public static void ViterbiLearning() { 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(state_count: 3, symbol_count: 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 ViterbiLearning(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 Console.WriteLine("l1: {0}", System.Math.Exp(l1)); Console.WriteLine("l2: {0}", System.Math.Exp(l2)); // 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 Console.WriteLine("l3: {0}", System.Math.Exp(l3)); Console.WriteLine("l4: {0}", System.Math.Exp(l4)); // 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 Console.WriteLine("l5: {0}", System.Math.Exp(l5)); Console.WriteLine("l6: {0}", System.Math.Exp(l6)); }
public void LearnTest4() { Accord.Math.Tools.SetupGenerator(0); 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(new Ergodic(3, random: true), 6); var teacher = new ViterbiLearning(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(0.078050218613091762, pl, 1e-10); Assert.AreEqual(0.008509757587448558, p0, 1e-10); Assert.AreEqual(0.010609567901234561, p1, 1e-10); Assert.AreEqual(0.008509757587448558, p2, 1e-10); }
public void LearnTest2() { Accord.Math.Tools.SetupGenerator(0); int[][] sequences = new int[500][]; for (int i = 0; i < sequences.Length; i++) { sequences[i] = new int[Accord.Math.Tools.Random.Next(20, 80)]; int start = Accord.Math.Tools.Random.Next(); for (int j = 0; j < sequences[i].Length; j++) { double s = Math.Sin(j + start); double u = ((s + 1) / 2.0); sequences[i][j] = (int)(u * 10); } } HiddenMarkovModel hmm1; double ll1; { Accord.Math.Tools.SetupGenerator(0); hmm1 = new HiddenMarkovModel(10, 10, true); var teacher = new ViterbiLearning(hmm1) { Iterations = 1, Tolerance = 1e-15, Batches = 1, UseLaplaceRule = true }; ll1 = teacher.Run(sequences); } HiddenMarkovModel hmm10; double ll10; { Accord.Math.Tools.SetupGenerator(0); hmm10 = new HiddenMarkovModel(10, 10, true); var teacher = new ViterbiLearning(hmm10) { Iterations = 100, Tolerance = 1e-15, Batches = 1, UseLaplaceRule = true }; ll10 = teacher.Run(sequences); } Assert.IsTrue(ll10 > ll1); Assert.AreNotEqual(ll1, ll10, 10); // Those results must match the ones in ViterbiLearningTest`1. Assert.AreEqual(-33.834836461044411, ll1); Assert.AreEqual(-23.362967205628703, ll10); Assert.IsFalse(AreEqual(hmm1, hmm10)); }
public void LearnTest6() { Accord.Math.Tools.SetupGenerator(0); // 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(new Forward(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 ViterbiLearning(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 }); // 0.613 double l2 = hmm.Evaluate(new int[] { 0, 1, 1, 1 }); // 0.500 // Sequences which do not start with zero have much lesser probability. double l3 = hmm.Evaluate(new int[] { 1, 1 }); // 0.186 double l4 = hmm.Evaluate(new int[] { 1, 0, 0, 0 }); // 0.003 // 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 }); // 0.033 double l6 = hmm.Evaluate(new int[] { 0, 1, 1, 1, 1, 1, 1, 0, 1 }); // 0.026 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(1.754393540912413, pl, 1e-6); Assert.AreEqual(0.61368718756104801, p1, 1e-6); Assert.AreEqual(0.50049466955818356, p2, 1e-6); Assert.AreEqual(0.18643340385264684, p3, 1e-6); Assert.AreEqual(0.00300262431355424, p4, 1e-6); Assert.AreEqual(0.03338686211012481, p5, 1e-6); Assert.AreEqual(0.02659161933179825, p6, 1e-6); Assert.IsTrue(l1 > l3 && l1 > l4); Assert.IsTrue(l2 > l3 && l2 > l4); }
public void LearnTest3() { Accord.Math.Tools.SetupGenerator(0); // 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(new Forward(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 ViterbiLearning(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); // 0.5394 double l2; hmm.Decode(new int[] { 0, 1, 1, 1 }, out l2); // 0.4485 // Sequences which do not start with zero have much lesser probability. double l3; hmm.Decode(new int[] { 1, 1 }, out l3); // 0.0864 double l4; hmm.Decode(new int[] { 1, 0, 0, 0 }, out l4); // 0.0004 // 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); // 0.0154 double l6; hmm.Decode(new int[] { 0, 1, 1, 1, 1, 1, 1, 0, 1 }, out l6); // 0.0154 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(1.754393540912413, ll, 1e-6); Assert.AreEqual(0.53946360153256712, l1, 1e-6); Assert.AreEqual(0.44850249229903377, l2, 1e-6); Assert.AreEqual(0.08646414524833077, l3, 1e-6); Assert.AreEqual(0.00041152263374485, l4, 1e-6); Assert.AreEqual(0.01541807695931400, l5, 1e-6); Assert.AreEqual(0.01541807695931400, l6, 1e-6); Assert.IsTrue(l1 > l3 && l1 > l4); Assert.IsTrue(l2 > l3 && l2 > l4); }
public void LearnTest() { Accord.Math.Tools.SetupGenerator(0); HiddenMarkovModel hmm = new HiddenMarkovModel(new Ergodic(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 ViterbiLearning(hmm) { Iterations = 650, Tolerance = 0 }; double ll = teacher.Run(observation); double[] pi = { 0.66, 0.33 }; double[,] A = { { 0.99, 0.01 }, { 0.50, 0.50 } }; double[,] B = { { 0.44, 0.27, 0.28 }, { 0.33, 0.33, 0.33 } }; 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, 0.1)); }
public void LearnTest5() { double[][][] sequences = new double[][][] { new double[][] { new double[] { 0 }, new double[] { 3 }, new double[] { 1 } }, new double[][] { new double[] { 0 }, new double[] { 2 } }, new double[][] { new double[] { 1 }, new double[] { 0 }, new double[] { 3 } }, new double[][] { new double[] { 3 }, new double[] { 4 } }, new double[][] { new double[] { 0 }, new double[] { 1 }, new double[] { 3 }, new double[] { 5 } }, new double[][] { new double[] { 0 }, new double[] { 3 }, new double[] { 4 } }, new double[][] { new double[] { 0 }, new double[] { 1 }, new double[] { 3 }, new double[] { 5 } }, new double[][] { new double[] { 0 }, new double[] { 1 }, new double[] { 3 }, new double[] { 5 } }, new double[][] { new double[] { 0 }, new double[] { 1 }, new double[] { 3 }, new double[] { 4 }, new double[] { 5 } }, }; var hmm = HiddenMarkovModel.CreateGeneric(3, 6); var teacher = new ViterbiLearning <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(0.077427215162407442, pl, 1e-6); Assert.AreEqual(0.009958847736625515, p0, 1e-6); Assert.AreEqual(0.006790123456790126, p1, 1e-6); Assert.AreEqual(0.009958847736625515, p2, 1e-6); Assert.AreEqual(1, hmm.Dimension); double[][] sequences2 = new double[][] { new double[] { 0, 3, 1 }, new double[] { 0, 2 }, new double[] { 1, 0, 3 }, new double[] { 3, 4 }, new double[] { 0, 1, 3, 5 }, new double[] { 0, 3, 4 }, new double[] { 0, 1, 3, 5 }, new double[] { 0, 1, 3, 5 }, new double[] { 0, 1, 3, 4, 5 }, }; hmm = HiddenMarkovModel.CreateGeneric(3, 6); teacher = new ViterbiLearning <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); }
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>(new Forward(5), density); var learning = new ViterbiLearning <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 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 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 ViterbiLearning <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) = 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(3340.6878090199571, a1); Assert.AreEqual(1855.791720669667, 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(0.0714285714285714, A[0, 0], 1e-6); Assert.AreEqual(0.9285714285714286, A[0, 1], 1e-6); Assert.AreEqual(0.9230769230769231, A[1, 0], 1e-6); Assert.AreEqual(0.0769230769230769, A[1, 1], 1e-6); }
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 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 ViterbiLearning <NormalDistribution>(model) { Tolerance = 0.0001, Iterations = 0, }; // Fit the model double logLikelihood = teacher.Run(sequences); // See the probability of the sequences learned double a1 = model.Evaluate(new[] { 0.1, 5.2, 0.3, 6.7, 0.1, 6.0 }); // 0.40 double a2 = model.Evaluate(new[] { 0.2, 6.2, 0.3, 6.3, 0.1, 5.0 }); // 0.46 // See the probability of an unrelated sequence double a3 = model.Evaluate(new[] { 1.1, 2.2, 1.3, 3.2, 4.2, 1.0 }); // 1.42 double likelihood = Math.Exp(logLikelihood); a1 = Math.Exp(a1); a2 = Math.Exp(a2); a3 = Math.Exp(a3); Assert.AreEqual(1.5418305348314281, likelihood, 1e-10); Assert.AreEqual(0.4048936808991913, a1, 1e-10); Assert.AreEqual(0.4656014344844673, a2, 1e-10); Assert.AreEqual(1.4232710878429383E-48, 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(0.090, A[0, 0], 1e-3); Assert.AreEqual(0.909, A[0, 1], 1e-3); Assert.AreEqual(0.875, A[1, 0], 1e-3); Assert.AreEqual(0.125, A[1, 1], 1e-3); Assert.IsFalse(A.HasNaN()); }
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. 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(new Forward(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 ViterbiLearning <GeneralDiscreteDistribution>(hmm) { Tolerance = 0.0001, Iterations = 0, FittingOptions = new GeneralDiscreteOptions() { UseLaplaceRule = true } }; double ll = teacher.Run(sequences); // Calculate the probability that the given // sequences originated from the model double l1 = hmm.Evaluate(new double[] { 0, 1 }); // 0.613 double l2 = hmm.Evaluate(new double[] { 0, 1, 1, 1 }); // 0.500 // Sequences which do not start with zero have much lesser probability. double l3 = hmm.Evaluate(new double[] { 1, 1 }); // 0.186 double l4 = hmm.Evaluate(new double[] { 1, 0, 0, 0 }); // 0.003 // 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 double[] { 0, 1, 0, 1, 1, 1, 1, 1, 1 }); // 0.033 double l6 = hmm.Evaluate(new double[] { 0, 1, 1, 1, 1, 1, 1, 0, 1 }); // 0.026 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(1.754393540912413, pl, 1e-6); Assert.AreEqual(0.61368718756104801, p1, 1e-6); Assert.AreEqual(0.50049466955818356, p2, 1e-6); Assert.AreEqual(0.18643340385264684, p3, 1e-6); Assert.AreEqual(0.00300262431355424, p4, 1e-6); Assert.AreEqual(0.03338686211012481, p5, 1e-6); Assert.AreEqual(0.02659161933179825, p6, 1e-6); 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 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(new Forward(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 ViterbiLearning <GeneralDiscreteDistribution>(hmm) { Tolerance = 0.0001, Iterations = 0, FittingOptions = new GeneralDiscreteOptions() { UseLaplaceRule = true } }; 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(1.754393540912413, ll, 1e-6); Assert.AreEqual(0.53946360153256712, l1, 1e-6); Assert.AreEqual(0.44850249229903377, l2, 1e-6); Assert.AreEqual(0.08646414524833077, l3, 1e-6); Assert.AreEqual(0.00041152263374485, l4, 1e-6); Assert.AreEqual(0.01541807695931400, l5, 1e-6); Assert.AreEqual(0.01541807695931400, l6, 1e-6); Assert.IsTrue(l1 > l3 && l1 > l4); Assert.IsTrue(l2 > l3 && l2 > l4); Assert.AreEqual(1, hmm.Dimension); }
public void LearnTest2() { Accord.Math.Tools.SetupGenerator(0); double[][][] sequences = new double[500][][]; for (int i = 0; i < sequences.Length; i++) { sequences[i] = new double[Accord.Math.Tools.Random.Next(20, 80)][]; int start = Accord.Math.Tools.Random.Next(); for (int j = 0; j < sequences[i].Length; j++) { double s = Math.Sin(j + start); double u = ((s + 1) / 2.0); sequences[i][j] = new double[] { (int)(u * 10) }; } } HiddenMarkovModel <GeneralDiscreteDistribution> hmm1; double ll1; { Accord.Math.Tools.SetupGenerator(0); hmm1 = HiddenMarkovModel.CreateGeneric(10, 10, true); var teacher = new ViterbiLearning <GeneralDiscreteDistribution>(hmm1) { Iterations = 1, Tolerance = 1e-15, Batches = 1, UseLaplaceRule = true, FittingOptions = new GeneralDiscreteOptions { UseLaplaceRule = true } }; ll1 = teacher.Run(sequences); } HiddenMarkovModel <GeneralDiscreteDistribution> hmm10; double ll10; { Accord.Math.Tools.SetupGenerator(0); hmm10 = HiddenMarkovModel.CreateGeneric(10, 10, true); var teacher = new ViterbiLearning <GeneralDiscreteDistribution>(hmm10) { Iterations = 100, Tolerance = 1e-15, Batches = 1, UseLaplaceRule = true, FittingOptions = new GeneralDiscreteOptions { UseLaplaceRule = true } }; ll10 = teacher.Run(sequences); } Assert.IsTrue(ll10 > ll1); Assert.IsTrue(Math.Abs(ll1 - ll10) > 10); // Those results must match the ones in ViterbiLearningTest. Assert.AreEqual(-33.834836461044411, ll1); Assert.AreEqual(-23.362967205628703, ll10); Assert.IsFalse(AreEqual(hmm1, hmm10)); }