double[] weights, IFittingOptions options);
/// <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>
///
public override void Fit(double[][] observations, double[] weights, IFittingOptions options)
{
// Estimation parameters
double threshold = 1e-3;
IFittingOptions innerOptions = null;
#if DEBUG
for (int i = 0; i < weights.Length; i++)
{
if (Double.IsNaN(weights[i]) || Double.IsInfinity(weights[i]))
{
throw new Exception("Invalid numbers in the weight vector.");
}
}
#endif
if (options != null)
{
// Process optional arguments
MixtureOptions o = (MixtureOptions)options;
threshold = o.Threshold;
innerOptions = o.InnerOptions;
}
// 1. Initialize means, covariances and mixing coefficients
// and evaluate the initial value of the log-likelihood
int N = observations.Length;
int K = components.Length;
double weightSum = weights.Sum();
// Initialize responsibilities
double[] norms = new double[N];
double[][] gamma = new double[K][];
for (int k = 0; k < gamma.Length; k++)
{
gamma[k] = new double[N];
}
// Clone the current distribution values
double[] pi = (double[])coefficients.Clone();
T[] pdf = new T[components.Length];
for (int i = 0; i < components.Length; i++)
{
pdf[i] = (T)components[i].Clone();
}
// Prepare the iteration
double likelihood = logLikelihood(pi, pdf, observations, weights);
bool converged = false;
// Start
while (!converged)
{
// 2. Expectation: Evaluate the component distributions
// responsibilities using the current parameter values.
Array.Clear(norms, 0, norms.Length);
for (int k = 0; k < gamma.Length; k++)
{
for (int i = 0; i < observations.Length; i++)
{
norms[i] += gamma[k][i] = pi[k] * pdf[k].ProbabilityFunction(observations[i]);
}
}
for (int k = 0; k < gamma.Length; k++)
{
for (int i = 0; i < weights.Length; i++)
{
if (norms[i] != 0)
{
gamma[k][i] *= weights[i] / norms[i];
}
}
}
// 3. Maximization: Re-estimate the distribution parameters
// using the previously computed responsibilities
for (int k = 0; k < gamma.Length; k++)
{
double sum = gamma[k].Sum();
for (int i = 0; i < gamma[k].Length; i++)
{
gamma[k][i] /= sum;
}
pi[k] = sum / weightSum;
pdf[k].Fit(observations, gamma[k], innerOptions);
}
// 4. Evaluate the log-likelihood and check for convergence
double newLikelihood = logLikelihood(pi, pdf, observations, weights);
if (Double.IsNaN(newLikelihood) || Double.IsInfinity(newLikelihood))
{
throw new ConvergenceException("Fitting did not converge.");
}
if (Math.Abs(likelihood - newLikelihood) < threshold * Math.Abs(likelihood))
{
converged = true;
}
likelihood = newLikelihood;
}
// Become the newly fitted distribution.
this.initialize(pi, pdf);
}
/// <summary>
/// Initializes a new instance of the <see cref="IndependentOptions"/> class.
/// </summary>
///
/// <param name="innerOption">The fitting options for the inner
/// component distributions of the independent distributions.</param>
///
public IndependentOptions(IFittingOptions innerOption)
{
InnerOption = innerOption;
}
/// <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>
///
public override void Fit(double[] observations, double[] weights, IFittingOptions options)
{
if (options != null)
throw new ArgumentException("This method does not accept fitting options.");
double mean;
double var;
if (weights == null)
{
mean = observations.Mean();
var = observations.Variance(mean);
}
else
{
mean = observations.WeightedMean(weights);
var = observations.WeightedVariance(weights, mean);
}
if (var >= mean * (1.0 - mean))
throw new NotSupportedException();
double u = (mean * (1 - mean) / var) - 1.0;
double alpha = mean * u;
double beta = (1 - mean) * u;
init(alpha, beta);
}
/// <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>
///
public override void Fit(double[] observations, int[] weights, IFittingOptions options)
{
Fit(observations, weights, options as BetaOptions);
}
/// <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>
///
public override void Fit(double[][] observations, double[] weights, IFittingOptions options)
{
double[] means;
double[,] cov;
if (weights != null)
{
// Compute weighted mean vector
means = Statistics.Tools.Mean(observations, weights);
// Compute weighted covariance matrix
cov = Statistics.Tools.WeightedCovariance(observations, weights, means);
}
else
{
// Compute mean vector
means = Statistics.Tools.Mean(observations);
// Compute covariance matrix
cov = Statistics.Tools.Covariance(observations, means);
}
CholeskyDecomposition chol = new CholeskyDecomposition(cov, false, true);
if (options != null)
{
// Parse optional estimation options
NormalOptions o = (NormalOptions)options;
double regularization = o.Regularization;
if (regularization > 0)
{
int dimension = observations[0].Length;
while (!chol.PositiveDefinite)
{
for (int i = 0; i < dimension; i++)
cov[i, i] += regularization;
chol = new CholeskyDecomposition(cov, false, true);
}
}
}
if (!chol.PositiveDefinite)
{
throw new NonPositiveDefiniteMatrixException("Covariance matrix is not positive "
+ "definite. Try specifying a regularization constant in the fitting options.");
}
// Become the newly fitted distribution.
initialize(means, cov, chol);
}
/// <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>
///
public virtual void Fit(double[] observations, double[] weights, IFittingOptions options)
{
throw new NotSupportedException();
}
/// <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>
///
public override void Fit(double[] observations, double[] weights, IFittingOptions options)
{
if (immutable) throw new InvalidOperationException();
double mu, var;
if (weights != null)
{
#if DEBUG
for (int i = 0; i < weights.Length; i++)
if (Double.IsNaN(weights[i]) || Double.IsInfinity(weights[i]))
throw new Exception("Invalid numbers in the weight vector.");
#endif
// Compute weighted mean
mu = Statistics.Tools.WeightedMean(observations, weights);
// Compute weighted variance
var = Statistics.Tools.WeightedVariance(observations, weights, mu);
}
else
{
// Compute weighted mean
mu = Statistics.Tools.Mean(observations);
// Compute weighted variance
var = Statistics.Tools.Variance(observations, mu);
}
if (options != null)
{
// Parse optional estimation options
NormalOptions o = (NormalOptions)options;
double regularization = o.Regularization;
if (var == 0 || Double.IsNaN(var) || Double.IsInfinity(var))
var = regularization;
}
if (var <= 0)
{
throw new ArgumentException("Variance is zero. Try specifying "
+ "a regularization constant in the fitting options.");
}
initialize(mu, Math.Sqrt(var), var);
}
/// <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>
///
public override void Fit(double[][] observations, double[] weights, IFittingOptions options)
{
double[] pi = new double[probabilities.Length];
double size = weights.Length;
for (int c = 0; c < probabilities.Length; c++)
{
for (int i = 0; i < observations.Length; i++)
pi[c] += observations[i][c] * weights[i] * size;
pi[c] /= N;
}
initialize(N, pi);
}
/// <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="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>
///
void IDistribution.Fit(Array observations, IFittingOptions options)
{
(this as IDistribution).Fit(observations, null, options);
}
/// <summary>
/// This method is not supported.
/// </summary>
///
public override void Fit(double[] observations, double[] weights, IFittingOptions options)
{
throw new System.NotSupportedException();
}
/// <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>
///
public override void Fit(double[][] observations, int[] weights, IFittingOptions options)
{
Fit(observations, weights, options as MultivariateEmpiricalOptions);
}
/// <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>
///
public override void Fit(double[][] observations, double[] weights, IFittingOptions options)
{
if (options != null)
throw new ArgumentException("This method does not accept fitting options.");
if (observations.Length != weights.Length)
throw new ArgumentException("The weight vector should have the same size as the observations", "weights");
for (int i = 0; i < probabilities.Length; i++)
probabilities[i] = 0;
for (int i = 0; i < observations.Length; i++)
{
double[] x = observations[i];
int index = 0;
for (int j = 0; j < x.Length; j++)
index += (int)x[j] * positions[j];
probabilities[index] += weights[i];
}
double sum = 0;
for (int i = 0; i < probabilities.Length; i++)
sum += probabilities[i];
if (sum != 0 && sum != 1)
{
// avoid locking a parameter in zero.
// if (num == 0) num = 1e-10;
// assert that probabilities sum up to 1.
for (int i = 0; i < probabilities.Length; i++)
probabilities[i] /= sum;
}
}
/// <summary>
/// Initializes a new instance of the <see cref="IndependentOptions"/> class.
/// </summary>
///
/// <param name="innerOption">The fitting options for the inner
/// component distributions of the independent distributions.</param>
///
public IndependentOptions(IFittingOptions innerOption)
{
InnerOption = innerOption;
}
/// <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>
///
public override void Fit(double[] observations, double[] weights, IFittingOptions options)
{
if (options != null)
throw new ArgumentException("This method does not accept fitting options.");
// R. Kolar, R. Jirik, J. Jan (2004) "Estimator Comparison of the
// Nakagami-m Parameter and Its Application in Echocardiography",
// Radioengineering, 13 (1), 8–12
double[] x2 = Matrix.ElementwisePower(observations, 2);
double mean, var;
if (weights == null)
{
mean = Statistics.Tools.Mean(x2);
var = Statistics.Tools.Variance(x2);
}
else
{
mean = Statistics.Tools.WeightedMean(x2, weights);
var = Statistics.Tools.WeightedVariance(x2, weights);
}
double shape = (mean * mean) / var;
double spread = mean;
init(shape, spread);
}
/// <summary>
/// Not supported.
/// </summary>
///
public override void Fit(double[][,] observations, double[] weights, IFittingOptions options)
{
throw new NotSupportedException();
}
/// <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="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>
///
public virtual void Fit(double[] observations, IFittingOptions options)
{
Fit(observations, null, options);
}
/// <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>
///
public override void Fit(double[] observations, double[] weights, IFittingOptions options)
{
double mean = Statistics.Tools.WeightedMean(observations, weights);
initialize(mean);
}
/// <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="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>
///
void IDistribution.Fit(Array observations, IFittingOptions options)
{
double[] weights = new double[observations.Length];
// Create equal weights for the observations
double w = 1.0 / observations.Length;
for (int i = 0; i < weights.Length; i++)
weights[i] = w;
(this as IDistribution).Fit(observations, weights, options);
}
/// <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> /// public abstract void Fit(double[] observations, double[] weights, IFittingOptions options);
/// <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="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>
///
public virtual void Fit(double[][] observations, IFittingOptions options)
{
double[] weights = new double[observations.Length];
// Create equal weights for the observations
double w = 1.0 / observations.Length;
for (int i = 0; i < weights.Length; i++)
weights[i] = w;
Fit(observations, weights, options);
}
/// <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>
///
public override void Fit(double[] observations, double[] weights, IFittingOptions options)
{
Fit(observations, weights, options as TriangularOptions);
}
/// <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>
///
public override void Fit(double[] observations, double[] weights, IFittingOptions options)
{
if (options != null)
throw new ArgumentException("This method does not accept fitting options.");
double mean;
double lambda;
int n = observations.Length;
if (weights == null)
{
mean = observations.Mean();
double sum = 0;
for (int i = 0; i < observations.Length; i++)
sum += (1.0 / observations[i] - 1.0 / mean);
lambda = (n * n) / sum;
}
else
{
mean = observations.WeightedMean(observations);
double sum = 0;
for (int i = 0; i < observations.Length; i++)
sum += weights[i] * (1.0 / observations[i] - 1.0 / mean);
lambda = n / sum;
}
init(mean, lambda);
}
/// <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>
///
public override void Fit(double[] observations, double[] weights, IFittingOptions options)
{
throw new NotImplementedException();
}
