* Implementation using independent samplers. *
* Mixture network specification: * *
* m >> (theta[m] | alpha) >> x[m][n]
* m, x[m][n] >> (thetax[m,x] | gamma[x]) >> y[m][n]
* m, y[m][n] >> (thetay[m,y] | delta[y]) >> z[m][n]
* z[m][n] >> (phi[z] | beta) >> w[m][n]
*
*
* elements:
*
* document m
* type: {ROOT|E3COUPLED}
* parents: (root)
* children: theta thetax thetay
* range: M
* ----
* doc-topic (theta[m] | alpha)
* type: {SEQUENCE|C1ROOT}
* parents: m
* children: x
* components: theta, domain: M, range: K
* counts: nmx, sum: null
* index: m, selector: null
* hyperparams: alpha, dimension 1, fixed: false
* ----
* topic-topic (thetax[m,x] | gamma[x])
* type: {SEQUENCE|C1BSEQADD}
* parents: m x
* children: y
* components: thetax, domain: M * K, range: L
* counts: nmxy, sum: nmxysum
* index: mx, selector: m,x
* hyperparams: gamma, dimension: K * L, selector: x, fixed: false
* ----
* topic-topic (thetay[m,y] | delta[y])
* type: {SEQUENCE|C1BSEQADD}
* parents: m y
* children: z
* components: thetay, domain: M * L, range: J
* counts: nmyz, sum: nmyzsum
* index: my, selector: m,y
* hyperparams: delta, dimension: L * J, selector: y, fixed: false
* ----
* topic x[m][n]
* type: {HIDDEN|E1SINGLE}
* parents: theta
* children: thetax
* range: K
* ----
* topic y[m][n]
* type: {HIDDEN|E1SINGLE}
* parents: thetax
* children: thetay
* range: L
* ----
* topic z[m][n]
* type: {HIDDEN|E1SINGLE}
* parents: thetay
* children: phi
* range: J
* ----
* topic-word (phi[z] | beta)
* type: {TOPIC|C1ASINGLE}
* parents: z
* children: w
* components: phi, domain: J, range: V
* counts: nzw, sum: nzwsum
* index: z, selector: null
* hyperparams: beta, dimension 1, fixed: false
* ----
* word w[m][n]
* type: {VISIBLE|E1SINGLE}
* parents: phi
* children: (leaf)
* range: V
* ----
* sequences:
*
* words [m][n]
* parent: (root), children: []
* edges: m x y z w
*
*
* @author Gregor Heinrich, gregor :: arbylon : net (via MixNetKernelGenerator)
* @date generated on 11 Mar 2011
*/
// constructor
public class Pam5iGibbsSampler {
// //////////////// fields //////////////////
// fields
Random rand;
int iter;
int niter;
// root edge: document
int M;
int Mq;
// sequence node: doc-topic
int[][] nmx;
int[][] nmxq;
double alpha;
double alphasum;// sequence node: topic-topic
int[][] nmxy;
int[][] nmxyq;
int[] nmxysum;
int[] nmxysumq;
double[][] gamma;
double[] gammasum;// sequence node: topic-topic
int[][] nmyz;
int[][] nmyzq;
int[] nmyzsum;
int[] nmyzsumq;
double[][] delta;
double[] deltasum;// hidden edge: topic
int[][] x;
int[][] xq;
int K;
// hidden edge: topic
int[][] y;
int[][] yq;
int L;
// hidden edge: topic
int[][] z;
int[][] zq;
int J;
// topic node: topic-word
int[][] nzw;
int[] nzwsum;
double beta;
double betasum;
double[][] phi;
// visible edge: word
int[][] w;
int[][] wq;
int V;
// sequence: words
int W;
int Wq;
// sampling weights
double[] pp;
// //////////////// main //////////////////
// standard main routine
public static void main(String[] args) {
String filebase = "nips/nips";
Random rand = new CokusRandom();
// set up corpus
LabelNumCorpus corpus = new LabelNumCorpus(filebase);
corpus.split(10, 1, rand);
LabelNumCorpus train = (LabelNumCorpus) corpus.getTrainCorpus();
LabelNumCorpus test = (LabelNumCorpus) corpus.getTestCorpus();
// TODO: adjust data source
int[][] w = train.getDocWords(rand);
int[][] wq = test.getDocWords(rand);
int V = corpus.getNumTerms();
// parameters
int K = 20;
int L = 20;
int J = 20;
double alpha = 0.1;
double gamma = 0.1;
double delta = 0.1;
double beta = 0.1;
int niter = 10, niterq = 5;
// create sampler
Pam5iGibbsSampler gs = new Pam5iGibbsSampler(alpha, gamma, delta, K, L,
J, beta, w, wq, V, rand);
gs.init();
System.out.println(gs);
// initial test
gs.initq();
gs.runq(niterq);
System.out.println(gs.ppx());
// run sampler
StopWatch.start();
gs.init();
gs.run(niter);
System.out.println(StopWatch.format(StopWatch.stop()));
// final test
gs.initq();
gs.runq(niterq);
System.out.println(gs.ppx());
System.out.println(gs);
} // main
// //////////////// constructor //////////////////
public Pam5iGibbsSampler(double alpha, double gamma, double delta, int K,
int L, int J, double beta, int[][] w, int[][] wq, int V, Random rand) {
// assign
this.K = K;
this.L = L;
this.J = J;
this.w = w;
this.wq = wq;
this.V = V;
this.alpha = alpha;
this.alphasum = K * alpha;
this.gamma = new double[K][L];
this.gammasum = new double[K];
for (int mxj = 0; mxj < K; mxj++) {
for (int t = 0; t < L; t++) {
this.gamma[mxj][t] = gamma;
} // for t
this.gammasum[mxj] = L * gamma;
} // for mxj
this.delta = new double[L][J];
this.deltasum = new double[L];
for (int myj = 0; myj < L; myj++) {
for (int t = 0; t < J; t++) {
this.delta[myj][t] = delta;
} // for t
this.deltasum[myj] = J * delta;
} // for myj
this.beta = beta;
this.betasum = V * beta;
// count tokens
M = w.length;
W = 0;
for (int m = 0; m < M; m++) {
W += w[m].length;
}
Mq = wq.length;
Wq = 0;
for (int m = 0; m < Mq; m++) {
Wq += wq[m].length;
}
this.rand = rand;
// allocate sampling weights
int T = K;
T = Math.max(T, L);
T = Math.max(T, J);
pp = new double[T];
} // c'tor
// //////////////// initialisation //////////////////
// initialisation
public void init() {
// component selectors
int mxsel = -1;
int mxjsel = -1;
int mysel = -1;
int myjsel = -1;
// sequence node
nmx = new int[M][K];
// sequence node
nmxy = new int[M * K][L];
nmxysum = new int[M * K];
// sequence node
nmyz = new int[M * L][J];
nmyzsum = new int[M * L];
// hidden edge
x = new int[M][];
for (int m = 0; m < M; m++) {
x[m] = new int[w[m].length];
}
// hidden edge
y = new int[M][];
for (int m = 0; m < M; m++) {
y[m] = new int[w[m].length];
}
// hidden edge
z = new int[M][];
for (int m = 0; m < M; m++) {
z[m] = new int[w[m].length];
}
// topic node
nzw = new int[J][V];
nzwsum = new int[J];
// initialise randomly
// major loop, sequence [m][n]
for (int m = 0; m < M; m++) {
// minor loop, sequence [m][n]
for (int n = 0; n < w[m].length; n++) {
// sample edge values
int hx = rand.nextInt(K);
int hy = rand.nextInt(L);
int hz = rand.nextInt(J);
// assign topics
x[m][n] = hx;
y[m][n] = hy;
z[m][n] = hz;
// increment counts
nmx[m][hx]++;
mxsel = K * m + hx;
nmxy[mxsel][hy]++;
nmxysum[mxsel]++;
mysel = L * m + hy;
nmyz[mysel][hz]++;
nmyzsum[mysel]++;
nzw[hz][w[m][n]]++;
nzwsum[hz]++;
} // for n
} // for m
} // init
// //////////////// query initialisation //////////////////
// initialisation
public void initq() {
// component selectors
int mxsel = -1;
int mxjsel = -1;
int mysel = -1;
int myjsel = -1;
// sequence node
nmxq = new int[Mq][K];
// sequence node
nmxyq = new int[Mq * K][L];
nmxysumq = new int[Mq * K];
// sequence node
nmyzq = new int[Mq * L][J];
nmyzsumq = new int[Mq * L];
// hidden edge
xq = new int[Mq][];
for (int m = 0; m < Mq; m++) {
xq[m] = new int[wq[m].length];
}
// hidden edge
yq = new int[Mq][];
for (int m = 0; m < Mq; m++) {
yq[m] = new int[wq[m].length];
}
// hidden edge
zq = new int[Mq][];
for (int m = 0; m < Mq; m++) {
zq[m] = new int[wq[m].length];
}
// topic node
// compute parameters
phi = new double[J][V];
for (int hz = 0; hz < J; hz++) {
for (int t = 0; t < V; t++) {
phi[hz][t] = (nzw[hz][t] + beta) / (nzwsum[hz] + betasum);
} // t
} // h
// initialise randomly
// major loop, sequence [m][n]
for (int m = 0; m < Mq; m++) {
// minor loop, sequence [m][n]
for (int n = 0; n < wq[m].length; n++) {
// sample edge values
int hx = rand.nextInt(K);
int hy = rand.nextInt(L);
int hz = rand.nextInt(J);
// assign topics
xq[m][n] = hx;
yq[m][n] = hy;
zq[m][n] = hz;
// increment counts
nmxq[m][hx]++;
mxsel = K * m + hx;
nmxyq[mxsel][hy]++;
nmxysumq[mxsel]++;
mysel = L * m + hy;
nmyzq[mysel][hz]++;
nmyzsumq[mysel]++;
} // for n
} // for m
} // initq
// //////////////// main kernel //////////////////
// Gibbs kernel
public void run(int niter) {
// iteration loop
for (int iter = 0; iter < niter; iter++) {
System.out.println(iter);
// major loop, sequence [m][n]
for (int m = 0; m < M; m++) {
// component selectors
int mxsel = -1;
int mxjsel = -1;
int mysel = -1;
int myjsel = -1;
// minor loop, sequence [m][n]
for (int n = 0; n < w[m].length; n++) {
double psum;
double u;
// *** sample topic x[m][n] ***
// assign topics
int hx = x[m][n];
// decrement counts
nmx[m][hx]--;
mxsel = K * m + hx;
nmxy[mxsel][y[m][n]]--;
nmxysum[mxsel]--;
// compute weights
/*
* &p(x_{m,n} \eq x\; |\;\vec x_{-m,n}, \vec y, \vec z, \vec
* w, \cdot) \notag\\ &\qquad\propto (n^{-mn}_{m,x} + \alpha
* ) \cdot \frac{n^{-mn}_{mx,y} + \gamma_{x, y} }{\sum_{y}
* n^{-mn}_{mx,y} + \gamma_{x, y}}
*/
psum = 0;
// hidden edge
for (hx = 0; hx < K; hx++) {
mxsel = K * m + hx;
mxjsel = hx;
pp[hx] = (nmx[m][hx] + alpha)
* (nmxy[mxsel][y[m][n]] + gamma[mxjsel][y[m][n]])
/ (nmxysum[mxsel] + gammasum[mxjsel]);
psum += pp[hx];
} // for h
// sample topics
u = rand.nextDouble() * psum;
psum = 0;
// each edge value
for (hx = 0; hx < K; hx++) {
psum += pp[hx];
if (u <= psum)
break;
} // h
// assign topics
x[m][n] = hx;
// increment counts
nmx[m][hx]++;
mxsel = K * m + hx;
nmxy[mxsel][y[m][n]]++;
nmxysum[mxsel]++;
// *** sample topic y[m][n] ***
// assign topics
int hy = y[m][n];
// decrement counts
nmxy[mxsel][hy]--;
nmxysum[mxsel]--;
mysel = L * m + hy;
nmyz[mysel][z[m][n]]--;
nmyzsum[mysel]--;
// compute weights
/*
* &p(y_{m,n} \eq y\; |\;\vec x, \vec y_{-m,n}, \vec z, \vec
* w, \cdot) \notag\\ &\qquad\propto \frac{n^{-mn}_{mx,y} +
* \gamma_{x, y} }{\sum_{y} n^{-mn}_{mx,y} + \gamma_{x, y}}
* \cdot \frac{n^{-mn}_{my,z} + \delta_{y, z} }{\sum_{z}
* n^{-mn}_{my,z} + \delta_{y, z}}
*/
psum = 0;
// hidden edge
for (hy = 0; hy < L; hy++) {
mysel = L * m + hy;
myjsel = hy;
pp[hy] = (nmxy[mxsel][hy] + gamma[mxjsel][hy])
/ (nmxysum[mxsel] + gammasum[mxjsel])
* (nmyz[mysel][z[m][n]] + delta[myjsel][z[m][n]])
/ (nmyzsum[mysel] + deltasum[myjsel]);
psum += pp[hy];
} // for h
// sample topics
u = rand.nextDouble() * psum;
psum = 0;
// each edge value
for (hy = 0; hy < L; hy++) {
psum += pp[hy];
if (u <= psum)
break;
} // h
// assign topics
y[m][n] = hy;
// increment counts
nmxy[mxsel][hy]++;
nmxysum[mxsel]++;
mysel = L * m + hy;
nmyz[mysel][z[m][n]]++;
nmyzsum[mysel]++;
// *** sample topic z[m][n] ***
// assign topics
int hz = z[m][n];
// decrement counts
nmyz[mysel][hz]--;
nmyzsum[mysel]--;
nzw[hz][w[m][n]]--;
nzwsum[hz]--;
// compute weights
/*
* &p(z_{m,n} \eq z\; |\;\vec x, \vec y, \vec z_{-m,n}, \vec
* w, \cdot) \notag\\ &\qquad\propto \frac{n^{-mn}_{my,z} +
* \delta_{y, z} }{\sum_{z} n^{-mn}_{my,z} + \delta_{y, z}}
* \cdot \frac{n^{-mn}_{z,w} + \beta }{\sum_{w}
* n^{-mn}_{z,w} + \beta}
*/
psum = 0;
// hidden edge
for (hz = 0; hz < J; hz++) {
pp[hz] = (nmyz[mysel][hz] + delta[myjsel][hz])
/ (nmyzsum[mysel] + deltasum[myjsel])
* (nzw[hz][w[m][n]] + beta)
/ (nzwsum[hz] + betasum);
psum += pp[hz];
} // for h
// sample topics
u = rand.nextDouble() * psum;
psum = 0;
// each edge value
for (hz = 0; hz < J; hz++) {
psum += pp[hz];
if (u <= psum)
break;
} // h
// assign topics
z[m][n] = hz;
// increment counts
nmyz[mysel][hz]++;
nmyzsum[mysel]++;
nzw[hz][w[m][n]]++;
nzwsum[hz]++;
} // for n
} // for m
// estimate hyperparameters
estAlpha();
} // for iter
} // for run
// //////////////// query kernel //////////////////
// Gibbs kernel
public void runq(int niterq) {
// iteration loop
for (int iter = 0; iter < niterq; iter++) {
System.out.println(iter);
// major loop, sequence [m][n]
for (int m = 0; m < Mq; m++) {
// component selectors
int mxsel = -1;
int mxjsel = -1;
int mysel = -1;
int myjsel = -1;
// minor loop, sequence [m][n]
for (int n = 0; n < wq[m].length; n++) {
double psum;
double u;
// *** sample topic x[m][n] ***
// assign topics
int hx = xq[m][n];
// decrement counts
nmxq[m][hx]--;
mxsel = K * m + hx;
nmxyq[mxsel][yq[m][n]]--;
nmxysumq[mxsel]--;
// compute weights
/*
* &p(x_{m,n} \eq x\; |\;\vec x_{-m,n}, \vec y, \vec z, \vec
* w, \cdot) \notag\\ &\qquad\propto (n^{-mn}_{m,x} + \alpha
* ) \cdot \frac{n^{-mn}_{mx,y} + \gamma_{x, y} }{\sum_{y}
* n^{-mn}_{mx,y} + \gamma_{x, y}}
*/
psum = 0;
// hidden edge
for (hx = 0; hx < K; hx++) {
mxsel = K * m + hx;
mxjsel = hx;
pp[hx] = (nmxq[m][hx] + alpha)
* (nmxyq[mxsel][yq[m][n]] + gamma[mxjsel][yq[m][n]])
/ (nmxysumq[mxsel] + gammasum[mxjsel]);
psum += pp[hx];
} // for h
// sample topics
u = rand.nextDouble() * psum;
psum = 0;
// each edge value
for (hx = 0; hx < K; hx++) {
psum += pp[hx];
if (u <= psum)
break;
} // h
// assign topics
xq[m][n] = hx;
// increment counts
nmxq[m][hx]++;
mxsel = K * m + hx;
nmxyq[mxsel][yq[m][n]]++;
nmxysumq[mxsel]++;
// *** sample topic y[m][n] ***
// assign topics
int hy = yq[m][n];
// decrement counts
nmxyq[mxsel][hy]--;
nmxysumq[mxsel]--;
mysel = L * m + hy;
nmyzq[mysel][zq[m][n]]--;
nmyzsumq[mysel]--;
// compute weights
/*
* &p(y_{m,n} \eq y\; |\;\vec x, \vec y_{-m,n}, \vec z, \vec
* w, \cdot) \notag\\ &\qquad\propto \frac{n^{-mn}_{mx,y} +
* \gamma_{x, y} }{\sum_{y} n^{-mn}_{mx,y} + \gamma_{x, y}}
* \cdot \frac{n^{-mn}_{my,z} + \delta_{y, z} }{\sum_{z}
* n^{-mn}_{my,z} + \delta_{y, z}}
*/
psum = 0;
// hidden edge
for (hy = 0; hy < L; hy++) {
mysel = L * m + hy;
myjsel = hy;
pp[hy] = (nmxyq[mxsel][hy] + gamma[mxjsel][hy])
/ (nmxysumq[mxsel] + gammasum[mxjsel])
* (nmyzq[mysel][zq[m][n]] + delta[myjsel][zq[m][n]])
/ (nmyzsumq[mysel] + deltasum[myjsel]);
psum += pp[hy];
} // for h
// sample topics
u = rand.nextDouble() * psum;
psum = 0;
// each edge value
for (hy = 0; hy < L; hy++) {
psum += pp[hy];
if (u <= psum)
break;
} // h
// assign topics
yq[m][n] = hy;
// increment counts
nmxyq[mxsel][hy]++;
nmxysumq[mxsel]++;
mysel = L * m + hy;
nmyzq[mysel][zq[m][n]]++;
nmyzsumq[mysel]++;
// *** sample topic z[m][n] ***
// assign topics
int hz = zq[m][n];
// decrement counts
nmyzq[mysel][hz]--;
nmyzsumq[mysel]--;
// compute weights
/*
* &p(z_{m,n} \eq z\; |\;\vec x, \vec y, \vec z_{-m,n}, \vec
* w, \cdot) \notag\\ &\qquad\propto \frac{n^{-mn}_{my,z} +
* \delta_{y, z} }{\sum_{z} n^{-mn}_{my,z} + \delta_{y, z}}
* \cdot \phi_{z,w}
*/
psum = 0;
// hidden edge
for (hz = 0; hz < J; hz++) {
pp[hz] = (nmyzq[mysel][hz] + delta[myjsel][hz])
/ (nmyzsumq[mysel] + deltasum[myjsel])
* phi[hz][wq[m][n]];
psum += pp[hz];
} // for h
// sample topics
u = rand.nextDouble() * psum;
psum = 0;
// each edge value
for (hz = 0; hz < J; hz++) {
psum += pp[hz];
if (u <= psum)
break;
} // h
// assign topics
zq[m][n] = hz;
// increment counts
nmyzq[mysel][hz]++;
nmyzsumq[mysel]++;
} // for n
} // for m
} // for iter
} // for runq
// //////////////// hyperparameters //////////////////
// update hyperparameters
public void estAlpha() {
if (iter < 15) {
return;
}
// component selectors
int mxsel = -1;
int mxjsel = -1;
int mysel = -1;
int myjsel = -1;
// Note: assuming non-informative gamma priors (1,0)
// hyperparameter for theta
int[] nmxsum = new int[M];
// all components
for (int m = 0; m < M; m++) {
nmxsum[m] = w[m].length;
} // for m
double xalpha = DirichletEstimation.estimateAlphaMap(nmx, nmxsum,
alpha, 1., 0.);
if (alpha < 2.) {
alpha = (alpha + xalpha) / 2;
} // < 2
// hyperparameter for thetax
// filter nkt and nktsum though jSel index space.
int[] mx2j = new int[Mq * K];
// for parent values
for (int m = 0; m < M; m++) {
// for parent values
for (int hx = 0; hx < K; hx++) {
mxsel = K * m + hx;
mxjsel = hx;
mx2j[mxsel] = mxjsel;
} // for h
} // for h
double[][] xgamma = DirichletEstimation.estimateAlphaMapSub(nmxy,
nmxysum, mx2j, gamma, 1., 0.);
if (gamma[0][0] < 2.) {
// all component groups
for (int j = 0; j < K; j++) {
// all values
for (int t = 0; t < L; t++) {
gamma[j][t] = (xgamma[j][t] + gamma[j][t]) / 2;
} // for t
} // for j
} // < 2
// hyperparameter for thetay
// filter nkt and nktsum though jSel index space.
int[] my2j = new int[Mq * L];
// for parent values
for (int m = 0; m < M; m++) {
// for parent values
for (int hy = 0; hy < L; hy++) {
mysel = L * m + hy;
myjsel = hy;
my2j[mysel] = myjsel;
} // for h
} // for h
double[][] xdelta = DirichletEstimation.estimateAlphaMapSub(nmyz,
nmyzsum, my2j, delta, 1., 0.);
if (delta[0][0] < 2.) {
// all component groups
for (int j = 0; j < L; j++) {
// all values
for (int t = 0; t < J; t++) {
delta[j][t] = (xdelta[j][t] + delta[j][t]) / 2;
} // for t
} // for j
} // < 2
// hyperparameter for phi
double xbeta = DirichletEstimation.estimateAlphaMap(nzw, nzwsum, beta,
1., 0.);
if (beta < 2.) {
beta = (beta + xbeta) / 2;
} // < 2
} // updateHyper
// //////////////// perplexity //////////////////
// calculate perplexity value
public double ppx() {
double loglik = 0;
// component selectors
int mxsel = -1;
int mxjsel = -1;
int mysel = -1;
int myjsel = -1;
// compute sequence node parameters
double[][] thetaq = new double[Mq][K];
// for parent values
for (int m = 0; m < Mq; m++) {
int nmxmq = 0;
for (int x = 0; x < K; x++) {
nmxmq += nmxq[m][x];
} // for x
for (int x = 0; x < K; x++) {
thetaq[m][x] = (nmxq[m][x] + alpha) / (nmxmq + alphasum);
} // for x
} // for parent h
double[][] thetaxq = new double[Mq * K][L];
// for parent values
for (int m = 0; m < Mq; m++) {
// for parent values
for (int hx = 0; hx < K; hx++) {
for (int y = 0; y < L; y++) {
mxsel = K * m + hx;
mxjsel = hx;
thetaxq[mxsel][y] = (nmxyq[mxsel][y] + gamma[mxjsel][y])
/ (nmxysumq[mxsel] + gammasum[mxjsel]);
} // for y
} // for parent h
} // for parent h
double[][] thetayq = new double[Mq * L][J];
// for parent values
for (int m = 0; m < Mq; m++) {
// for parent values
for (int hy = 0; hy < L; hy++) {
for (int z = 0; z < J; z++) {
mysel = L * m + hy;
myjsel = hy;
thetayq[mysel][z] = (nmyzq[mysel][z] + delta[myjsel][z])
/ (nmyzsumq[mysel] + deltasum[myjsel]);
} // for z
} // for parent h
} // for parent h
// compute ppx
// major loop, sequence [m][n]
for (int m = 0; m < Mq; m++) {
// minor loop, sequence [m][n]
for (int n = 0; n < wq[m].length; n++) {
double sum = 0;
// hidden edge
for (int hx = 0; hx < K; hx++) {
// hidden edge
for (int hy = 0; hy < L; hy++) {
// hidden edge
for (int hz = 0; hz < J; hz++) {
mxsel = K * m + hx;
mysel = L * m + hy;
sum += thetaq[m][hx] * thetaxq[mxsel][hy]
* thetayq[mysel][hz] * phi[hz][wq[m][n]];
} // for h
} // for h
} // for h
loglik += Math.log(sum);
} // for n
} // for m
return Math.exp(-loglik / Wq);
} // ppx
// //////////////// monitor string //////////////////
// describe class and parameters
public String toString() {
return "PAM5:\nm >> (theta[m] | alpha) >> x[m][n]\n\t"
+ "m, x[m][n] >> (thetax[m,x] | gamma[x]) >> y[m][n]\n\t"
+ "m, y[m][n] >> (thetay[m,y] | delta[y]) >> z[m][n]\n\t"
+ "z[m][n] >> (phi[z] | beta) >> w[m][n]\n\t"
+ "\n\t"
+ "\n"
+ String.format(
"Pam5iGibbsSampler: \n"
+ "M = %d Mq = %d W = %d Wq = %d \n"
+ "K = %d L = %d J = %d V = %d \n"
+ "alpha = %2.5f gamma[0][0] = %2.5f delta[0][0] = %2.5f beta = %2.5f ",
M, Mq, W, Wq, K, L, J, V, alpha, gamma[0][0],
delta[0][0], beta);
}
} // Pam5iGibbsSampler