HMM Error for training the model

[hessinemaaoui]

Hi,

I am training a HMM with SuanShu but once it got errors in some cases. I tried a few different settings but the errors still occurred. Let me summarize how the error occurs.

Set HMM with 3 states with 5 discrete values in the emission probability at each state. Then I randomized a matrix A of size 3 x 3 and matrix B of size 3 x 5. Now I also get 100 observations, where the first 99 values are between 1 and 4, and the 100th value is 5. Then it runs out an infinite value matrices A and B. I suspect the issue is due to that the training algorithm finds that the value 5 cannot be found from the previous occurrences and cannot determine the probability of the model at value 5 in observation. For more details, you can refer to the following .java.

Is it an algorithmic issue or something would be fixed? Thanks.

Main Program:

<br /> package com.numericalmethod.suanshu.examples;<br /> import com.numericalmethod.suanshu.matrix.doubles.Matrix;<br /> import com.numericalmethod.suanshu.stats.hmm.rabiner.HmmTrainByEM;<br /> import com.numericalmethod.suanshu.stats.hmm.rabiner.HiddenMarkovModel;<br /> import com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.DenseMatrix;<br /> import com.numericalmethod.suanshu.vector.doubles.dense.DenseVector;<br /> import org.junit.Test;<br /> import java.io.*;<br /> import java.util.*;<br /> <br /> /**<br /> *<br /> * @author Chan<br /> */<br /> <br /> <br /> public class Test_HMM_20120120 {<br />         public static void main( String args[]) {     <br />         org.junit.runner.JUnitCore.main("com.numericalmethod.suanshu.examples.Test_HMM_20120120");<br />     }<br />     @Test<br />     public void test_0010(){<br />         // Initialization<br />         double ThresholdValue = 0.500;                                          //Input 1<br />         int[] ActiveCol = {1, 2, 3};                                            //Input 2<br />         int number_row_a = 3, number_col_a = number_row_a;                      //Input 3<br />         int NumberofTotalCol = 5;                                              //Input 4<br />         int number_row_b = number_row_a, number_col_b = ActiveCol.length*2-1;<br />         int WinSize = 100;               <br />         int nTraining = 10;<br />         DenseVector PI_0 = new DenseVector(MarkovModel_pre_20120119.GenerateRandomMatrix(1, number_row_a).t());       <br />         DenseMatrix A_0 = new DenseMatrix(MarkovModel_pre_20120119.GenerateRandomMatrix(number_row_a, number_col_a));<br />         DenseMatrix B_0 = new DenseMatrix(MarkovModel_pre_20120119.GenerateRandomMatrix(number_row_b, number_col_b));           <br />         HiddenMarkovModel model_0 = new HiddenMarkovModel(PI_0, A_0, B_0);<br />        <br />         DenseVector Obs = new DenseVector(MarkovModel_pre_20120119.GenerateRandomMatrix(1, WinSize).t());<br />         System.out.print(Obs.toString());<br />         int[] TempArray = new int[WinSize+1];<br />         for (int i = 0; i&lt;WinSize; i++){           <br />             if (Obs.get(i+1)&lt;0.25/WinSize)<br />                 TempArray<i> = 1;<br />             else if (Obs.get(i+1)&gt;=0.25/WinSize &amp;&amp; Obs.get(i+1)&lt;0.5/WinSize)<br />                 TempArray</i><i> = 2;<br />             else if (Obs.get(i+1)&gt;=0.5/WinSize &amp;&amp; Obs.get(i+1)&lt;0.75/WinSize)<br />                 TempArray</i><i> = 3;<br />             else<br />                 TempArray</i><i> = 4;<br />             System.out.println(TempArray</i><i>);<br />         }<br />        <br />         TempArray[WinSize] = 4;<br />         for (int k=0; k&lt;nTraining; k++)                                //train nTraining times<br />             model_0 = new HmmTrainByEM().train(model_0, TempArray);<br />        <br />         System.out.println(model_0.A().toString()); <br />         System.out.println(model_0.B().toString());<br />     }<br /> }<br /> <br /> </i>

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<br /> package com.numericalmethod.suanshu.examples;<br /> import com.numericalmethod.suanshu.matrix.doubles.Matrix;<br /> import com.numericalmethod.suanshu.stats.hmm.rabiner.HmmTrainByEM;<br /> import com.numericalmethod.suanshu.stats.hmm.rabiner.HiddenMarkovModel;<br /> import com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.DenseMatrix;<br /> import com.numericalmethod.suanshu.vector.doubles.dense.DenseVector;<br /> import org.junit.Test;<br /> import java.io.*;<br /> import java.util.*;<br /> <br /> /**<br /> *<br /> * @author Chan<br /> */<br /> <br /> <br /> public class Test_HMM_20120120 {<br />         public static void main( String args[]) {     <br />         org.junit.runner.JUnitCore.main("com.numericalmethod.suanshu.examples.Test_HMM_20120120");<br />     }<br />     @Test<br />     public void test_0010(){<br />         // Initialization<br />         double ThresholdValue = 0.500;                                          //Input 1<br />         int[] ActiveCol = {1, 2, 3};                                            //Input 2<br />         int number_row_a = 3, number_col_a = number_row_a;                      //Input 3<br />         int NumberofTotalCol = 5;                                               //Input 4<br />         int number_row_b = number_row_a, number_col_b = ActiveCol.length*2-1;<br />         int WinSize = 100;               <br />         int nTraining = 10;<br />         DenseVector PI_0 = new DenseVector(MarkovModel_pre_20120119.GenerateRandomMatrix(1, number_row_a).t());       <br />         DenseMatrix A_0 = new DenseMatrix(MarkovModel_pre_20120119.GenerateRandomMatrix(number_row_a, number_col_a));<br />         DenseMatrix B_0 = new DenseMatrix(MarkovModel_pre_20120119.GenerateRandomMatrix(number_row_b, number_col_b));           <br />         HiddenMarkovModel model_0 = new HiddenMarkovModel(PI_0, A_0, B_0);<br />        <br />         DenseVector Obs = new DenseVector(MarkovModel_pre_20120119.GenerateRandomMatrix(1, WinSize).t());<br />         System.out.print(Obs.toString());<br />         int[] TempArray = new int[WinSize+1];<br />         for (int i = 0; i&lt;WinSize; i++){           <br />             if (Obs.get(i+1)&lt;0.25/WinSize)<br />                 TempArray<i> = 1;<br />             else if (Obs.get(i+1)&gt;=0.25/WinSize &amp;&amp; Obs.get(i+1)&lt;0.5/WinSize)<br />                 TempArray</i><i> = 2;<br />             else if (Obs.get(i+1)&gt;=0.5/WinSize &amp;&amp; Obs.get(i+1)&lt;0.75/WinSize)<br />                 TempArray</i><i> = 3;<br />             else<br />                 TempArray</i><i> = 4;<br />             System.out.println(TempArray</i><i>);<br />         }<br />        <br />         TempArray[WinSize] = 4;<br />         for (int k=0; k&lt;nTraining; k++)                                //train nTraining times<br />             model_0 = new HmmTrainByEM().train(model_0, TempArray);<br />        <br />         System.out.println(model_0.A().toString()); <br />         System.out.println(model_0.B().toString());<br />     }<br /> }<br /> <br /> </i>

It depends to another .java with method GenerateRandomMatrix from class MarkovModel_pre_20120119. Just copy it in another .java and use it in the main program.  Method GenerateRandomMatrix is to generate random matrices.

<br /> <br /> package com.numericalmethod.suanshu.examples;<br /> <br /> import com.numericalmethod.suanshu.matrix.doubles.Matrix;<br /> import com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.DenseMatrix;<br /> import java.util.*;<br /> import java.io.*;<br /> <br /> /**<br /> *<br /> * @author Chan<br /> */<br /> <br /> <br /> public class MarkovModel_pre_20120119 {<br />     public static void main(String args[]) {<br />         // Test out the functions<br />         //Matrix A = new DenseMatrix(GetObservationState(readData("C:\text.txt", 2, 100), 0.005));             <br />         //System.out.println(A.toString());       <br />     }<br />    <br />    <br />     public static DenseMatrix readData(String FilePath, int ColSize, int WinSize, int[] ActiveCol)<br />       {<br />          <br />           // Col1 = Date; Col2 = Closed price; Col3 = Return;<br />           DenseMatrix temp_Data = new DenseMatrix(new double[1000][ActiveCol.length +1]);<br />           // Col1 = Date; Col2 = Closed price; Col3 = Normalized return;<br />           DenseMatrix output_Data = new DenseMatrix(new double [1000][ActiveCol.length +1]);<br /> <br />          <br />           try{<br />               // Open the file that is the first<br />               // command line parameter<br />               FileInputStream fstream = new FileInputStream(FilePath);<br />              <br />               // Get the object of DataInputStream<br />               DataInputStream in = new DataInputStream(fstream);<br />               BufferedReader br = new BufferedReader(new InputStreamReader(in));<br />               String strLine;<br />               //Read File Line By Line<br />               int i =1;<br />               strLine = br.readLine();<br />               while ((strLine = br.readLine()) != null &amp;&amp; i &lt;= 1000)  {                 <br />                   // Input the first col and second col to date and close price<br />                   int colCount = 1;<br />                   for (int col = 1; col &lt;= ColSize; col++)<br />                   {                                                                 <br />                       for (int ActiveColn = 1; ActiveColn&lt;=ActiveCol.length; ActiveColn++)<br />                           if (col == ActiveCol[ActiveColn-1]){                           <br />                             temp_Data.set(i, colCount++, Double.parseDouble(strLine.split(",")[col-1])) ;                     <br />                             break;<br />                       }<br />                   }<br />                   i++;<br />                 }<br />               //Close the input stream<br />               in.close();<br />             }catch (Exception e){//Catch exception if any<br />                     System.err.println("Error: " + e.getMessage());<br />           }<br />          <br />           // Calculate the return, the first one return cannot be calculated<br />             for (int i = 1000; i&gt;=2; i--){<br />                 if (temp_Data.get(i, 1)&gt;0)<br />                     for (int col=ActiveCol.length +1; col &gt;=3 ;col--)<br />                         temp_Data.set(i, col, (temp_Data.get(i, col-1)-temp_Data.get(i-1, col-1))/temp_Data.get(i-1, col-1));<br />             }<br /> <br />             // Assign date and price<br />             for (int i = 1000; i&gt;WinSize; i-- ){               <br />                 output_Data.set(i-WinSize, 1, temp_Data.get(i, 1));<br />                 output_Data.set(i-WinSize, 2, temp_Data.get(i, 2));<br />             }<br />            <br />             // Assign all the observations<br />             for (int col = 3; col&lt;=ActiveCol.length +1; col++)<br />             {<br />                 for (int i = 1000; i&gt;WinSize; i-- ){<br />                     double mean = 0, variance = 0;<br />                     for (int j = 0; i&lt;WinSize; j++)<br />                         mean+=temp_Data.get(i-j, 3);                   <br />                     mean = mean/WinSize;<br /> <br />                     for (int j = 0; j&lt;WinSize; j++)<br />                         variance+=(temp_Data.get(i-j, 3)-mean)*(temp_Data.get(i-j, 3)-mean);                   <br />                     variance = variance/WinSize;<br />                     output_Data.set(i-WinSize, col, (temp_Data.get(i,col)-mean)/Math.sqrt(variance));<br />                 }<br />             }<br />           return output_Data;<br />       }<br />    <br />     public static DenseMatrix GetObservationState(DenseMatrix Obser, double Threshold)<br />     {<br />         // Find out the size of a non-zero submatrix of Obser<br />         int NonZeroRowSize = 0;<br />         for (int i = 1; i &lt;= Obser.nRows(); i++)<br />             if (Obser.get(i,1)&gt;0) NonZeroRowSize++;<br />        <br />         DenseMatrix output_GetObser = new DenseMatrix (new double[NonZeroRowSize][Obser.nCols()]);<br />         for (int i = 1; i&lt;=NonZeroRowSize; i++)<br />         {<br />                 // Assign Date<br />                 output_GetObser.set(i, 1, Obser.get(i, 1));<br />                 // Assign Price<br />                 output_GetObser.set(i, 2, Obser.get(i, 2));<br />                 // Assign state<br />                 for (int col = 3; col &lt;= Obser.nCols(); col++)<br />                 {<br />                     if (Obser.get(i, col)&lt;(-1)*Threshold)<br />                         output_GetObser.set(i, col, 1);<br />                     else if (Obser.get(i, col)&gt; Threshold)<br />                         output_GetObser.set(i, col, 3);<br />                     else<br />                         output_GetObser.set(i, col, 2);<br />                 }<br />            <br />         }<br />        <br />         return GenerateObservationValue(output_GetObser);<br />     }<br /> <br />    <br /> // It generate the state by the weighted average of observation state (default factors 1)<br /> // If the observation<i> = {1, 2, 3, 3, 2}, then translate it to {-1, 0, 1, 1, 0}<br /> // Add all those observation value. Max value = Size; Min Value = -Size<br />     public static DenseMatrix GenerateObservationValue(DenseMatrix output_GetObser)<br />     {<br />         DenseMatrix OutMx = new DenseMatrix(new double [output_GetObser.nRows()][3]);<br />         for (int row = 1; row&lt;=output_GetObser.nRows(); row ++)<br />         {<br />             int SumObservation = 0;<br />             for (int col = 3; col &lt;= output_GetObser.nCols(); col++)<br />                 SumObservation += output_GetObser.get(row, col);<br />             // Consider there are two observations, min_value = 2 and max_value = 6<br />             // We need to transfer it to observation values from 1 to 5<br />             OutMx.set(row, 1, output_GetObser.get(row, 1));<br />             OutMx.set(row, 2, output_GetObser.get(row, 2));<br />             OutMx.set(row, 3, SumObservation-(output_GetObser.nCols()-3));<br />         }       <br />         return OutMx;<br />     }<br />    <br />     // Return a random matrix<br />     public static DenseMatrix GenerateRandomMatrix(int rowsize, int colsize){<br />         Random generator = new Random();<br /> <br />         double r1 = generator.nextDouble();<br />         double r2 = generator.nextDouble();<br />         double sum = r1 + r2;<br />         r1 = r1/sum;<br />         r2 = r2/sum;               <br />         double sum_a;       <br />        <br />         DenseMatrix ResultMatrix = new DenseMatrix(new double[rowsize][colsize]);<br />         double[] r_a = new double[colsize+1];<br />        <br />        <br />         for ( int j = 1; j&lt;=rowsize;j++){<br />             sum_a =0;<br />             for (int i=1;i&lt;=colsize;i++){<br />                 r_a</i><i> = generator.nextDouble();<br />                 sum_a = r_a</i><i> + sum_a;<br />             }<br />             for (int i=1;i&lt;=colsize;i++){<br />               r_a</i><i> = r_a</i><i>/sum_a;<br />             }<br />             for ( int k = 1;k&lt;= colsize;k++){<br />                 ResultMatrix.set(j, k, r_a[k]);<br />             }<br />         }<br />         return ResultMatrix;<br />     }<br /> }<br /> </i>

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<br /> <br /> package com.numericalmethod.suanshu.examples;<br /> <br /> import com.numericalmethod.suanshu.matrix.doubles.Matrix;<br /> import com.numericalmethod.suanshu.matrix.doubles.matrixtype.dense.DenseMatrix;<br /> import java.util.*;<br /> import java.io.*;<br /> <br /> /**<br /> *<br /> * @author Chan<br /> */<br /> <br /> <br /> public class MarkovModel_pre_20120119 {<br />     public static void main(String args[]) {<br />         // Test out the functions<br />         //Matrix A = new DenseMatrix(GetObservationState(readData("C:\text.txt", 2, 100), 0.005));             <br />         //System.out.println(A.toString());       <br />     }<br />    <br />    <br />     public static DenseMatrix readData(String FilePath, int ColSize, int WinSize, int[] ActiveCol)<br />       {<br />          <br />           // Col1 = Date; Col2 = Closed price; Col3 = Return;<br />           DenseMatrix temp_Data = new DenseMatrix(new double[1000][ActiveCol.length +1]);<br />           // Col1 = Date; Col2 = Closed price; Col3 = Normalized return;<br />           DenseMatrix output_Data = new DenseMatrix(new double [1000][ActiveCol.length +1]);<br /> <br />          <br />           try{<br />               // Open the file that is the first<br />               // command line parameter<br />               FileInputStream fstream = new FileInputStream(FilePath);<br />              <br />               // Get the object of DataInputStream<br />               DataInputStream in = new DataInputStream(fstream);<br />               BufferedReader br = new BufferedReader(new InputStreamReader(in));<br />               String strLine;<br />               //Read File Line By Line<br />               int i =1;<br />               strLine = br.readLine();<br />               while ((strLine = br.readLine()) != null &amp;&amp; i &lt;= 1000)   {                 <br />                   // Input the first col and second col to date and close price<br />                   int colCount = 1;<br />                   for (int col = 1; col &lt;= ColSize; col++)<br />                   {                                                                 <br />                       for (int ActiveColn = 1; ActiveColn&lt;=ActiveCol.length; ActiveColn++)<br />                           if (col == ActiveCol[ActiveColn-1]){                           <br />                             temp_Data.set(i, colCount++, Double.parseDouble(strLine.split(",")[col-1])) ;                     <br />                             break;<br />                       }<br />                   }<br />                   i++;<br />                 }<br />               //Close the input stream<br />               in.close();<br />             }catch (Exception e){//Catch exception if any<br />                     System.err.println("Error: " + e.getMessage());<br />           }<br />          <br />           // Calculate the return, the first one return cannot be calculated<br />             for (int i = 1000; i&gt;=2; i--){<br />                 if (temp_Data.get(i, 1)&gt;0)<br />                     for (int col=ActiveCol.length +1; col &gt;=3 ;col--)<br />                         temp_Data.set(i, col, (temp_Data.get(i, col-1)-temp_Data.get(i-1, col-1))/temp_Data.get(i-1, col-1));<br />             }<br /> <br />             // Assign date and price<br />             for (int i = 1000; i&gt;WinSize; i-- ){               <br />                 output_Data.set(i-WinSize, 1, temp_Data.get(i, 1));<br />                 output_Data.set(i-WinSize, 2, temp_Data.get(i, 2));<br />             }<br />            <br />             // Assign all the observations<br />             for (int col = 3; col&lt;=ActiveCol.length +1; col++)<br />             {<br />                 for (int i = 1000; i&gt;WinSize; i-- ){<br />                     double mean = 0, variance = 0;<br />                     for (int j = 0; i&lt;WinSize; j++)<br />                         mean+=temp_Data.get(i-j, 3);                   <br />                     mean = mean/WinSize;<br /> <br />                     for (int j = 0; j&lt;WinSize; j++)<br />                         variance+=(temp_Data.get(i-j, 3)-mean)*(temp_Data.get(i-j, 3)-mean);                   <br />                     variance = variance/WinSize;<br />                     output_Data.set(i-WinSize, col, (temp_Data.get(i,col)-mean)/Math.sqrt(variance));<br />                 }<br />             }<br />           return output_Data;<br />       }<br />    <br />     public static DenseMatrix GetObservationState(DenseMatrix Obser, double Threshold)<br />     {<br />         // Find out the size of a non-zero submatrix of Obser<br />         int NonZeroRowSize = 0;<br />         for (int i = 1; i &lt;= Obser.nRows(); i++)<br />             if (Obser.get(i,1)&gt;0) NonZeroRowSize++;<br />        <br />         DenseMatrix output_GetObser = new DenseMatrix (new double[NonZeroRowSize][Obser.nCols()]);<br />         for (int i = 1; i&lt;=NonZeroRowSize; i++)<br />         {<br />                 // Assign Date<br />                 output_GetObser.set(i, 1, Obser.get(i, 1));<br />                 // Assign Price<br />                 output_GetObser.set(i, 2, Obser.get(i, 2));<br />                 // Assign state<br />                 for (int col = 3; col &lt;= Obser.nCols(); col++)<br />                 {<br />                     if (Obser.get(i, col)&lt;(-1)*Threshold)<br />                         output_GetObser.set(i, col, 1);<br />                     else if (Obser.get(i, col)&gt; Threshold)<br />                         output_GetObser.set(i, col, 3);<br />                     else<br />                         output_GetObser.set(i, col, 2);<br />                 }<br />            <br />         }<br />        <br />         return GenerateObservationValue(output_GetObser);<br />     }<br /> <br />    <br /> // It generate the state by the weighted average of observation state (default factors 1)<br /> // If the observation<i> = {1, 2, 3, 3, 2}, then translate it to {-1, 0, 1, 1, 0}<br /> // Add all those observation value. Max value = Size; Min Value = -Size<br />     public static DenseMatrix GenerateObservationValue(DenseMatrix output_GetObser)<br />     {<br />         DenseMatrix OutMx = new DenseMatrix(new double [output_GetObser.nRows()][3]);<br />         for (int row = 1; row&lt;=output_GetObser.nRows(); row ++)<br />         {<br />             int SumObservation = 0;<br />             for (int col = 3; col &lt;= output_GetObser.nCols(); col++)<br />                 SumObservation += output_GetObser.get(row, col);<br />             // Consider there are two observations, min_value = 2 and max_value = 6<br />             // We need to transfer it to observation values from 1 to 5<br />             OutMx.set(row, 1, output_GetObser.get(row, 1));<br />             OutMx.set(row, 2, output_GetObser.get(row, 2));<br />             OutMx.set(row, 3, SumObservation-(output_GetObser.nCols()-3));<br />         }       <br />         return OutMx;<br />     }<br />    <br />     // Return a random matrix<br />     public static DenseMatrix GenerateRandomMatrix(int rowsize, int colsize){<br />         Random generator = new Random();<br /> <br />         double r1 = generator.nextDouble();<br />         double r2 = generator.nextDouble();<br />         double sum = r1 + r2;<br />         r1 = r1/sum;<br />         r2 = r2/sum;               <br />         double sum_a;       <br />        <br />         DenseMatrix ResultMatrix = new DenseMatrix(new double[rowsize][colsize]);<br />         double[] r_a = new double[colsize+1];<br />        <br />        <br />         for ( int j = 1; j&lt;=rowsize;j++){<br />             sum_a =0;<br />             for (int i=1;i&lt;=colsize;i++){<br />                 r_a</i><i> = generator.nextDouble();<br />                 sum_a = r_a</i><i> + sum_a;<br />             }<br />             for (int i=1;i&lt;=colsize;i++){<br />                r_a</i><i> = r_a</i><i>/sum_a;<br />             }<br />             for ( int k = 1;k&lt;= colsize;k++){<br />                 ResultMatrix.set(j, k, r_a[k]);<br />             }<br />         }<br />         return ResultMatrix;<br />     }<br /> }<br /> </i>

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