/// <summary>
/// Predicts the next observation occurring after a given observation sequence.
/// </summary>
///
public double[] Predict(double[] observations, int next, out double logLikelihood)
{
if (multivariate)
{
throw new ArgumentException("Model is multivariate.", "observations");
}
if (observations == null)
{
throw new ArgumentNullException("observations");
}
// Convert to multivariate observations
double[][] obs = MarkovHelperMethods.convertNoCheck(observations, dimension);
// Matrix to store the probabilities in assuming the next
// observations (prediction) will belong to each state.
double[][] weights;
// Compute the next observations
double[][] prediction = predict(obs, next, out logLikelihood, out weights);
// Return the first (single) dimension of the next observations.
return(Accord.Math.Matrix.Concatenate(prediction));
}
/// <summary>
/// Calculates the log-likelihood that this model has generated the
/// given observation sequence along the given state path.
/// </summary>
///
/// <param name="observations">A sequence of observations. </param>
/// <param name="path">A sequence of states. </param>
///
/// <returns>
/// The log-likelihood that the given sequence of observations has
/// been generated by this model along the given sequence of states.
/// </returns>
///
public double Evaluate(Array observations, int[] path)
{
if (observations == null)
{
throw new ArgumentNullException("observations");
}
if (path == null)
{
throw new ArgumentNullException("path");
}
if (observations.Length == 0)
{
return(Double.NegativeInfinity);
}
double[][] x = MarkovHelperMethods.checkAndConvert(observations, dimension);
double logLikelihood = Probabilities[path[0]]
+ Emissions[path[0]].LogProbabilityFunction(x[0]);
for (int i = 1; i < observations.Length; i++)
{
logLikelihood = Accord.Math.Special.LogSum(logLikelihood, Transitions[path[i - 1],
path[i]] + Emissions[path[i]].LogProbabilityFunction(x[i]));
}
// Return the sequence probability
return(logLikelihood);
}
/// <summary>
/// Predicts the next observation occurring after a given observation sequence.
/// </summary>
///
public double Predict(double[] observations, out double logLikelihood)
{
if (multivariate)
{
throw new ArgumentException("Model is multivariate.", "observations");
}
if (observations == null)
{
throw new ArgumentNullException("observations");
}
// Convert to multivariate observations
double[][] obs = MarkovHelperMethods.convertNoCheck(observations, dimension);
// Matrix to store the probabilities in assuming the next
// observations (prediction) will belong to each state.
double[][] weights;
// Compute the next observation (currently only one ahead is supported).
double[][] prediction = predict(obs, 1, out logLikelihood, out weights);
return(prediction[0][0]);
}
/// <summary>
/// Calculates the likelihood that this model has generated the given sequence.
/// </summary>
///
/// <remarks>
/// Evaluation problem. Given the HMM M = (A, B, pi) and the observation
/// sequence O = {o1, o2, ..., oK}, calculate the probability that model
/// M has generated sequence O. This can be computed efficiently using the
/// either the Viterbi or the Forward algorithms.
/// </remarks>
///
/// <param name="observations">
/// A sequence of observations.
/// </param>
/// <returns>
/// The log-likelihood that the given sequence has been generated by this model.
/// </returns>
///
public double Evaluate(Array observations)
{
if (observations == null)
{
throw new ArgumentNullException("observations");
}
if (observations.Length == 0)
{
return(Double.NegativeInfinity);
}
double[][] x = MarkovHelperMethods.checkAndConvert(observations, dimension);
// Forward algorithm
double logLikelihood;
// Compute forward probabilities
ForwardBackwardAlgorithm.LogForward(this, x, out logLikelihood);
// Return the sequence probability
return(logLikelihood);
}
/// <summary>
/// Calculates the probability of each hidden state for each
/// observation in the observation vector.
/// </summary>
///
/// <remarks>
/// If there are 3 states in the model, and the <paramref name="observations"/>
/// array contains 5 elements, the resulting vector will contain 5 vectors of
/// size 3 each. Each vector of size 3 will contain probability values that sum
/// up to one. By following those probabilities in order, we may decode those
/// probabilities into a sequence of most likely states. However, the sequence
/// of obtained states may not be valid in the model.
/// </remarks>
///
/// <param name="observations">A sequence of observations.</param>
///
/// <returns>A vector of the same size as the observation vectors, containing
/// the probabilities for each state in the model for the current observation.
/// If there are 3 states in the model, and the <paramref name="observations"/>
/// array contains 5 elements, the resulting vector will contain 5 vectors of
/// size 3 each. Each vector of size 3 will contain probability values that sum
/// up to one.</returns>
///
public double[][] Posterior(Array observations)
{
// Reference: C. S. Foo, CS262 Winter 2007, Lecture 5, Stanford
// http://ai.stanford.edu/~serafim/CS262_2007/notes/lecture5.pdf
if (observations == null)
{
throw new ArgumentNullException("observations");
}
double[][] x = MarkovHelperMethods.checkAndConvert(observations, dimension);
double logLikelihood;
// Compute forward and backward probabilities
double[,] lnFwd = ForwardBackwardAlgorithm.LogForward(this, x, out logLikelihood);
double[,] lnBwd = ForwardBackwardAlgorithm.LogBackward(this, x);
double[][] probabilities = new double[observations.Length][];
for (int i = 0; i < probabilities.Length; i++)
{
double[] states = probabilities[i] = new double[States];
for (int j = 0; j < states.Length; j++)
{
states[j] = Math.Exp(lnFwd[i, j] + lnBwd[i, j] - logLikelihood);
}
}
return(probabilities);
}
internal static void CheckObservationDimensions <TObservation, TDistribution>(TObservation[][] x, HiddenMarkovModel <TDistribution, TObservation> hmm) where TDistribution : IFittableDistribution <TObservation>
{
int expected = MarkovHelperMethods.GetObservationDimensions(x);
int actual = hmm.NumberOfInputs;
if (actual != expected)
{
throw new InvalidOperationException(String.Format("The specified emission distributions do not model observations with the same name of dimensions " +
"as the training data. The training data has {0}-dimensional observations, but the emissions can model up to {1} dimensions.", expected, actual));
}
}
/// <summary>
/// Calculates the most likely sequence of hidden states
/// that produced the given observation sequence.
/// </summary>
///
/// <remarks>
/// Decoding problem. Given the HMM M = (A, B, pi) and the observation sequence
/// O = {o1,o2, ..., oK}, calculate the most likely sequence of hidden states Si
/// that produced this observation sequence O. This can be computed efficiently
/// using the Viterbi algorithm.
/// </remarks>
///
/// <param name="observations">A sequence of observations.</param>
/// <param name="logLikelihood">The log-likelihood along the most likely sequence.</param>
///
/// <returns>The sequence of states that most likely produced the sequence.</returns>
///
public int[] Decode(Array observations, out double logLikelihood)
{
if (observations == null)
{
throw new ArgumentNullException("observations");
}
if (observations.Length == 0)
{
logLikelihood = Double.NegativeInfinity;
return(new int[0]);
}
// Argument check
double[][] x = MarkovHelperMethods.checkAndConvert(observations, dimension);
return(viterbi(x, out logLikelihood));
}
/// <summary>
/// Calculates the log-likelihood that this model has generated the
/// given observation sequence along the given state path.
/// </summary>
///
/// <param name="observations">A sequence of observations. </param>
/// <param name="path">A sequence of states. </param>
///
/// <returns>
/// The log-likelihood that the given sequence of observations has
/// been generated by this model along the given sequence of states.
/// </returns>
///
public double Evaluate(Array observations, int[] path)
{
if (observations == null)
{
throw new ArgumentNullException("observations");
}
if (path == null)
{
throw new ArgumentNullException("path");
}
if (observations.Length == 0)
{
return(Double.NegativeInfinity);
}
double[][] x = MarkovHelperMethods.checkAndConvert(observations, dimension);
try
{
double logLikelihood = Probabilities[path[0]]
+ Emissions[path[0]].LogProbabilityFunction(x[0]);
for (int i = 1; i < observations.Length; i++)
{
double a = Transitions[path[i - 1], path[i]];
double b = Emissions[path[i]].LogProbabilityFunction(x[i]);
logLikelihood += a + b;
}
// Return the sequence probability
return(logLikelihood);
}
catch (IndexOutOfRangeException ex)
{
checkHiddenStates(ex, path);
throw;
}
}
/// <summary>
/// Predicts the next observation occurring after a given observation sequence.
/// </summary>
///
private double[] predict <TUnivariate>(double[] observations,
out double logLikelihood, out Mixture <TUnivariate> probabilities)
where TUnivariate : DistributionBase, TDistribution, IUnivariateDistribution
{
// Convert to multivariate observations
double[][] obs = MarkovHelperMethods.convertNoCheck(observations, dimension);
// Matrix to store the probabilities in assuming the next
// observations (prediction) will belong to each state.
double[][] weights;
// Compute the next observation (currently only one ahead is supported).
double[][] prediction = predict(obs, 1, out logLikelihood, out weights);
// Create the mixture distribution defining the model likelihood in
// assuming the next observation belongs will belong to each state.
TUnivariate[] b = Array.ConvertAll(B, x => (TUnivariate)x);
probabilities = new Mixture <TUnivariate>(weights[1].Exp(), b);
return(prediction[0]);
}
/// <summary>
/// Calculates the most likely sequence of hidden states
/// that produced the given observation sequence.
/// </summary>
///
/// <remarks>
/// Decoding problem. Given the HMM M = (A, B, pi) and the observation sequence
/// O = {o1,o2, ..., oK}, calculate the most likely sequence of hidden states Si
/// that produced this observation sequence O. This can be computed efficiently
/// using the Viterbi algorithm.
/// </remarks>
///
/// <param name="observations">A sequence of observations.</param>
/// <param name="logLikelihood">The log-likelihood along the most likely sequence.</param>
/// <returns>The sequence of states that most likely produced the sequence.</returns>
///
public int[] Decode(Array observations, out double logLikelihood)
{
if (observations == null)
{
throw new ArgumentNullException("observations");
}
if (observations.Length == 0)
{
logLikelihood = Double.NegativeInfinity;
return(new int[0]);
}
// Argument check
double[][] x = MarkovHelperMethods.checkAndConvert(observations, dimension);
// Viterbi-forward algorithm.
int T = x.Length;
int states = States;
int maxState;
double maxWeight;
double weight;
double[] logPi = Probabilities;
double[,] logA = Transitions;
int[,] s = new int[states, T];
double[,] lnFwd = new double[states, T];
// Base
for (int i = 0; i < states; i++)
{
lnFwd[i, 0] = logPi[i] + B[i].LogProbabilityFunction(x[0]);
}
// Induction
for (int t = 1; t < T; t++)
{
double[] observation = x[t];
for (int j = 0; j < states; j++)
{
maxState = 0;
maxWeight = lnFwd[0, t - 1] + logA[0, j];
for (int i = 1; i < states; i++)
{
weight = lnFwd[i, t - 1] + logA[i, j];
if (weight > maxWeight)
{
maxState = i;
maxWeight = weight;
}
}
lnFwd[j, t] = maxWeight + B[j].LogProbabilityFunction(observation);
s[j, t] = maxState;
}
}
// Find maximum value for time T-1
maxState = 0;
maxWeight = lnFwd[0, T - 1];
for (int i = 1; i < states; i++)
{
if (lnFwd[i, T - 1] > maxWeight)
{
maxState = i;
maxWeight = lnFwd[i, T - 1];
}
}
// Trackback
int[] path = new int[T];
path[T - 1] = maxState;
for (int t = T - 2; t >= 0; t--)
{
path[t] = s[path[t + 1], t + 1];
}
// Returns the sequence probability as an out parameter
logLikelihood = maxWeight;
// Returns the most likely (Viterbi path) for the given sequence
return(path);
}
