public void LearnTest10_Independent()
{
// Let's say we have 2 meteorological sensors gathering data
// from different time periods of the day. Those periods are
// represented below:
double[][][] data =
{
new double[][] // first sequence (we just repeated the measurements
{ // once, so there is only one observation sequence)
new double[] { 1, 2 }, // Day 1, 15:00 pm
new double[] { 6, 7 }, // Day 1, 16:00 pm
new double[] { 2, 3 }, // Day 1, 17:00 pm
new double[] { 2, 2 }, // Day 1, 18:00 pm
new double[] { 9, 8 }, // Day 1, 19:00 pm
new double[] { 1, 0 }, // Day 1, 20:00 pm
new double[] { 1, 3 }, // Day 1, 21:00 pm
new double[] { 8, 9 }, // Day 1, 22:00 pm
new double[] { 3, 3 }, // Day 1, 23:00 pm
new double[] { 1, 3 }, // Day 2, 00:00 am
new double[] { 1, 1 }, // Day 2, 01:00 am
}
};
// Let's assume those sensors are unrelated (for simplicity). As
// such, let's assume the data gathered from the sensors may reside
// into circular centroids denoting each state the underlying system
// might be in.
NormalDistribution[] initial_components =
{
new NormalDistribution(), // initial value for the first variable's distribution
new NormalDistribution() // initial value for the second variable's distribution
};
// Specify a initial independent normal distribution for the samples.
var density = new Independent<NormalDistribution, double>(initial_components);
// Creates a continuous hidden Markov Model with two states organized in an Ergodic
// topology and an underlying independent Normal distribution as probability density.
var model = new HiddenMarkovModel<Independent<NormalDistribution>, double[]>(new Ergodic(2), density);
// Configure the learning algorithms to train the sequence classifier until the
// difference in the average log-likelihood changes only by as little as 0.0001
var teacher = new BaumWelchLearning<Independent<NormalDistribution>, double[]>(model)
{
Tolerance = 0.0001,
Iterations = 0,
};
// Fit the model
teacher.Learn(data);
double error = teacher.LogLikelihood;
// Get the hidden state associated with each observation
//
double logLikelihood; // log-likelihood of the Viterbi path
int[] hidden_states = model.Decode(data[0], out logLikelihood);
Assert.AreEqual(-33.978800850637882, error);
Assert.AreEqual(-33.9788008509802, logLikelihood);
Assert.AreEqual(11, hidden_states.Length);
}
public void LearnTest9()
{
var observations = new double[][][]
{
#region example
new double[][]
{
new double[] {2.58825719356537, -6.10018078957452, -3.51826652951428,},
new double[] {1.5637531876564, -8.92844874836103, -9.09330631370717,},
new double[] {2.12242007255554, -14.8117769726059, -9.04211363915664,},
new double[] {0.39045587182045, -10.3548189544216, -7.69608701297759,},
new double[] {-0.553155690431595, -34.9185135663671, 14.6941023804174,},
new double[] {-0.923129916191101, -6.06337512248124, 8.28106954197084,},
new double[] {0.478342920541763, -4.93066650122859, 3.1120912556361,},
},
new double[][]
{
new double[] {1.89824998378754, -8.21581113387553, -7.88790716806936,},
new double[] {2.24453508853912, -10.281886698766, -9.67846789539227,},
new double[] {0.946296751499176, -22.0276392511088, -6.52238763834787,},
new double[] {-0.251136720180511, -13.3010653290676, 8.47499524273859,},
new double[] {-2.35625505447388, -18.1542111199742, 6.25564428645639,},
new double[] {0.200483202934265, -5.48215328147925, 5.88811639894938,},
},
new double[][]
{
new double[] {2.7240589261055, -3.71720542338046, -3.75092324997593,},
new double[] {2.19917744398117, -7.18434871865373, -4.92539999824263,},
new double[] {1.40723958611488, -11.5545592998714, -5.14780194932221,},
new double[] {1.61909088492393, -12.5262932665595, -6.34366687651826,},
new double[] {-2.54745036363602, -8.64924529565274, 4.15127988308386,},
new double[] {0.815489888191223, -33.8531051237431, 4.3954106953589,},
new double[] {-2.2090271115303, -7.17818258102413, 8.9117419130814,},
new double[] {-1.9000232219696, -2.4331659041997, 6.91224717766923,},
},
new double[][]
{
new double[] {4.88746017217636, -4.36384651224969, -5.45526891285354,},
new double[] {1.07786506414413, -12.9399071692788, -5.88248026843442,},
new double[] {2.28888094425201, -15.4017823367163, -9.36490649113217,},
new double[] {-1.16468518972397, -35.4200913138333, 5.44735305966353,},
new double[] {-1.1483296751976, -13.5454911068913, 7.83577905727326,},
new double[] {-2.58188247680664, -1.10149600205281, 10.5928750605715,},
new double[] {-0.277529656887054, -6.96828661824016, 4.59381106840823,},
},
new double[][]
{
new double[] {3.39118540287018, -2.9173207268871, -5.66795398530988,},
new double[] {1.44856870174408, -9.21319243840922, -5.74986260778932,},
new double[] {1.45215392112732, -10.3989582187704, -7.06932768129103,},
new double[] {0.640938431024551, -15.319525165245, -7.68866476960221,},
new double[] {-0.77500119805336, -20.8335910793105, -1.56702420087282,},
new double[] {-3.48337143659592, -18.0461677940976, 12.3393172987974,},
new double[] {-1.17014795541763, -5.59624373275155, 6.09176828712909,},
},
new double[][]
{
new double[] {-3.984335064888, -6.2406475893692, -8.13815178201645,},
new double[] {-2.12110131978989, -5.60649378910647, -7.69551693188544,},
new double[] {-1.62762850522995, -24.1160212319193, -14.9683354815265,},
new double[] {-1.15231424570084, -17.1336790735458, -5.70731951079186,},
new double[] {0.00514835119247437, -35.4256585588532, 11.0357975880744,},
new double[] {0.247226655483246, -4.87705331087666, 8.47028869639136,},
new double[] {-1.28729045391083, -4.4684855254196, 4.45432778840328,},
},
new double[][]
{
new double[] {-5.14926165342331, -14.4168633009146, -14.4808205022332,},
new double[] {-3.93681302666664, -13.6040611430423, -9.52852874304709,},
new double[] {-4.0200162678957, -17.9772444010218, -10.9145425003168,},
new double[] {2.99205146729946, -11.3995995445577, 10.0112700536762,},
new double[] {-1.80960297584534, -25.9626088707583, 3.84153700324761,},
new double[] {-0.47445073723793, -3.15995343875038, 3.81288679772555,},
},
new double[][]
{
new double[] {-3.10730338096619, -4.90623566171983, -7.71155001801384,},
new double[] {-2.58265435695648, -12.8249488039327, -7.81701695282102,},
new double[] {-3.70455086231232, -10.9642675851383, -10.3474496036822,},
new double[] {2.34457105398178, -22.575668228196, -4.00681935468317,},
new double[] {-0.137023627758026, -22.8846781066673, 6.49448229892285,},
new double[] {-1.04487389326096, -10.8106353197974, 6.89123118904132,},
new double[] {-0.807777792215347, -6.72485967042486, 6.44026679233423,},
new double[] {-0.0864192843437195, -1.82784244477527, 5.21446167464657,},
},
new double[][]
{
new double[] {-3.68375554680824, -8.91158395500054, -9.35894038244743,},
new double[] {-3.42774018645287, -8.90966793048099, -12.0502934183779,},
new double[] {-2.21796408295631, -20.1283824753482, -9.3404551995806,},
new double[] {0.275979936122894, -24.8898254667703, -1.95441472953041,},
new double[] {2.8757631778717, -25.5929744730134, 15.9213204397452,},
new double[] {-0.0532664358615875, -5.41014381829368, 7.0702071664098,},
new double[] {-0.523447245359421, -2.21351362388411, 5.47910029515575,},
},
new double[][]
{
new double[] {-2.87790596485138, -4.67335526533981, -5.23215633615683,},
new double[] {-2.4156779050827, -3.99829080603495, -4.85576151355235,},
new double[] {-2.6987336575985, -7.76589206730162, -5.81054787011341,},
new double[] {-2.65482440590858, -10.5628263066491, -5.60468502395908,},
new double[] {-2.54620611667633, -13.0387387107748, -5.36223367466908,},
new double[] {-0.349991768598557, -6.54244110985515, -4.35843018634009,},
new double[] {1.43021196126938, -14.1423935327282, 11.3171592025544,},
new double[] {-0.248833745718002, -25.6880129237476, 3.6943247495434,},
new double[] {-0.191526114940643, -7.40986142342928, 5.01053017361167,},
new double[] {0.0262223184108734, -2.32355649224634, 5.02960958030255,},
},
new double[][]
{
new double[] {-0.491838902235031, -6.14010393559236, 0.827477332024586,},
new double[] {-0.806065648794174, -7.15029676810841, -1.19623376104369,},
new double[] {-0.376655906438828, -8.79062775480082, -1.90518908829517,},
new double[] {0.0747844576835632, -8.78933441325732, -1.96265207353993,},
new double[] {-0.375023484230042, 3.89681155173501, 9.01643231817069,},
new double[] {-2.8106614947319, -11.460008093918, 2.27801912994775,},
new double[] {8.87353122234344, -36.8569805718597, 6.36432395690119,},
new double[] {2.17160433530808, -6.57312981892095, 6.99683358454453,},
},
new double[][]
{
new double[] {-2.59969010949135, -3.67992698430228, 1.09594294144671,},
new double[] {-1.09673067927361, -5.84256216502719, -0.576662929456575,},
new double[] {-1.31642892956734, -7.75851355520771, -2.38379618379558,},
new double[] {-0.119869410991669, -8.5749576027529, -1.84393133510667,},
new double[] {1.6157403588295, -8.50491836461337, 1.75083250596366,},
new double[] {1.66225507855415, -26.4882911957686, 1.98153904369032,},
new double[] {2.55657434463501, -10.5098938623168, 11.632377227365,},
new double[] {1.91832333803177, -9.98753621777953, 7.38483383044985,},
new double[] {2.16058492660522, -2.7784029746222, 7.8378896386686,},
},
#endregion
};
var density = new MultivariateNormalDistribution(3);
var model = new HiddenMarkovModel<MultivariateNormalDistribution, double[]>(new Forward(5), density);
var learning = new BaumWelchLearning<MultivariateNormalDistribution, double[]>(model)
{
Tolerance = 0.0001,
Iterations = 0,
FittingOptions = new NormalOptions() { Regularization = 0.0001 }
};
learning.Learn(observations);
double logLikelihood = learning.LogLikelihood;
Assert.IsFalse(Double.IsNaN(logLikelihood));
foreach (double value in model.LogTransitions.ToMatrix())
Assert.IsFalse(Double.IsNaN(value));
foreach (double value in model.LogInitial)
Assert.IsFalse(Double.IsNaN(value));
}
public void LearnTest10()
{
// Create sequences of vector-valued observations. In the
// sequence below, a single observation is composed of two
// coordinate values, such as (x, y). There seems to be two
// states, one for (x,y) values less than (5,5) and another
// for higher values. The states seems to be switched on
// every observation.
double[][][] sequences =
{
new double[][] // sequence 1
{
new double[] { 1, 2 }, // observation 1 of sequence 1
new double[] { 6, 7 }, // observation 2 of sequence 1
new double[] { 2, 3 }, // observation 3 of sequence 1
},
new double[][] // sequence 2
{
new double[] { 2, 2 }, // observation 1 of sequence 2
new double[] { 9, 8 }, // observation 2 of sequence 2
new double[] { 1, 0 }, // observation 3 of sequence 2
},
new double[][] // sequence 3
{
new double[] { 1, 3 }, // observation 1 of sequence 3
new double[] { 8, 9 }, // observation 2 of sequence 3
new double[] { 3, 3 }, // observation 3 of sequence 3
},
};
// Specify a initial normal distribution for the samples.
var density = new MultivariateNormalDistribution(dimension: 2);
// Creates a continuous hidden Markov Model with two states organized in a forward
// topology and an underlying univariate Normal distribution as probability density.
var model = new HiddenMarkovModel<MultivariateNormalDistribution, double[]>(new Forward(2), density);
// Configure the learning algorithms to train the sequence classifier until the
// difference in the average log-likelihood changes only by as little as 0.0001
var teacher = new BaumWelchLearning<MultivariateNormalDistribution, double[]>(model)
{
Tolerance = 0.0001,
Iterations = 0,
};
// Fit the model
teacher.Learn(sequences);
double logLikelihood = teacher.LogLikelihood;
// See the likelihood of the sequences learned
double a1 = Math.Exp(model.Evaluate(new[] {
new double[] { 1, 2 },
new double[] { 6, 7 },
new double[] { 2, 3 }})); // 0.000208
double a2 = Math.Exp(model.Evaluate(new[] {
new double[] { 2, 2 },
new double[] { 9, 8 },
new double[] { 1, 0 }})); // 0.0000376
// See the likelihood of an unrelated sequence
double a3 = Math.Exp(model.Evaluate(new[] {
new double[] { 8, 7 },
new double[] { 9, 8 },
new double[] { 1, 0 }})); // 2.10 x 10^(-89)
Assert.AreEqual(0.00020825319093038984, a1);
Assert.AreEqual(0.000037671116792519834, a2, 1e-15);
Assert.AreEqual(2.1031924118199194E-89, a3);
}
public void LearnTest7()
{
// Create continuous sequences. In the sequences below, there
// seems to be two states, one for values between 0 and 1 and
// another for values between 5 and 7. The states seems to be
// switched on every observation.
double[][] sequences = new double[][]
{
new double[] { 0.1, 5.2, 0.3, 6.7, 0.1, 6.0 },
new double[] { 0.2, 6.2, 0.3, 6.3, 0.1, 5.0 },
new double[] { 0.1, 7.0, 0.1, 7.0, 0.2, 5.6 },
};
// Specify a initial normal distribution for the samples.
var density = new NormalDistribution();
// Creates a continuous hidden Markov Model with two states organized in a forward
// topology and an underlying univariate Normal distribution as probability density.
var model = new HiddenMarkovModel<NormalDistribution, double>(new Ergodic(2), density);
// Configure the learning algorithms to train the sequence classifier until the
// difference in the average log-likelihood changes only by as little as 0.0001
var teacher = new BaumWelchLearning<NormalDistribution, double>(model)
{
Tolerance = 0.0001,
Iterations = 0,
};
// Fit the model
teacher.Learn(sequences);
double logLikelihood = teacher.LogLikelihood;
// See the log-probability of the sequences learned
double a1 = model.Evaluate(new[] { 0.1, 5.2, 0.3, 6.7, 0.1, 6.0 }); // -0.12799388666109757
double a2 = model.Evaluate(new[] { 0.2, 6.2, 0.3, 6.3, 0.1, 5.0 }); // 0.01171157434400194
// See the probability of an unrelated sequence
double a3 = model.Evaluate(new[] { 1.1, 2.2, 1.3, 3.2, 4.2, 1.0 }); // -298.7465244473417
double likelihood = Math.Exp(logLikelihood);
a1 = Math.Exp(a1); // 0.879
a2 = Math.Exp(a2); // 1.011
a3 = Math.Exp(a3); // 0.000
// We can also ask the model to decode one of the sequences. After
// this step the resulting sequence will be: { 0, 1, 0, 1, 0, 1 }
//
int[] states = model.Decode(new[] { 0.1, 5.2, 0.3, 6.7, 0.1, 6.0 });
Assert.IsTrue(states.IsEqual(new[] { 0, 1, 0, 1, 0, 1 }));
Assert.AreEqual(1.496360383340358, likelihood, 1e-10);
Assert.AreEqual(0.8798587580029778, a1, 1e-10);
Assert.AreEqual(1.0117804233450216, a2, 1e-10);
Assert.AreEqual(1.8031545195073828E-130, a3, 1e-10);
Assert.AreEqual(2, model.Emissions.Length);
var state1 = (model.Emissions[0] as NormalDistribution);
var state2 = (model.Emissions[1] as NormalDistribution);
Assert.AreEqual(0.16666666666666, state1.Mean, 1e-10);
Assert.AreEqual(6.11111111111111, state2.Mean, 1e-10);
Assert.IsFalse(Double.IsNaN(state1.Mean));
Assert.IsFalse(Double.IsNaN(state2.Mean));
Assert.AreEqual(0.007499999999999, state1.Variance, 1e-10);
Assert.AreEqual(0.538611111111111, state2.Variance, 1e-10);
Assert.IsFalse(Double.IsNaN(state1.Variance));
Assert.IsFalse(Double.IsNaN(state2.Variance));
Assert.AreEqual(2, model.LogTransitions.GetLength(0));
Assert.AreEqual(2, model.LogTransitions.Columns());
var A = model.LogTransitions.Exp();
Assert.AreEqual(0, A[0][0], 1e-16);
Assert.AreEqual(1, A[0][1], 1e-16);
Assert.AreEqual(1, A[1][0], 1e-16);
Assert.AreEqual(0, A[1][1], 1e-16);
Assert.IsFalse(A.HasNaN());
}
public void LearnTest8()
{
// Create continuous sequences. In the sequence below, there
// seems to be two states, one for values equal to 1 and another
// for values equal to 2.
double[][] sequences = new double[][]
{
new double[] { 1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2 }
};
// Specify a initial normal distribution for the samples.
var density = new NormalDistribution();
// Creates a continuous hidden Markov Model with two states organized in a forward
// topology and an underlying univariate Normal distribution as probability density.
var model = new HiddenMarkovModel<NormalDistribution, double>(new Ergodic(2), density);
// Configure the learning algorithms to train the sequence classifier until the
// difference in the average log-likelihood changes only by as little as 0.0001
var teacher = new BaumWelchLearning<NormalDistribution, double>(model)
{
Tolerance = 0.0001,
Iterations = 0,
// However, we will need to specify a regularization constant as the
// variance of each state will likely be zero (all values are equal)
FittingOptions = new NormalOptions() { Regularization = double.Epsilon }
};
// Fit the model
teacher.Learn(sequences);
double likelihood = teacher.LogLikelihood;
// See the probability of the sequences learned
double a1 = model.Evaluate(new double[] { 1, 2, 1, 2, 1, 2, 1, 2, 1 }); // exp(a1) = infinity
double a2 = model.Evaluate(new double[] { 1, 2, 1, 2, 1 }); // exp(a2) = infinity
// See the probability of an unrelated sequence
double a3 = model.Evaluate(new double[] { 1, 2, 3, 2, 1, 2, 1 }); // exp(a3) = 0
double a4 = model.Evaluate(new double[] { 1.1, 2.2, 1.3, 3.2, 4.2, 1.0 }); // exp(a4) = 0
Assert.AreEqual(double.PositiveInfinity, System.Math.Exp(likelihood));
Assert.AreEqual(3341.7098768473734, a1);
Assert.AreEqual(1856.5054871374298, a2);
Assert.AreEqual(0.0, Math.Exp(a3));
Assert.AreEqual(0.0, Math.Exp(a4));
Assert.AreEqual(2, model.Emissions.Length);
var state1 = (model.Emissions[0] as NormalDistribution);
var state2 = (model.Emissions[1] as NormalDistribution);
Assert.AreEqual(1.0, state1.Mean, 1e-10);
Assert.AreEqual(2.0, state2.Mean, 1e-10);
Assert.IsFalse(Double.IsNaN(state1.Mean));
Assert.IsFalse(Double.IsNaN(state2.Mean));
Assert.IsTrue(state1.Variance < 1e-30);
Assert.IsTrue(state2.Variance < 1e-30);
var A = model.LogTransitions.Exp();
Assert.AreEqual(2, A.GetLength(0));
Assert.AreEqual(2, A.Columns());
Assert.AreEqual(0, A[0][0]);
Assert.AreEqual(1, A[0][1]);
Assert.AreEqual(1, A[1][0]);
Assert.AreEqual(0, A[1][1]);
}
public void LearnTest3()
{
double[][] sequences = new double[][]
{
new double[] { 0,1,1,1,1,0,1,1,1,1 },
new double[] { 0,1,1,1,0,1,1,1,1,1 },
new double[] { 0,1,1,1,1,1,1,1,1,1 },
new double[] { 0,1,1,1,1,1 },
new double[] { 0,1,1,1,1,1,1 },
new double[] { 0,1,1,1,1,1,1,1,1,1 },
new double[] { 0,1,1,1,1,1,1,1,1,1 },
};
// Creates a new Hidden Markov Model with 3 states
var hmm = CreateDiscrete(3, 2);
// Try to fit the model to the data until the difference in
// the average log-likelihood changes only by as little as 0.0001
var teacher = new BaumWelchLearning<GeneralDiscreteDistribution, int>(hmm)
{
Topology = new Ergodic(3),
Tolerance = 0.0001
};
var hmm2 = teacher.Learn(sequences.ToInt32());
double ll = teacher.LogLikelihood;
// Calculate the probability that the given
// sequences originated from the model
double l1; hmm.Decode(new int[] { 0, 1 }, out l1); // 0.4999
double l2; hmm.Decode(new int[] { 0, 1, 1, 1 }, out l2); // 0.1145
double l3; hmm.Decode(new int[] { 1, 1 }, out l3); // 0.0000
double l4; hmm.Decode(new int[] { 1, 0, 0, 0 }, out l4); // 0.0000
double l5; hmm.Decode(new int[] { 0, 1, 0, 1, 1, 1, 1, 1, 1 }, out l5); // 0.0002
double l6; hmm.Decode(new int[] { 0, 1, 1, 1, 1, 1, 1, 0, 1 }, out l6); // 0.0002
ll = System.Math.Exp(ll);
l1 = System.Math.Exp(l1);
l2 = System.Math.Exp(l2);
l3 = System.Math.Exp(l3);
l4 = System.Math.Exp(l4);
l5 = System.Math.Exp(l5);
l6 = System.Math.Exp(l6);
Assert.AreEqual(1.2114235662225716, ll, 1e-4);
Assert.AreEqual(0.4999419764097881, l1, 1e-4);
Assert.AreEqual(0.1145702973735144, l2, 1e-4);
Assert.AreEqual(0.0000529972606821, l3, 1e-4);
Assert.AreEqual(0.0000000000000001, l4, 1e-4);
Assert.AreEqual(0.0002674509390361, l5, 1e-4);
Assert.AreEqual(0.0002674509390361, l6, 1e-4);
Assert.IsTrue(l1 > l3 && l1 > l4);
Assert.IsTrue(l2 > l3 && l2 > l4);
Assert.AreEqual(1, hmm.NumberOfInputs);
}
public void LearnTest6()
{
// Continuous Markov Models can operate using any
// probability distribution, including discrete ones.
// In the following example, we will try to create a
// Continuous Hidden Markov Model using a discrete
// distribution to detect if a given sequence starts
// with a zero and has any number of ones after that.
int[][] sequences = new double[][]
{
new double[] { 0,1,1,1,1,0,1,1,1,1 },
new double[] { 0,1,1,1,0,1,1,1,1,1 },
new double[] { 0,1,1,1,1,1,1,1,1,1 },
new double[] { 0,1,1,1,1,1 },
new double[] { 0,1,1,1,1,1,1 },
new double[] { 0,1,1,1,1,1,1,1,1,1 },
new double[] { 0,1,1,1,1,1,1,1,1,1 },
}.ToInt32();
// Create a new Hidden Markov Model with 3 states and
// a generic discrete distribution with two symbols
var hmm = CreateDiscrete(3, 2);
// Try to fit the model to the data until the difference in
// the average log-likelihood changes only by as little as 0.0001
var teacher = new BaumWelchLearning<GeneralDiscreteDistribution, int>(hmm)
{
Tolerance = 0.0001,
Iterations = 0
};
var hmm2 = teacher.Learn(sequences);
Assert.AreSame(hmm, hmm2);
double ll = Math.Exp(teacher.LogLikelihood);
// Calculate the probability that the given
// sequences originated from the model
double l1 = Math.Exp(hmm.Evaluate(new int[] { 0, 1 })); // 0.999
double l2 = Math.Exp(hmm.Evaluate(new int[] { 0, 1, 1, 1 })); // 0.916
// Sequences which do not start with zero have much lesser probability.
double l3 = Math.Exp(hmm.Evaluate(new int[] { 1, 1 })); // 0.000
double l4 = Math.Exp(hmm.Evaluate(new int[] { 1, 0, 0, 0 })); // 0.000
// Sequences which contains few errors have higher probability
// than the ones which do not start with zero. This shows some
// of the temporal elasticity and error tolerance of the HMMs.
double l5 = Math.Exp(hmm.Evaluate(new int[] { 0, 1, 0, 1, 1, 1, 1, 1, 1 })); // 0.034
double l6 = Math.Exp(hmm.Evaluate(new int[] { 0, 1, 1, 1, 1, 1, 1, 0, 1 })); // 0.034
Assert.AreEqual(1.2114235662225716, ll, 1e-4);
Assert.AreEqual(0.99996863060890995, l1, 1e-4);
Assert.AreEqual(0.91667240076011669, l2, 1e-4);
Assert.AreEqual(0.00002335133758386, l3, 1e-4);
Assert.AreEqual(0.00000000000000012, l4, 1e-4);
Assert.AreEqual(0.03423723144322685, l5, 1e-4);
Assert.AreEqual(0.03423719592053246, l6, 1e-4);
Assert.IsFalse(Double.IsNaN(ll));
Assert.IsFalse(Double.IsNaN(l1));
Assert.IsFalse(Double.IsNaN(l2));
Assert.IsFalse(Double.IsNaN(l3));
Assert.IsFalse(Double.IsNaN(l4));
Assert.IsFalse(Double.IsNaN(l5));
Assert.IsFalse(Double.IsNaN(l6));
Assert.IsTrue(l1 > l3 && l1 > l4);
Assert.IsTrue(l2 > l3 && l2 > l4);
}
public void FittingOptionsTest()
{
// Create a degenerate problem
double[][][] sequences = new double[][]
{
new double[] { 1,1,1,1,1,0,1,1,1,1 },
new double[] { 1,1,1,1,0,1,1,1,1,1 },
new double[] { 1,1,1,1,1,1,1,1,1,1 },
new double[] { 1,1,1,1,1,1 },
new double[] { 1,1,1,1,1,1,1 },
new double[] { 1,1,1,1,1,1,1,1,1,1 },
new double[] { 1,1,1,1,1,1,1,1,1,1 },
}.Apply((xi, i, j) => new[] { xi });
// Creates a continuous hidden Markov Model with two states organized in a ergodic
// topology and an underlying multivariate Normal distribution as density.
var density = new MultivariateNormalDistribution(1);
var model = new HiddenMarkovModel<MultivariateNormalDistribution, double[]>(new Ergodic(2), density);
// Configure the learning algorithms to train the sequence classifier
var teacher = new BaumWelchLearning<MultivariateNormalDistribution, double[]>(model)
{
Tolerance = 0.0001,
Iterations = 0,
// Configure options for fitting the normal distribution
FittingOptions = new NormalOptions() { Regularization = 0.0001, }
};
// Fit the model. No exceptions will be thrown
teacher.Learn(sequences);
double logLikelihood = teacher.LogLikelihood;
double likelihood = Math.Exp(logLikelihood);
Assert.AreEqual(5.3782215178437722, logLikelihood, 1e-15);
Assert.IsFalse(double.IsNaN(logLikelihood));
Assert.AreEqual(0.0001, (teacher.FittingOptions as NormalOptions).Regularization);
// Try without a regularization constant to get an exception
bool thrown;
thrown = false;
density = new MultivariateNormalDistribution(1);
model = new HiddenMarkovModel<MultivariateNormalDistribution, double[]>(new Ergodic(2), density);
teacher = new BaumWelchLearning<MultivariateNormalDistribution, double[]>(model) { Tolerance = 0.0001, Iterations = 0, };
Assert.IsNull(teacher.FittingOptions);
try { teacher.Learn(sequences); }
catch { thrown = true; }
Assert.IsTrue(thrown);
thrown = false;
density = new Accord.Statistics.Distributions.Multivariate.MultivariateNormalDistribution(1);
model = new HiddenMarkovModel<MultivariateNormalDistribution, double[]>(new Ergodic(2), density);
teacher = new BaumWelchLearning<MultivariateNormalDistribution, double[]>(model)
{
Tolerance = 0.0001,
Iterations = 0,
FittingOptions = new NormalOptions() { Regularization = 0 }
};
Assert.IsNotNull(teacher.FittingOptions);
try { teacher.Learn(sequences); }
catch { thrown = true; }
Assert.IsTrue(thrown);
}
private static void checkDegenerate(double[][][] observations, int states)
{
bool thrown = false;
try
{
var density = new MultivariateNormalDistribution(2);
var model = new HiddenMarkovModel<MultivariateNormalDistribution, double[]>(new Forward(states), density);
var learning = new BaumWelchLearning<MultivariateNormalDistribution, double[]>(model)
{
Tolerance = 0.0001,
Iterations = 0,
};
learning.Learn(observations);
Assert.AreEqual(0, learning.LogLikelihood);
}
catch (NonPositiveDefiniteMatrixException)
{
thrown = true;
}
Assert.IsTrue(thrown);
{
var density = new MultivariateNormalDistribution(2);
var model = new HiddenMarkovModel<MultivariateNormalDistribution, double[]>(new Forward(states), density);
var learning = new BaumWelchLearning<MultivariateNormalDistribution, double[]>(model)
{
Tolerance = 0.0001,
Iterations = 0,
FittingOptions = new NormalOptions() { Robust = true }
};
learning.Learn(observations);
Assert.IsFalse(Double.IsNaN(learning.LogLikelihood));
foreach (double value in model.LogTransitions.ToMatrix())
Assert.IsFalse(Double.IsNaN(value));
foreach (double value in model.LogInitial)
Assert.IsFalse(Double.IsNaN(value));
}
}
public void LearnTest_EmptySequence()
{
double[][] sequences =
{
new double[] { -0.223, -1.05, -0.574, 0.965, -0.448, 0.265, 0.087, 0.362, 0.717, -0.032 },
new double[] { -1.05, -0.574, 0.965, -0.448, 0.265, 0.087, 0.362, 0.717, -0.032, -0.346 },
new double[] { },
new double[] { 0.965, -0.448, 0.265, 0.087, 0.362, 0.717, -0.032, -0.346, -0.989, -0.619 },
new double[] { -0.448, 0.265, 0.087, 0.362, 0.717, -0.032, -0.346, -0.989, -0.619, 0.02 },
new double[] { 0.265, 0.087, 0.362, 0.717, -0.032, -0.346, -0.989, -0.619, 0.02, -0.297 },
};
var model = new HiddenMarkovModel<NormalDistribution, double>(new Ergodic(2), new NormalDistribution());
var teacher = new BaumWelchLearning<NormalDistribution, double>(model)
{
Tolerance = 0.0001,
Iterations = 0,
};
teacher.Learn(sequences);
}
public void LearnTest12()
{
// Suppose we have a set of six sequences and we would like to
// fit a hidden Markov model with mixtures of Normal distributions
// as the emission densities.
// First, let's consider a set of univariate sequences:
double[][] sequences =
{
new double[] { -0.223, -1.05, -0.574, 0.965, -0.448, 0.265, 0.087, 0.362, 0.717, -0.032 },
new double[] { -1.05, -0.574, 0.965, -0.448, 0.265, 0.087, 0.362, 0.717, -0.032, -0.346 },
new double[] { -0.574, 0.965, -0.448, 0.265, 0.087, 0.362, 0.717, -0.032, -0.346, -0.989 },
new double[] { 0.965, -0.448, 0.265, 0.087, 0.362, 0.717, -0.032, -0.346, -0.989, -0.619 },
new double[] { -0.448, 0.265, 0.087, 0.362, 0.717, -0.032, -0.346, -0.989, -0.619, 0.02 },
new double[] { 0.265, 0.087, 0.362, 0.717, -0.032, -0.346, -0.989, -0.619, 0.02, -0.297 },
};
// Now we can begin specifying a initial Gaussian mixture distribution. It is
// better to add some different initial parameters to the mixture components:
var density = new Mixture<NormalDistribution>(
new NormalDistribution(mean: 2, stdDev: 1.0), // 1st component in the mixture
new NormalDistribution(mean: 0, stdDev: 0.6), // 2nd component in the mixture
new NormalDistribution(mean: 4, stdDev: 0.4), // 3rd component in the mixture
new NormalDistribution(mean: 6, stdDev: 1.1) // 4th component in the mixture
);
// Let's then create a continuous hidden Markov Model with two states organized in a forward
// topology with the underlying univariate Normal mixture distribution as probability density.
var model = new HiddenMarkovModel<Mixture<NormalDistribution>, double>(new Forward(2), density);
// Now we should configure the learning algorithms to train the sequence classifier. We will
// learn until the difference in the average log-likelihood changes only by as little as 0.0001
var teacher = new BaumWelchLearning<Mixture<NormalDistribution>, double>(model)
{
Tolerance = 0.0001,
Iterations = 0,
// Note, however, that since this example is extremely simple and we have only a few
// data points, a full-blown mixture wouldn't really be needed. Thus we will have a
// great chance that the mixture would become degenerated quickly. We can avoid this
// by specifying some regularization constants in the Normal distribution fitting:
FittingOptions = new MixtureOptions()
{
Iterations = 1, // limit the inner e-m to a single iteration
InnerOptions = new NormalOptions()
{
Regularization = 1e-5 // specify a regularization constant
}
}
};
// Finally, we can fit the model
teacher.Learn(sequences);
double logLikelihood = teacher.LogLikelihood;
// And now check the likelihood of some approximate sequences.
double[] newSequence = { -0.223, -1.05, -0.574, 0.965, -0.448, 0.265, 0.087, 0.362, 0.717, -0.032 };
double a1 = Math.Exp(model.Evaluate(newSequence)); // 11729312967893.566
int[] path = model.Decode(newSequence);
// We can see that the likelihood of an unrelated sequence is much smaller:
double a3 = Math.Exp(model.Evaluate(new double[] { 8, 2, 6, 4, 1 })); // 0.0
Assert.IsTrue(a1 > 1e+10);
Assert.IsTrue(a3 < 1e+10);
}
public void LearnTest11()
{
// Suppose we have a set of six sequences and we would like to
// fit a hidden Markov model with mixtures of Normal distributions
// as the emission densities.
// First, let's consider a set of univariate sequences:
double[][] sequences =
{
new double[] { 1, 1, 2, 2, 2, 3, 3, 3 },
new double[] { 1, 2, 2, 2, 3, 3 },
new double[] { 1, 2, 2, 3, 3, 5 },
new double[] { 2, 2, 2, 2, 3, 3, 3, 4, 5, 5, 1 },
new double[] { 1, 1, 1, 2, 2, 5 },
new double[] { 1, 2, 2, 4, 4, 5 },
};
// Now we can begin specifying a initial Gaussian mixture distribution. It is
// better to add some different initial parameters to the mixture components:
var density = new Mixture<NormalDistribution>(
new NormalDistribution(mean: 2, stdDev: 1.0), // 1st component in the mixture
new NormalDistribution(mean: 0, stdDev: 0.6), // 2nd component in the mixture
new NormalDistribution(mean: 4, stdDev: 0.4), // 3rd component in the mixture
new NormalDistribution(mean: 6, stdDev: 1.1) // 4th component in the mixture
);
// Let's then create a continuous hidden Markov Model with two states organized in a forward
// topology with the underlying univariate Normal mixture distribution as probability density.
var model = new HiddenMarkovModel<Mixture<NormalDistribution>, double>(new Forward(2), density);
// Now we should configure the learning algorithms to train the sequence classifier. We will
// learn until the difference in the average log-likelihood changes only by as little as 0.0001
var teacher = new BaumWelchLearning<Mixture<NormalDistribution>, double>(model)
{
Tolerance = 0.0001,
Iterations = 0,
// Note, however, that since this example is extremely simple and we have only a few
// data points, a full-blown mixture wouldn't really be needed. Thus we will have a
// great chance that the mixture would become degenerated quickly. We can avoid this
// by specifying some regularization constants in the Normal distribution fitting:
FittingOptions = new MixtureOptions()
{
Iterations = 1, // limit the inner e-m to a single iteration
InnerOptions = new NormalOptions()
{
Regularization = 1e-5 // specify a regularization constant
}
}
};
// Finally, we can fit the model
teacher.Learn(sequences);
double logLikelihood = teacher.LogLikelihood;
// And now check the likelihood of some approximate sequences.
double a1 = Math.Exp(model.Evaluate(new double[] { 1, 1, 2, 2, 3 })); // 2.3413833128741038E+45
double a2 = Math.Exp(model.Evaluate(new double[] { 1, 1, 2, 5, 5 })); // 9.94607618459872E+19
// We can see that the likelihood of an unrelated sequence is much smaller:
double a3 = Math.Exp(model.Evaluate(new double[] { 8, 2, 6, 4, 1 })); // 1.5063654166181737E-44
Assert.IsTrue(a1 > 1e+6);
Assert.IsTrue(a2 > 1e+6);
Assert.IsTrue(a3 < 1e-6);
Assert.IsFalse(Double.IsNaN(a1));
Assert.IsFalse(Double.IsNaN(a2));
Assert.IsFalse(Double.IsNaN(a3));
}