public static HiddenMarkovModel CreateModel2()
{
int states = 3;
int symbols = 3;
int[][] sequences = new int[][]
{
new int[] { 0, 1, 1, 1, 2 },
new int[] { 0, 1, 1, 1, 2, 2, 2 },
new int[] { 0, 0, 1, 1, 2, 2 },
new int[] { 0, 1, 1, 1, 2, 2, 2 },
new int[] { 0, 1, 1, 1, 2, 1 },
new int[] { 0, 1, 1, 2, 2 },
new int[] { 0, 0, 1, 1, 1, 2, 1 },
new int[] { 0, 0, 0, 1, 1, 1, 2, 1 },
new int[] { 0, 1, 1, 2, 2, 2 },
};
HiddenMarkovModel hmm = new HiddenMarkovModel(new Forward(states), symbols);
var teacher = new BaumWelchLearning(hmm) { Iterations = 100, Tolerance = 0 };
double ll = teacher.Run(sequences);
return hmm;
}
public StochasticGenerator(MelodySequence[] seqs)
{
if(seqs != null && seqs.Length > 0)
this.base_seq = seqs[0];
int count = seqs.Length;
List<int[]> notes = new List<int[]>();
List<int[]> bayesInputs = new List<int[]>();
List<int> bayesOutputs = new List<int>();
notes_map = new Dictionary<int, int>();
int max_notes = 0;
int note = 0;
foreach (MelodySequence m in seqs)
{
Note[] song = m.ToArray();
int[] _notes = new int[song.Length];
int[] _durations = new int[20];
for (int i = 0; i < song.Length; i++)
{
var unote = song[i].Pitch + song[i].Duration*128;
if (notes_map.ContainsKey(unote))
_notes[i] = notes_map[unote];
else
{
notes_map[unote] = note++;
_notes[i] = notes_map[unote];
}
}
notes.Add(_notes);
}
max_notes = note;
Console.WriteLine("Training Pitches");
pitch_hmm = new HiddenMarkovModel(50, max_notes);
var teacher = new BaumWelchLearning(pitch_hmm) { Tolerance = 0.0001, Iterations = 0 };
var __pitches = notes.ToArray();
teacher.Run(__pitches);
teacher.Run(__pitches);
Console.WriteLine("Done training");
this.MaxGenerations = 2000;
}
/*public static void SaveSequenceList(SequenceList seqList, string path)
{
Stream writeStream = new FileStream(path, FileMode.Create, FileAccess.Write, FileShare.None);
seqList.Save(writeStream);
writeStream.Close();
}
public static SequenceList LoadSequenceList(string path)
{
Stream readStream = new FileStream(path, FileMode.Open, FileAccess.Read, FileShare.Read);
SequenceList seqList = SequenceList.Load(readStream);
readStream.Close();
return seqList;
}*/
public static HiddenMarkovModel<MultivariateNormalDistribution> CreateModelFromFrames(List<List<Frame>> frames)
{
SequenceList sequences = Utils.FramesToSequenceList(frames);
HiddenMarkovModel<MultivariateNormalDistribution> hmm;
MultivariateNormalDistribution mnd = new MultivariateNormalDistribution(sequences.GetDimensions());
hmm = new HiddenMarkovModel<MultivariateNormalDistribution>(new Forward(5), mnd);
var teacher = new BaumWelchLearning<MultivariateNormalDistribution>(hmm);
teacher.Tolerance = 0.0001;
teacher.Iterations = 0;
teacher.FittingOptions = new NormalOptions()
{
Diagonal = true, // only diagonal covariance matrices
Regularization = 1e-5 // avoid non-positive definite errors
};
teacher.Run(sequences.GetArray());
return hmm;
}
public MarkovGenerator(MelodySequence[] seqs, PatchNames instrument = PatchNames.Acoustic_Grand)
{
this.instrument = instrument;
int count = seqs.Length;
note_map = new Dictionary<Note, int>();
int pitch = 0;
int j = 0;
pitches = new int[seqs.Length][];
foreach (MelodySequence m in seqs)
{
Note[] song = m.ToArray();
pitches[j] = new int[m.Length];
for (int i = 0; i < song.Length; i++)
{
if (note_map.ContainsKey(song[i]))
{
}
else
{
note_map[song[i]] = pitch++;
}
pitches[j][i] = note_map[song[i]];
}
j++;
if (m.Length > max_length)
max_length = m.Length;
}
hmm = new HiddenMarkovModel(3, pitch+1);
var teacher = new BaumWelchLearning(hmm);
teacher.Iterations = 10000;
teacher.Run(pitches);
Console.WriteLine("Done training");
}
public void PredictTest3()
{
// We will try to create a Hidden Markov Model which
// can recognize (and predict) the following sequences:
int[][] sequences =
{
new[] { 1, 2, 3, 4, 5 },
new[] { 1, 2, 4, 3, 5 },
new[] { 1, 2, 5 },
};
// Creates a new left-to-right (forward) Hidden Markov Model
// with 4 states for an output alphabet of six characters.
HiddenMarkovModel hmm = new HiddenMarkovModel(new Forward(4), 6);
// Try to fit the model to the data until the difference in
// the average log-likelihood changes only by as little as 0.0001
BaumWelchLearning teacher = new BaumWelchLearning(hmm)
{
Tolerance = 0.0001,
Iterations = 0
};
// Run the learning algorithm on the model
double logLikelihood = teacher.Run(sequences);
// Now, we will try to predict the next
// observations after a base sequence
int[] input = { 1, 2 }; // base sequence for prediction
double[] logLikelihoods;
// Predict the next observation in sequence
int prediction = hmm.Predict(input, out logLikelihoods);
var probs = Matrix.Exp(logLikelihoods);
// At this point, prediction probabilities
// should be equilibrated around 3, 4 and 5
Assert.AreEqual(probs.Length, 6);
Assert.AreEqual(probs[0], 0.00, 0.01);
Assert.AreEqual(probs[1], 0.00, 0.01);
Assert.AreEqual(probs[2], 0.00, 0.01);
Assert.AreEqual(probs[3], 0.33, 0.05);
Assert.AreEqual(probs[4], 0.33, 0.05);
Assert.AreEqual(probs[5], 0.33, 0.05);
double[][] probabilities2;
// Predict the next 2 observation2 in sequence
int[] prediction2 = hmm.Predict(input, 2, out probabilities2);
Assert.AreEqual(probabilities2.Length, 2);
Assert.AreEqual(probabilities2[0].Length, 6);
Assert.AreEqual(probabilities2[1].Length, 6);
Assert.IsTrue(probabilities2[0].IsEqual(logLikelihoods));
}
public void PredictTest()
{
int[][] sequences = new int[][]
{
new int[] { 0, 3, 1, 2 },
};
HiddenMarkovModel hmm = new HiddenMarkovModel(new Forward(4), 4);
var teacher = new BaumWelchLearning(hmm) { Tolerance = 1e-10, Iterations = 0 };
double ll = teacher.Run(sequences);
double l11, l12, l13, l14;
int p1 = hmm.Predict(new int[] { 0 }, 1, out l11)[0];
int p2 = hmm.Predict(new int[] { 0, 3 }, 1, out l12)[0];
int p3 = hmm.Predict(new int[] { 0, 3, 1 }, 1, out l13)[0];
int p4 = hmm.Predict(new int[] { 0, 3, 1, 2 }, 1, out l14)[0];
Assert.AreEqual(3, p1);
Assert.AreEqual(1, p2);
Assert.AreEqual(2, p3);
Assert.AreEqual(2, p4);
double l21 = hmm.Evaluate(new int[] { 0, 3 });
double l22 = hmm.Evaluate(new int[] { 0, 3, 1 });
double l23 = hmm.Evaluate(new int[] { 0, 3, 1, 2 });
double l24 = hmm.Evaluate(new int[] { 0, 3, 1, 2, 2 });
Assert.AreEqual(l11, l21, 1e-10);
Assert.AreEqual(l12, l22, 1e-10);
Assert.AreEqual(l13, l23, 1e-10);
Assert.AreEqual(l14, l24, 1e-10);
Assert.IsFalse(double.IsNaN(l11));
Assert.IsFalse(double.IsNaN(l12));
Assert.IsFalse(double.IsNaN(l13));
Assert.IsFalse(double.IsNaN(l14));
Assert.IsFalse(double.IsNaN(l21));
Assert.IsFalse(double.IsNaN(l22));
Assert.IsFalse(double.IsNaN(l23));
Assert.IsFalse(double.IsNaN(l24));
double ln1;
int[] pn = hmm.Predict(new int[] { 0 }, 4, out ln1);
Assert.AreEqual(4, pn.Length);
Assert.AreEqual(3, pn[0]);
Assert.AreEqual(1, pn[1]);
Assert.AreEqual(2, pn[2]);
Assert.AreEqual(2, pn[3]);
double ln2 = hmm.Evaluate(new int[] { 0, 3, 1, 2, 2 });
Assert.AreEqual(ln1, ln2, 1e-10);
}
public void LearnTest3()
{
// We will try to create a Hidden Markov Model which
// can detect if a given sequence starts with a zero
// and has any number of ones after that.
int[][] sequences = new int[][]
{
new int[] { 0,1,1,1,1,0,1,1,1,1 },
new int[] { 0,1,1,1,0,1,1,1,1,1 },
new int[] { 0,1,1,1,1,1,1,1,1,1 },
new int[] { 0,1,1,1,1,1 },
new int[] { 0,1,1,1,1,1,1 },
new int[] { 0,1,1,1,1,1,1,1,1,1 },
new int[] { 0,1,1,1,1,1,1,1,1,1 },
};
// Creates a new Hidden Markov Model with 3 states for
// an output alphabet of two characters (zero and one)
HiddenMarkovModel hmm = new HiddenMarkovModel(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(hmm) { Tolerance = 0.0001, Iterations = 0 };
double ll = teacher.Run(sequences);
// 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
// Sequences which do not start with zero have much lesser probability.
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
// 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; 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(0.95151126952069587, 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);
}
public void LearnTest4()
{
int[][] sequences = new int[][]
{
new int[] { 0, 3, 1 },
new int[] { 0, 2 },
new int[] { 1, 0, 3 },
new int[] { 3, 4 },
new int[] { 0, 1, 3, 5 },
new int[] { 0, 3, 4 },
new int[] { 0, 1, 3, 5 },
new int[] { 0, 1, 3, 5 },
new int[] { 0, 1, 3, 4, 5 },
};
HiddenMarkovModel hmm = new HiddenMarkovModel(3, 6);
var teacher = new BaumWelchLearning(hmm) { Iterations = 100, Tolerance = 0 };
double ll = teacher.Run(sequences);
double l0; hmm.Decode(sequences[0], out l0);
double l1; hmm.Decode(sequences[1], out l1);
double l2; hmm.Decode(sequences[2], out l2);
double pl = System.Math.Exp(ll);
double p0 = System.Math.Exp(l0);
double p1 = System.Math.Exp(l1);
double p2 = System.Math.Exp(l2);
Assert.AreEqual(0.49788370872923726, pl, 1e-10);
Assert.AreEqual(0.014012065043262294, p0, 1e-10);
Assert.AreEqual(0.016930905415294094, p1, 1e-10);
Assert.AreEqual(0.001936595918966074, p2, 1e-10);
}
public void LearnTest9()
{
// Include this example in the documentattion
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>(new Forward(5), density);
var learning = new BaumWelchLearning<MultivariateNormalDistribution>(model)
{
Tolerance = 0.0001,
Iterations = 0,
FittingOptions = new NormalOptions() { Regularization = 0.0001 }
};
double logLikelihood = learning.Run(observations);
Assert.IsFalse(Double.IsNaN(logLikelihood));
foreach (double value in model.Transitions)
Assert.IsFalse(Double.IsNaN(value));
foreach (double value in model.Probabilities)
Assert.IsFalse(Double.IsNaN(value));
}
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>(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>(model)
{
Tolerance = 0.0001,
Iterations = 0,
};
// Fit the model
double logLikelihood = teacher.Run(sequences);
// 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(0, 1, 0, 1, 0, 1));
Assert.AreEqual(1.1341500279562791, 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.IsFalse(double.IsNaN(logLikelihood));
Assert.IsFalse(double.IsNaN(a1));
Assert.IsFalse(double.IsNaN(a2));
Assert.IsFalse(double.IsNaN(a3));
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.Transitions.GetLength(0));
Assert.AreEqual(2, model.Transitions.GetLength(1));
var A = Matrix.Exp(model.Transitions);
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());
}
private TRADETYPE PredictNextTrade()
{
var res = TRADETYPE.WINNING;
if (_tradeReturns.Count == 4) {
HiddenMarkovModel hmm = new HiddenMarkovModel(states: 3, symbols: 3);
int[] observationSequence = GetSequence (_tradeReturns);
BaumWelchLearning teacher = new BaumWelchLearning(hmm);
// and call its Run method to start learning
double error = teacher.Run(observationSequence);
int[] predict = hmm.Predict (observationSequence, 1);
if (predict [0] == 0) {
res = TRADETYPE.LOSING;
} else if (predict [0] == 1) {
res = TRADETYPE.NEUTRAL;
} else if (predict [0] == 2) {
res = TRADETYPE.WINNING;
}
}
return res;
}
private static HiddenMarkovModel<MultivariateNormalDistribution> createModel()
{
double[][][] sequences =
{
new double[][]
{
new double[] { 1, 2 },
new double[] { 6, 7 },
new double[] { 2, 3 },
},
new double[][]
{
new double[] { 2, 2 },
new double[] { 9, 8 },
new double[] { 1, 0 },
},
new double[][]
{
new double[] { 1, 3 },
new double[] { 8, 9 },
new double[] { 3, 3 },
},
};
var density = new MultivariateNormalDistribution(dimension: 2);
var model = new HiddenMarkovModel<MultivariateNormalDistribution>(new Forward(2), density);
var teacher = new BaumWelchLearning<MultivariateNormalDistribution>(model)
{
Tolerance = 0.0001,
Iterations = 0,
};
double logLikelihood = teacher.Run(sequences);
return model;
}
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>>(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>>(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
double logLikelihood = teacher.Run(sequences);
// 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));
}
static void runArbitraryDensityHiddenMarkovModelLearningExample()
{
// 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[][] observationSequences = 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 },
};
// Creates a continuous hidden Markov Model with two states organized in a ergoric topology
// and an underlying univariate Normal distribution as probability density.
var hmm = new HiddenMarkovModel<NormalDistribution>(topology: new Ergodic(states: 2), emissions: new NormalDistribution());
// 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 trainer = new BaumWelchLearning<NormalDistribution>(hmm)
{
Tolerance = 0.0001,
Iterations = 0,
};
// Fit the model.
double averageLogLikelihood = trainer.Run(observationSequences);
Console.WriteLine("average log-likelihood for the observations = {0}", averageLogLikelihood);
// The log-probability of the sequences learned.
double logLik1 = hmm.Evaluate(new[] { 0.1, 5.2, 0.3, 6.7, 0.1, 6.0 }); // -0.12799388666109757.
double logLik2 = hmm.Evaluate(new[] { 0.2, 6.2, 0.3, 6.3, 0.1, 5.0 }); // 0.01171157434400194.
// The log-probability of an unrelated sequence.
double logLik3 = hmm.Evaluate(new[] { 1.1, 2.2, 1.3, 3.2, 4.2, 1.0 }); // -298.7465244473417.
// Transform the log-probabilities to actual probabilities.
Console.WriteLine("probability = {0}", Math.Exp(logLik1)); // 0.879.
Console.WriteLine("probability = {0}", Math.Exp(logLik2)); // 1.011.
Console.WriteLine("probability = {0}", Math.Exp(logLik3)); // 0.000.
// Ask the model to decode one of the sequences.
// The state variable will contain: { 0, 1, 0, 1, 0, 1 }.
double logLikelihood = 0.0;
int[] path = hmm.Decode(new[] { 0.1, 5.2, 0.3, 6.7, 0.1, 6.0 }, out logLikelihood);
Console.Write("log-likelihood = {0}, Viterbi path = [", logLikelihood);
foreach (int state in path)
Console.Write("{0},", state);
Console.WriteLine("]");
}
static void runDiscreteDensityHiddenMarkovModelLearningExample()
{
int[][] observationSequences =
{
new[] { 0, 1, 2, 3 },
new[] { 0, 0, 0, 1, 1, 2, 2, 3, 3 },
new[] { 0, 0, 1, 2, 2, 2, 3, 3 },
new[] { 0, 1, 2, 3, 3, 3, 3 },
};
{
// Create a hidden Markov model with arbitrary probabilities.
HiddenMarkovModel hmm = new HiddenMarkovModel(states: 4, symbols: 4);
// Create a Baum-Welch learning algorithm to teach it.
BaumWelchLearning trainer = new BaumWelchLearning(hmm);
// Call its Run method to start learning.
double averageLogLikelihood = trainer.Run(observationSequences);
Console.WriteLine("average log-likelihood for the observations = {0}", averageLogLikelihood);
// Check the probability of some sequences.
double logLik1 = hmm.Evaluate(new[] { 0, 1, 2, 3 }); // 0.013294354967987107.
Console.WriteLine("probability = {0}", Math.Exp(logLik1));
double logLik2 = hmm.Evaluate(new[] { 0, 0, 1, 2, 2, 3 }); // 0.002261813011419950.
Console.WriteLine("probability = {0}", Math.Exp(logLik2));
double logLik3 = hmm.Evaluate(new[] { 0, 0, 1, 2, 3, 3 }); // 0.002908045300397080.
Console.WriteLine("probability = {0}", Math.Exp(logLik3));
// Violate the form of the training set.
double logLik4 = hmm.Evaluate(new[] { 3, 2, 1, 0 }); // 0.000000000000000000.
Console.WriteLine("probability = {0}", Math.Exp(logLik4));
double logLik5 = hmm.Evaluate(new[] { 0, 0, 1, 3, 1, 1 }); // 0.000000000113151816.
Console.WriteLine("probability = {0}", Math.Exp(logLik5));
}
{
// Create a hidden Markov model with arbitrary probabilities.
var hmm = new HiddenMarkovModel<GeneralDiscreteDistribution>(states: 4, emissions: new GeneralDiscreteDistribution(symbols: 4));
// Create a Baum-Welch learning algorithm to teach it
// until the difference in the average log-likelihood changes only by as little as 0.0001
// and the number of iterations is less than 1000.
var trainer = new BaumWelchLearning<GeneralDiscreteDistribution>(hmm)
{
Tolerance = 0.0001,
Iterations = 1000,
};
// Call its Run method to start learning.
double averageLogLikelihood = trainer.Run(observationSequences);
Console.WriteLine("average log-likelihood for the observations = {0}", averageLogLikelihood);
// Check the probability of some sequences.
double logLik1 = hmm.Evaluate(new[] { 0, 1, 2, 3 }); // 0.013294354967987107.
Console.WriteLine("probability = {0}", Math.Exp(logLik1));
double logLik2 = hmm.Evaluate(new[] { 0, 0, 1, 2, 2, 3 }); // 0.002261813011419950.
Console.WriteLine("probability = {0}", Math.Exp(logLik2));
double logLik3 = hmm.Evaluate(new[] { 0, 0, 1, 2, 3, 3 }); // 0.002908045300397080.
Console.WriteLine("probability = {0}", Math.Exp(logLik3));
// Violate the form of the training set.
double logLik4 = hmm.Evaluate(new[] { 3, 2, 1, 0 }); // 0.000000000000000000.
Console.WriteLine("probability = {0}", Math.Exp(logLik4));
double logLik5 = hmm.Evaluate(new[] { 0, 0, 1, 3, 1, 1 }); // 0.000000000113151816.
Console.WriteLine("probability = {0}", Math.Exp(logLik5));
}
}
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 = HiddenMarkovModel.CreateGeneric(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>(hmm) { Tolerance = 0.0001 };
double ll = teacher.Run(sequences);
// Calculate the probability that the given
// sequences originated from the model
double l1; hmm.Decode(new double[] { 0, 1 }, out l1); // 0.4999
double l2; hmm.Decode(new double[] { 0, 1, 1, 1 }, out l2); // 0.1145
double l3; hmm.Decode(new double[] { 1, 1 }, out l3); // 0.0000
double l4; hmm.Decode(new double[] { 1, 0, 0, 0 }, out l4); // 0.0000
double l5; hmm.Decode(new double[] { 0, 1, 0, 1, 1, 1, 1, 1, 1 }, out l5); // 0.0002
double l6; hmm.Decode(new double[] { 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(0.95151018769760853, 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.Dimension);
}
public void LearnTest6()
{
// Continuous Markov Models can operate using any
// probability distribution, including discrete ones.
// In the follwing 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.
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 },
};
// Create a new Hidden Markov Model with 3 states and
// a generic discrete distribution with two symbols
var hmm = HiddenMarkovModel.CreateGeneric(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>(hmm)
{
Tolerance = 0.0001,
Iterations = 0
};
double ll = Math.Exp(teacher.Run(sequences));
// Calculate the probability that the given
// sequences originated from the model
double l1 = Math.Exp(hmm.Evaluate(new double[] { 0, 1 })); // 0.999
double l2 = Math.Exp(hmm.Evaluate(new double[] { 0, 1, 1, 1 })); // 0.916
// Sequences which do not start with zero have much lesser probability.
double l3 = Math.Exp(hmm.Evaluate(new double[] { 1, 1 })); // 0.000
double l4 = Math.Exp(hmm.Evaluate(new double[] { 1, 0, 0, 0 })); // 0.000
// Sequences which contains few errors have higher probabability
// 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 double[] { 0, 1, 0, 1, 1, 1, 1, 1, 1 })); // 0.034
double l6 = Math.Exp(hmm.Evaluate(new double[] { 0, 1, 1, 1, 1, 1, 1, 0, 1 })); // 0.034
Assert.AreEqual(0.95151018769760853, 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 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>(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>(model)
{
Tolerance = 0.0001,
Iterations = 0,
};
// Fit the model
double logLikelihood = teacher.Run(sequences);
// 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);
Assert.AreEqual(2.1031924118199194E-89, a3);
}
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>(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>(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
double likelihood = teacher.Run(sequences);
// See the probability of the sequences learned
double a1 = model.Evaluate(new double[] { 1, 2, 1, 2, 1, 2, 1, 2, 1 }); // exp(a1) = inf
double a2 = model.Evaluate(new double[] { 1, 2, 1, 2, 1 }); // exp(a2) = inf
// 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(302.59496915947972, a1);
Assert.AreEqual(168.26234890650207, 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 = Matrix.Exp(model.Transitions);
Assert.AreEqual(2, A.GetLength(0));
Assert.AreEqual(2, A.GetLength(1));
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 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 specifing 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>>(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>>(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
double logLikelihood = teacher.Run(sequences);
// 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.AreEqual(11729312967893.566, a1);
Assert.AreEqual(0.0, a3);
Assert.IsFalse(Double.IsNaN(a1));
Assert.IsFalse(Double.IsNaN(a3));
}
public static double BaumWelchLearning(double[][] data)
{
// Specify a initial normal distribution for the samples.
NormalDistribution 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>(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>(model)
{
Tolerance = 0.001,
Iterations = 0,
};
// Fit the model
double likelihood = teacher.Run(data);
// See the log-probability of the sequences learned
double a1 = model.Evaluate(new[] { 0.999999999999928, 0 , 0.999999999999988 , 0 , 0.999999999999988 }); // -0.12799388666109757
return a1;
}
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 },
};
// 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>(new Ergodic(2), density);
// Configure the learning algorithms to train the sequence classifier
var teacher = new BaumWelchLearning<MultivariateNormalDistribution>(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
double logLikelihood = teacher.Run(sequences);
double likelihood = Math.Exp(logLikelihood);
Assert.AreEqual(47.434837528491286, 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>(new Ergodic(2), density);
teacher = new BaumWelchLearning<MultivariateNormalDistribution>(model) { Tolerance = 0.0001, Iterations = 0, };
Assert.IsNull(teacher.FittingOptions);
try { teacher.Run(sequences); }
catch { thrown = true; }
Assert.IsTrue(thrown);
thrown = false;
density = new Accord.Statistics.Distributions.Multivariate.MultivariateNormalDistribution(1);
model = new HiddenMarkovModel<MultivariateNormalDistribution>(new Ergodic(2), density);
teacher = new BaumWelchLearning<MultivariateNormalDistribution>(model)
{
Tolerance = 0.0001,
Iterations = 0,
FittingOptions = new NormalOptions() { Regularization = 0 }
};
Assert.IsNotNull(teacher.FittingOptions);
try { teacher.Run(sequences); }
catch { thrown = true; }
Assert.IsTrue(thrown);
}
public void LearnTest()
{
HiddenMarkovModel hmm = new HiddenMarkovModel(2, 3);
int[] observation = new int[]
{
0,1,1,2,2,1,1,1,0,0,0,0,0,0,0,0,2,2,0,0,1,1,1,2,0,0,
0,0,0,0,1,2,1,1,1,0,2,0,1,0,2,2,2,0,0,2,0,1,2,2,0,1,
1,2,2,2,0,0,1,1,2,2,0,0,2,2,0,0,1,0,1,2,0,0,0,0,2,0,
2,0,1,1,0,1,0,0,0,1,2,1,1,2,0,2,0,2,2,0,0,1
};
int[] observation2 = new int[]
{
0,1,0,0,2,1,1,0,0,2,1,0,1,1,2,0,1,1,1,0,0,2,0,0,2,1,
1,1,2,0,2,2,1,0,1,2,0,2,1,0,2,1,1,2,0,1,0,1,1,0,1,2,
1,0,2,0,1,0,1,2,0,0,2,0,2,0,0,1,0,0,0,0,1,1,2,2,1,2,
0,1,1,1,2,2,1,1,1,2,2,0,2,1,1,2,0,0,1,1,1,1,1,1,1,0,
0,1,0,1,0,1,0,0,2,0,1,0,2,0,0,0,0,1,1,1,1,1,1,0,2,0,
2,2,1,2,1,2,1,0,2,1,1,2,1,2,1,0,0,2,0,0,2,2,2,0,0,1,
0,1,0,1,0,1,0,0,0,0,0,1,1,1,2,0,0,0,0,0,0,2,2,0,0,0,
0,0,1,0,2,2,2,2,2,1,2,0,1,0,1,2,2,1,0,1,1,2,1,1,1,2,
2,2,0,1,1,1,1,2,1,0,1,0,1,1,0,2,2,2,1,1,1,1,0,2,1,0,
2,1,1,1,2,0,0,1,1,1,1,2,1,1,2,0,0,0,0,0,2,2,2,0,1,1,
1,0,1,0,0,0,0,2,2,2,2,0,1,1,0,1,2,1,2,1,1,0,0,0,0,2,
2,1,1,0,1,0,0,0,0,1,0,0,0,2,0,0,0,2,1,2,2,0,0,0,0,0,
0,2,0,0,2,0,0,0,2,0,1,1,2,2,1,2,1,2,0,0,0,0,2,0,2,0,
1,0,0,2,2,1,2,1,2,2,0,1,1,1,0,0,1,1,1,2,1,0,0,2,0,0,
0,0,1,2,0,0,1,2,0,0,0,2,1,1,1,1,1,2,2,0,0,1,1,1,0,0,
2,0,1,1,0,2,2,0,0,0,1,1,1,1,1,1,2,1,1,0,2,0,0,0,1,1,
1,2,1,0,0,0,1,1,0,1,1,1,0,0,0,1,1,1,2,2,2,0,2,0,2,1,
2,1,0,2,1,2,1,0,0,2,1,1,1,1,0,0,0,1,2,0,2,2,1,2,1,1,
1,0,1,0,0,0,0,2,0,1,1,1,0,2,0,1,0,2,1,2,2,0,2,1,0,0,
2,1,2,2,0,2,1,2,1,2,0,0,0,1,2,1,2,2,1,0,0,0,1,1,2,0,
2,1,0,0,0,1,0,0,1,2,0,0,1,2,2,2,0,1,2,0,1,0,1,0,2,2,
0,2,0,1,1,0,1,1,1,2,2,0,0,0,0,0,1,1,0,0,2,0,0,1,0,0,
1,0,2,1,1,1,1,1,2,0,0,2,0,1,2,0,1,1,1,2,0,0,0,1,2,0,
0,0,2,2,1,1,1,0,1,1,0,2,2,0,1,2,2,1,1,1,2,1,0,2,0,0,
1,1,1,1,1,1,2,1,2,1,0,1,0,2,2,0,1,2,1,1,2,1,0,1,2,1
};
var teacher = new BaumWelchLearning(hmm)
{
Iterations = 650,
Tolerance = 0
};
double ll = teacher.Run(observation);
double[] pi = { 1.0, 0.0 };
double[,] A =
{
{ 0.7, 0.3 },
{ 0.5, 0.5 }
};
double[,] B =
{
{ 0.6, 0.1, 0.3 },
{ 0.1, 0.7, 0.2 }
};
var hmmA = Matrix.Exp(hmm.Transitions);
var hmmB = Matrix.Exp(hmm.Emissions);
var hmmP = Matrix.Exp(hmm.Probabilities);
Assert.IsTrue(Matrix.IsEqual(A, hmmA, 0.1));
Assert.IsTrue(Matrix.IsEqual(B, hmmB, 0.1));
Assert.IsTrue(Matrix.IsEqual(pi, hmmP));
}
public void PredictTest()
{
double[][] sequences = new double[][]
{
new double[] { 0, 3, 1, 2 },
};
var hmm = HiddenMarkovModel.CreateGeneric(new Forward(4), 4);
var teacher = new BaumWelchLearning<GeneralDiscreteDistribution>(hmm)
{
Tolerance = 1e-10,
Iterations = 0
};
double ll = teacher.Run(sequences);
double l11, l12, l13, l14;
double p1 = hmm.Predict(new double[] { 0 }, out l11);
double p2 = hmm.Predict(new double[] { 0, 3 }, out l12);
double p3 = hmm.Predict(new double[] { 0, 3, 1 }, out l13);
double p4 = hmm.Predict(new double[] { 0, 3, 1, 2 }, out l14);
Assert.AreEqual(3, p1);
Assert.AreEqual(1, p2);
Assert.AreEqual(2, p3);
Assert.AreEqual(2, p4);
double l21 = hmm.Evaluate(new double[] { 0, 3 });
double l22 = hmm.Evaluate(new double[] { 0, 3, 1 });
double l23 = hmm.Evaluate(new double[] { 0, 3, 1, 2 });
double l24 = hmm.Evaluate(new double[] { 0, 3, 1, 2, 2 });
Assert.AreEqual(l11, l21, 1e-10);
Assert.AreEqual(l12, l22, 1e-10);
Assert.AreEqual(l13, l23, 1e-10);
Assert.AreEqual(l14, l24, 1e-2);
Assert.IsFalse(double.IsNaN(l11));
Assert.IsFalse(double.IsNaN(l12));
Assert.IsFalse(double.IsNaN(l13));
Assert.IsFalse(double.IsNaN(l14));
Assert.IsFalse(double.IsNaN(l21));
Assert.IsFalse(double.IsNaN(l22));
Assert.IsFalse(double.IsNaN(l23));
Assert.IsFalse(double.IsNaN(l24));
double ln1;
double[] pn = hmm.Predict(new double[] { 0 }, 4, out ln1);
Assert.AreEqual(4, pn.Length);
Assert.AreEqual(3, pn[0]);
Assert.AreEqual(1, pn[1]);
Assert.AreEqual(2, pn[2]);
Assert.AreEqual(2, pn[3]);
double ln2 = hmm.Evaluate(new double[] { 0, 3, 1, 2, 2 });
Assert.AreEqual(ln1, ln2, 1e-2);
Assert.IsFalse(double.IsNaN(ln1));
Assert.IsFalse(double.IsNaN(ln2));
// Get the mixture distribution defining next state likelihoods
Mixture<GeneralDiscreteDistribution> mixture = null;
double ml11;
double mp1 = hmm.Predict(new double[] { 0 }, out ml11, out mixture);
Assert.AreEqual(l11, ml11);
Assert.AreEqual(p1, mp1);
Assert.IsNotNull(mixture);
Assert.AreEqual(4, mixture.Coefficients.Length);
Assert.AreEqual(4, mixture.Components.Length);
Assert.AreEqual(0, mixture.Coefficients[0], 1e-10);
Assert.AreEqual(1, mixture.Coefficients[1], 1e-10);
Assert.AreEqual(0, mixture.Coefficients[2], 1e-10);
Assert.AreEqual(0, mixture.Coefficients[3], 1e-10);
for (int i = 0; i < mixture.Coefficients.Length; i++)
Assert.IsFalse(double.IsNaN(mixture.Coefficients[i]));
}
public void LearnTest6()
{
// We will try to create a Hidden Markov Model which
// can detect if a given sequence starts with a zero
// and has any number of ones after that.
int[][] sequences = new int[][]
{
new int[] { 0,1,1,1,1,0,1,1,1,1 },
new int[] { 0,1,1,1,0,1,1,1,1,1 },
new int[] { 0,1,1,1,1,1,1,1,1,1 },
new int[] { 0,1,1,1,1,1 },
new int[] { 0,1,1,1,1,1,1 },
new int[] { 0,1,1,1,1,1,1,1,1,1 },
new int[] { 0,1,1,1,1,1,1,1,1,1 },
};
// Creates a new Hidden Markov Model with 3 states for
// an output alphabet of two characters (zero and one)
HiddenMarkovModel hmm = new HiddenMarkovModel(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(hmm) { Tolerance = 0.0001, Iterations = 0 };
double ll = teacher.Run(sequences);
// Calculate the probability that the given
// sequences originated from the model
double l1 = hmm.Evaluate(new int[] { 0, 1 }); // 0.999
double l2 = hmm.Evaluate(new int[] { 0, 1, 1, 1 }); // 0.916
// Sequences which do not start with zero have much lesser probability.
double l3 = hmm.Evaluate(new int[] { 1, 1 }); // 0.000
double l4 = 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 = hmm.Evaluate(new int[] { 0, 1, 0, 1, 1, 1, 1, 1, 1 }); // 0.034
double l6 = hmm.Evaluate(new int[] { 0, 1, 1, 1, 1, 1, 1, 0, 1 }); // 0.034
double pl = System.Math.Exp(ll);
double p1 = System.Math.Exp(l1);
double p2 = System.Math.Exp(l2);
double p3 = System.Math.Exp(l3);
double p4 = System.Math.Exp(l4);
double p5 = System.Math.Exp(l5);
double p6 = System.Math.Exp(l6);
Assert.AreEqual(0.95151126952069587, pl, 1e-6);
Assert.AreEqual(0.99996863060890995, p1, 1e-6);
Assert.AreEqual(0.91667240076011669, p2, 1e-6);
Assert.AreEqual(0.00002335133758386, p3, 1e-6);
Assert.AreEqual(0.00000000000000012, p4, 1e-6);
Assert.AreEqual(0.034237231443226858, p5, 1e-6);
Assert.AreEqual(0.034237195920532461, p6, 1e-6);
Assert.IsTrue(l1 > l3 && l1 > l4);
Assert.IsTrue(l2 > l3 && l2 > l4);
}
public void PredictTest2()
{
// 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.
NormalDistribution 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>(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>(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
double likelihood = teacher.Run(sequences);
double a1 = model.Predict(new double[] { 1, 2, 1 });
double a2 = model.Predict(new double[] { 1, 2, 1, 2 });
Assert.AreEqual(2, a1, 1e-10);
Assert.AreEqual(1, a2, 1e-10);
Assert.IsFalse(Double.IsNaN(a1));
Assert.IsFalse(Double.IsNaN(a2));
double p1, p2;
Mixture<NormalDistribution> d1, d2;
double b1 = model.Predict(new double[] { 1, 2, 1 }, out p1, out d1);
double b2 = model.Predict(new double[] { 1, 2, 1, 2 }, out p2, out d2);
Assert.AreEqual(2, b1, 1e-10);
Assert.AreEqual(1, b2, 1e-10);
Assert.IsFalse(Double.IsNaN(b1));
Assert.IsFalse(Double.IsNaN(b2));
Assert.AreEqual(0, d1.Coefficients[0]);
Assert.AreEqual(1, d1.Coefficients[1]);
Assert.AreEqual(1, d2.Coefficients[0]);
Assert.AreEqual(0, d2.Coefficients[1]);
}
public void PredictTest2()
{
// We will try to create a Hidden Markov Model which
// can recognize (and predict) the following sequences:
int[][] sequences =
{
new[] { 1, 2, 3, 4, 5 },
new[] { 1, 2, 3, 3, 5 },
new[] { 1, 2, 3 },
};
// Creates a new left-to-right (forward) Hidden Markov Model
// with 4 states for an output alphabet of six characters.
HiddenMarkovModel hmm = new HiddenMarkovModel(new Forward(4), 6);
// Try to fit the model to the data until the difference in
// the average log-likelihood changes only by as little as 0.0001
BaumWelchLearning teacher = new BaumWelchLearning(hmm)
{
Tolerance = 0.0001,
Iterations = 0
};
// Run the learning algorithm on the model
double logLikelihood = teacher.Run(sequences);
// Now, we will try to predict the next
// observations after a base sequence
int length = 1; // number of observations to predict
int[] input = { 1, 2 }; // base sequence for prediction
// Predict the next 1 observation in sequence
int[] prediction = hmm.Predict(input, length);
// At this point, prediction should be int[] { 3 }
Assert.AreEqual(prediction.Length, 1);
Assert.AreEqual(prediction[0], 3);
}
public void PredictTest3()
{
// We will try to create a Hidden Markov Model which
// can recognize (and predict) the following sequences:
double[][] sequences =
{
new double[] { 1, 2, 3, 4, 5 },
new double[] { 1, 2, 4, 3, 5 },
new double[] { 1, 2, 5 },
};
// Creates a new left-to-right (forward) Hidden Markov Model
// with 4 states for an output alphabet of six characters.
var hmm = HiddenMarkovModel.CreateGeneric(new Forward(4), 6);
// 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>(hmm)
{
Tolerance = 0.0001,
Iterations = 0
};
// Run the learning algorithm on the model
double logLikelihood = teacher.Run(sequences);
// Now, we will try to predict the next
// observations after a base sequence
double[] input = { 1, 2 }; // base sequence for prediction
// Predict the next observation in sequence
Mixture<GeneralDiscreteDistribution> mixture = null;
double prediction = hmm.Predict(input, out mixture);
// At this point, prediction probabilities
// should be equilibrated around 3, 4 and 5
Assert.AreEqual(4, mixture.Mean, 0.1);
Assert.IsFalse(double.IsNaN(mixture.Mean));
double[] input2 = { 1 };
// The only possible value after 1 must be 2.
prediction = hmm.Predict(input2, out mixture);
Assert.AreEqual(2, prediction);
}
public void GenerateTest2()
{
Accord.Math.Tools.SetupGenerator(42);
// Consider some phrases:
//
string[][] phrases =
{
new[] { "those", "are", "sample", "words", "from", "a", "dictionary" },
new[] { "those", "are", "sample", "words" },
new[] { "sample", "words", "are", "words" },
new[] { "those", "words" },
new[] { "those", "are", "words" },
new[] { "words", "from", "a", "dictionary" },
new[] { "those", "are", "words", "from", "a", "dictionary" }
};
// Let's begin by transforming them to sequence of
// integer labels using a codification codebook:
var codebook = new Codification("Words", phrases);
// Now we can create the training data for the models:
int[][] sequence = codebook.Translate("Words", phrases);
// To create the models, we will specify a forward topology,
// as the sequences have definite start and ending points.
//
var topology = new Forward(states: 4);
int symbols = codebook["Words"].Symbols; // We have 7 different words
// Create the hidden Markov model
HiddenMarkovModel hmm = new HiddenMarkovModel(topology, symbols);
// Create the learning algorithm
BaumWelchLearning teacher = new BaumWelchLearning(hmm);
// Teach the model about the phrases
double error = teacher.Run(sequence);
// Now, we can ask the model to generate new samples
// from the word distributions it has just learned:
//
int[] sample = hmm.Generate(3);
// And the result will be: "those", "are", "words".
string[] result = codebook.Translate("Words", sample);
Assert.AreEqual("those", result[0]);
Assert.AreEqual("are", result[1]);
Assert.AreEqual("words", result[2]);
}
public void LearnIntegersTest5()
{
int[][][] sequences = new int[][][]
{
new int[][] { new int[] { 0 }, new int[] { 3 }, new int[] { 1} },
new int[][] { new int[] { 0 }, new int[] { 2 } },
new int[][] { new int[] { 1 }, new int[] { 0 }, new int[] { 3 } },
new int[][] { new int[] { 3 }, new int[] { 4 } },
new int[][] { new int[] { 0 }, new int[] { 1 }, new int[] { 3 }, new int[] { 5 } },
new int[][] { new int[] { 0 }, new int[] { 3 }, new int[] { 4 } },
new int[][] { new int[] { 0 }, new int[] { 1 }, new int[] { 3 }, new int[] { 5 } },
new int[][] { new int[] { 0 }, new int[] { 1 }, new int[] { 3 }, new int[] { 5 } },
new int[][] { new int[] { 0 }, new int[] { 1 }, new int[] { 3 }, new int[] { 4 }, new int[] { 5 } },
};
var hmm = HiddenMarkovModel.CreateGeneric(3, 6);
var teacher = new BaumWelchLearning<GeneralDiscreteDistribution>(hmm) { Iterations = 100, Tolerance = 0 };
double ll = teacher.Run(sequences);
double l0; hmm.Decode(sequences[0], out l0);
double l1; hmm.Decode(sequences[1], out l1);
double l2; hmm.Decode(sequences[2], out l2);
double pl = System.Math.Exp(ll);
double p0 = System.Math.Exp(l0);
double p1 = System.Math.Exp(l1);
double p2 = System.Math.Exp(l2);
Assert.AreEqual(0.49788370872923726, pl, 1e-6);
Assert.AreEqual(0.014012065043262257, p0, 1e-6);
Assert.AreEqual(0.016930905415294066, p1, 1e-6);
Assert.AreEqual(0.0019365959189660638, p2, 1e-6);
Assert.AreEqual(1, hmm.Dimension);
int[][] sequences2 = new int[][]
{
new int[] { 0, 3, 1 },
new int[] { 0, 2 },
new int[] { 1, 0, 3 },
new int[] { 3, 4 },
new int[] { 0, 1, 3, 5 },
new int[] { 0, 3, 4 },
new int[] { 0, 1, 3, 5 },
new int[] { 0, 1, 3, 5 },
new int[] { 0, 1, 3, 4, 5 },
};
hmm = HiddenMarkovModel.CreateGeneric(3, 6);
teacher = new BaumWelchLearning<GeneralDiscreteDistribution>(hmm) { Iterations = 100 };
double ll2 = teacher.Run(sequences2);
double l02; hmm.Decode(sequences2[0], out l02);
double l12; hmm.Decode(sequences2[1], out l12);
double l22; hmm.Decode(sequences2[2], out l22);
Assert.AreEqual(ll, ll2);
Assert.AreEqual(l0, l02);
Assert.AreEqual(l1, l12);
Assert.AreEqual(l2, l22);
Assert.AreEqual(1, hmm.Dimension);
}
