混合多項分布

私自身の混合多項分布の理解度はまだいまいちな気もするけど、とりあえず、ここにあったPythonのコードをJavaで書き直してみた。

public class MultinomialMixture {
double[][] dataset;
int num;
int dim;
int mNum;
double[][] c;
double[][] q;
public MultinomialMixture(double[][] dataset, int k) {
this.dataset = dataset;
num = dataset.length;
dim = dataset[0].length;
mNum = k;
q = new double[mNum][dim];
c = new double[num][mNum];
Random random = new Random(1);
for (int i = 0; i < mNum; i++) {
for (int j = 0; j < dim; j++) {
q[i][j] = random.nextDouble();
}
q[i] = normalize(q[i]);
}
}
public void execute(int loop) {
for (int i = 0; i < loop; i++) {
stepE();
stepM();
}
}
double[] normalize(double[] value) {
double[] ret = new double[value.length];
double sum = 0;
for (int i = 0; i < value.length; i++) {
sum += value[i];
}
for (int i = 0; i < value.length; i++) {
ret[i] = value[i] / sum;
}
return ret;
}
double multi(double[] u, double[] x) {
//    return prod([q[w] ** d[w] for w in range(W)])
double value = 1;
for (int i = 0; i < u.length; i++) {
value *= Math.pow(u[i], x[i]);
}
return value;
}
void stepE() {
//	    for n in range(N):
//       C[n] = normalize([multi(D[n], Q[k]) for k in range(K)])
for (int i = 0; i < num; i++) {
double[] dn = dataset[i];
for (int j = 0; j < mNum; j++) {
c[i][j] = multi(q[j], dn);
}
c[i] = normalize(c[i]);
}
}
void stepM() {
//	    for k in range(K):
//	        Q[k] = normalize([sum([C[n][k] * D[n][w] for n in range(N)]) for w in range(W)])
for (int i = 0; i < mNum; i++) {
double[] value = new double[dim];
for (int j = 0; j < dim; j++) {
value[j] = 0;
for (int k = 0; k < num; k++) {
value[j] += c[k][i] * dataset[k][j];
}
}
value = normalize(value);
q[i] = value;
}
}
double logLikelihood() {
//	    L = 0
//	    for n in range(N):
//	        p = [C[n][k] * multinomial(D[n], Q[k]) for k in range(K)]
//	        L += log(sum(p))
double l = 0;
for (int i = 0; i < num; i++) {
double sum = 0;
for (int j = 0; j < mNum; j++) {
sum += c[i][j] * multinomial(dataset[i], q[j]);
}
l += Math.log(sum);
}
return l;
}
double multinomial(double[] d, double[] q) {
//	    return factorial(sum(d)) / prod([factorial(d[w]) for w in range(W)]) * multi(d,q)
double prod = 1;
for (int i = 0; i < dim; i++) {
prod *= factorial(d[i]);
}
return factorial(sum(d)) / prod * multi(q, d);
}
double factorial(double x) {
//	    if x == 0: return 1
//	    return reduce(mul, xrange(1, x+1))
double prod = 1;
for (int i = 1; i < x + 1; i++) {
prod *= i;
}
return prod;
}
double sum(double[] v) {
double sum = 0;
for (int i = 0; i < v.length; i++) {
sum += v[i];
}
return sum;
}
public void print() {
System.out.println("L=" + logLikelihood());
//		c = new double[num][mNum];
StringBuilder buf = new StringBuilder();
buf.append("C=[");
for (int i = 0; i < num; i++) {
buf.append('[');
for (int j = 0; j < mNum; j++) {
buf.append(c[i][j]);
if (j != mNum - 1) {
buf.append(',');
}
}
buf.append(']');
if (i != num - 1) {
buf.append(',');
}
}
buf.append(']');
System.out.println(buf.toString());
//		q = new double[mNum][dim];
buf = new StringBuilder();
buf.append("Q=[");
for (int i = 0; i < mNum; i++) {
buf.append('[');
for (int j = 0; j < dim; j++) {
buf.append(q[i][j]);
if (j != dim - 1) {
buf.append(',');
}
}
buf.append(']');
if (i != mNum - 1) {
buf.append(',');
}
}
buf.append(']');
System.out.println(buf.toString());
}
}

使うときは以下の感じ。

int k = 2;
MultinomialMixture mm = new MultinomialMixture(dataset, k);
mm.execute(10);
mm.print();

かなり勢いで書いたから、細かいことは後で直すとして、Pythonのやつと同じ感じの結果だったからとりあえず、よしとする。

カテゴリー: Machine Learning パーマリンク

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