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LearningProb.java
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LearningProb.java
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package LearningProb;
abstract class HMM_ABS {
HMM hmm;
String x; //OBSERVATION SEQUENCE
public HMM_ABS(HMM hmm, String x){ this.hmm = hmm; this.x = x; }
static double logLIMIT(double p, double q) {
double max, diff;
if (p > q)
{
if (q == Double.NEGATIVE_INFINITY)
return p;
else {
max = p; diff = q - p;
}
}
else {
if (p == Double.NEGATIVE_INFINITY)
return q;
else {
max = q; diff = p - q;
}
}
// Now diff <= 0 so Math.exp(diff) will not overflow
return max + (diff < -37 ? 0 : Math.log(1 + Math.exp(diff)));
}
}
class Forward extends HMM_ABS {
double[][] f; // the matrix used to find the decoding
// f[i][k] = f_k(i) = log(P(x1..xi, pi_i=k))
private int L;
public Forward(HMM hmm, String x) {
super(hmm, x);
L = x.length();
f = new double[L+1][hmm.nstate];
f[0][0] = 0; // = log(1)
for (int k=1; k<hmm.nstate; k++)
f[0][k] = Double.NEGATIVE_INFINITY; // = log(0)
for (int i=1; i<=L; i++)
f[i][0] = Double.NEGATIVE_INFINITY; // = log(0)
for (int i=1; i<=L; i++)
for (int ell=1; ell<hmm.nstate; ell++) {
double sum = Double.NEGATIVE_INFINITY; // = log(0)
for (int k=0; k<hmm.nstate; k++)
sum = logLIMIT(sum, f[i-1][k] + hmm.log_transMat[k][ell]);
f[i][ell] = hmm.log_emiMat[ell][x.charAt(i-1)] + sum;
}
}
double logprob() {
double sum = Double.NEGATIVE_INFINITY; // = log(0)
for (int k=0; k<hmm.nstate; k++)
sum = logLIMIT(sum, f[L][k]);
return sum;
}
}
class HMM {
// State names and state-to-state transition probabilities
int nstate;
String[] state;
double[][] log_transMat;
// Emission names and emission probabilities
int nEmi_symb;
String Emi_symb;
double[][] log_emiMat;
public HMM(String[] state, double[][] trans_mat, String Emi_symb, double[][] emi_mat)
{
if (state.length != trans_mat.length)
throw new IllegalArgumentException("Error! Insufficent arguments");
if (trans_mat.length != emi_mat.length)
throw new IllegalArgumentException("Error! Insufficent arguments");
for (int i=0; i<trans_mat.length; i++) {
if (state.length != trans_mat[i].length)
throw new IllegalArgumentException("Error!transition mat is non-square");
if (Emi_symb.length() != emi_mat[i].length)
throw new IllegalArgumentException("Error! emission symbols and emission mat disagree");
}
nstate = state.length + 1;
this.state = new String[nstate];
log_transMat = new double[nstate][nstate];
this.state[0] = "Init"; // initial state
// P(start -> start) = 0
log_transMat[0][0] = Double.NEGATIVE_INFINITY; // = log(0)
// P(start -> other) = 1.0/state.length
double fromstart = Math.log(1.0/state.length);
for (int j=1; j<nstate; j++)
log_transMat[0][j] = fromstart;
for (int i=1; i<nstate; i++) {
// Reverse state names for efficient backwards concatenation
this.state[i] = new StringBuffer(state[i-1]).reverse().toString();
// P(other -> start) = 0
log_transMat[i][0] = Double.NEGATIVE_INFINITY; // = log(0)
for (int j=1; j<nstate; j++)
log_transMat[i][j] = Math.log(trans_mat[i-1][j-1]);
}
// Set up the emission matrix
this.Emi_symb = Emi_symb;
nEmi_symb = Emi_symb.length();
// Assume all Emi_symbs are uppercase letters (ASCII <= 91)
log_emiMat = new double[emi_mat.length+1][91];
for (int b=0; b<nEmi_symb; b++) {
// Use the emitted character, not its number, as index into log_emiMat:
char eb = Emi_symb.charAt(b);
// P(emit xi in state 0) = 0
log_emiMat[0][eb] = Double.NEGATIVE_INFINITY; // = log(0)
for (int k=0; k<emi_mat.length; k++)
log_emiMat[k+1][eb] = Math.log(emi_mat[k][b]);
}
}
private static double[] uniformd(int n) {
double[] p = new double[n];
for (int i=0; i<n; i++)
p[i] = 1.0/n;
return p;
}
private static double[] randomd(int n) {
double[] p = new double[n];
double sum = 0;
// Generate random numbers
for (int i=0; i<n; i++) {
p[i] = Math.random();
sum += p[i];
}
// Scale to obtain a discrete probability distribution
for (int i=0; i<n; i++)
p[i] /= sum;
return p;
}
private static double fwdbwd(HMM hmm, String[] xs, Forward[] fwds, Backward[] bwds, double[] logP) {
double loglikelihood = 0;
for (int s=0; s<xs.length; s++) {
fwds[s] = new Forward(hmm, xs[s]);
bwds[s] = new Backward(hmm, xs[s]);
logP[s] = fwds[s].logprob();
loglikelihood += logP[s];
}
return loglikelihood;
}
// xs is the set of training sequences
// state is the set of HMM state names
// Emi_symb is the set of emissible symbols
public static HMM baumwelch(String[] xs, String[] state, String Emi_symb, final double threshold) {
int nstate = state.length;
int nseqs = xs.length;
int nEmi_symb = Emi_symb.length();
Forward[] fwds = new Forward[nseqs];
Backward[] bwds = new Backward[nseqs];
double[] logP = new double[nseqs];
double[][] trans_mat = new double[nstate][];
double[][] emi_mat = new double[nstate][];
// Set up the inverse of b -> Emi_symb.charAt(b); assume all Emi_symbs <= 'Z'
int[] Emi_symbinv = new int[91];
for (int i=0; i<Emi_symbinv.length; i++)
Emi_symbinv[i] = -1;
for (int b=0; b<nEmi_symb; b++)
Emi_symbinv[Emi_symb.charAt(b)] = b;
// Initialize mats with random variables
for (int k=0; k<nstate; k++) {
trans_mat[k] = randomd(nstate);
emi_mat[k] = randomd(nEmi_symb);
}
HMM hmm = new HMM(state, trans_mat, Emi_symb, emi_mat);
double prev_likelihood;
// Compute Forward and Backward tables for the sequences
double cur_likelihood = fwdbwd(hmm, xs, fwds, bwds, logP);
System.out.println("log likelihood = " + cur_likelihood);
do {
prev_likelihood = cur_likelihood;
// Compute estimates for A and E
double[][] A = new double[nstate][nstate];
double[][] E = new double[nstate][nEmi_symb];
for (int s=0; s<nseqs; s++) {
String x = xs[s];
Forward fwd = fwds[s];
Backward bwd = bwds[s];
int L = x.length();
double P = logP[s];
for (int i=0; i<L; i++)
{
for (int k=0; k<nstate; k++)
E[k][Emi_symbinv[x.charAt(i)]] += expo(fwd.f[i+1][k+1] + bwd.b[i+1][k+1] - P);
}
for (int i=0; i<L-1; i++)
for (int k=0; k<nstate; k++)
for (int ell=0; ell<nstate; ell++)
A[k][ell] += expo(fwd.f[i+1][k+1] + hmm.log_transMat[k+1][ell+1] + hmm.log_emiMat[ell+1][x.charAt(i+1)] + bwd.b[i+2][ell+1] - P);
}
// Estimate new model parameters
for (int k=0; k<nstate; k++) {
double Aksum = 0;
for (int ell=0; ell<nstate; ell++)
Aksum += A[k][ell];
for (int ell=0; ell<nstate; ell++)
trans_mat[k][ell] = A[k][ell] / Aksum;
double Eksum = 0;
for (int b=0; b<nEmi_symb; b++)
Eksum += E[k][b];
for (int b=0; b<nEmi_symb; b++)
emi_mat[k][b] = E[k][b] / Eksum;
}
// Create new model
hmm = new HMM(state, trans_mat, Emi_symb, emi_mat);
cur_likelihood = fwdbwd(hmm, xs, fwds, bwds, logP);
System.out.println("log likelihood = " + cur_likelihood);
// hmm.print(new SystemOut());
} while (Math.abs(prev_likelihood - cur_likelihood) > threshold);
return hmm;
}
public static double expo(double x) {
if (x == Double.NEGATIVE_INFINITY)
return 0;
else
return Math.exp(x);
}
}
class Backward extends HMM_ABS {
double[][] b;// the matrix used to find the decoding // b[i][k] = b_k(i) = log(P(x(i+1)..xL, pi_i=k))
public Backward(HMM hmm, String x) {
super(hmm, x);
int L = x.length();
b = new double[L+1][hmm.nstate];
for (int k=1; k<hmm.nstate; k++)
b[L][k] = 0; // = log(1) // should be hmm.log_transMat[k][0]
for (int i=L-1; i>=1; i--)
for (int k=0; k<hmm.nstate; k++) {
double sum = Double.NEGATIVE_INFINITY; // = log(0)
for (int ell=1; ell<hmm.nstate; ell++)
sum = logLIMIT(sum, hmm.log_transMat[k][ell]
+ hmm.log_emiMat[ell][x.charAt(i)]
+ b[i+1][ell]);
b[i][k] = sum;
}
}
double logprob() {
double sum = Double.NEGATIVE_INFINITY; // = log(0)
for (int ell=0; ell<hmm.nstate; ell++)
sum = logLIMIT(sum, hmm.log_transMat[0][ell] + hmm.log_emiMat[ell][x.charAt(0)]+ b[1][ell]);
return sum;
}
}
public class LearningProb {
public static void main(String[] args) {
String[] state = { "F", "L" };
double[][] aprob = { { 0.95, 0.05 },
{ 0.10, 0.90 } };
String esym = "123456ABCDEFGH";
double[][] eprob = { { 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14},
{ 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14, 1.0/14} };
HMM hmm = new HMM(state, aprob, esym, eprob);
String x =
"315116246446644245311321631164152133625144543631656626566666"
+ "ABECDE122345F6ABDFGH14E56EGFH234E56ABEDGH14E23F456ABDFGH1F43"
+ "222555441666566563564324364131513465146353411126414626253356"
+ "366163666466232534413661661163252562462255265252266435353336"
+ "CD1223456ABGH1456GH56AB3456ABDGHCD1223456AB3456ABDGH14423456";
String x2 =
"ABECDE122345F6ABDFGH14E56EGFH234E56ABEDGH14E23F456ABDFGH1F43"
+ "CD1223456ABGH1456GH56AB3456ABDGHCD1223456AB3456ABDGH14423456";
String[] xs = { x , x2};
HMM estimate = HMM.baumwelch(xs, state, esym, 0.00001);
System.out.println("\nTransition probabilities:");
for (int i=1; i<estimate.nstate; i++) {
for (int j=1; j<estimate.nstate; j++) {
Double xtemp = estimate.log_transMat[i][j];
if (xtemp == Double.NEGATIVE_INFINITY)
System.out.print("0.000000 ");
else System.out.printf("%.6f ", Math.exp(xtemp));
}
System.out.println();
}
System.out.println("\nEmission probabilities:");
for (int j=0; j<estimate.nEmi_symb; j++)
{
System.out.print(estimate.Emi_symb.charAt(j)+" ");
}System.out.println();
for (int i=1; i<estimate.nstate; i++) {
for (int j=0; j<estimate.nEmi_symb; j++) {
Double xtemp = estimate.log_emiMat[i][estimate.Emi_symb.charAt(j)];
if (xtemp == Double.NEGATIVE_INFINITY)
System.out.print("0.000000 ");
else System.out.printf("%.6f ", Math.exp(xtemp));
}
System.out.println();
}
}
}