/**
computes matrices of n and m variables (expected values for how often a
certain parameter from A or B is used)
computes Baum-Welch variables implicit
@return 0/-1 success/error
@param mo: pointer to a ghmm_dmodel
@param alpha: matrix of forward variables
@param backward: matrix of backward variables
@param scale: scaling vector from forward-backward-algorithm
@param seq: sequence in internal representation
@param seq_len: length of sequence
@param matrix_b: matrix for parameters from B (n_b or m_b)
@param matrix_a: matrix for parameters from A (n_a or m_a)
@param vec_pi: vector for parameters in PI (n_pi or m_pi)
*/
int ghmm_dmodel_label_gradient_expectations (ghmm_dmodel* mo, double **alpha,
double **beta, double *scale, int *seq,
int seq_len, double **matrix_b,
double *matrix_a, double *vec_pi)
{
#define CUR_PROC "ghmm_dmodel_label_gradient_expectations"
int h, i, j, t;
int size, j_id, e_index;
double gamma, xi;
double foba_sum;
/* initialise matrices with zeros */
for (i = 0; i < mo->N; i++) {
for (j = 0; j < mo->N; j++)
matrix_a[i * mo->N + j] = 0;
size = ghmm_ipow (mo, mo->M, mo->order[i] + 1);
for (h = 0; h < size; h++)
matrix_b[i][h] = 0;
}
for (t = 0; t < seq_len; t++) {
/* sum products of forward and backward variables over all states: */
foba_sum = 0.0;
for (i = 0; i < mo->N; i++)
foba_sum += alpha[t][i] * beta[t][i];
if (GHMM_EPS_PREC > fabs (foba_sum)) {
printf
("gradescent_compute_expect: foba_sum (%g) smaller as EPS_PREC (%g). t = %d.\n",
foba_sum, GHMM_EPS_PREC, t);
return -1;
}
for (i = 0; i < mo->N; i++) {
/* compute gamma implicit */
gamma = alpha[t][i] * beta[t][i] / foba_sum;
/* n_pi is easiest: n_pi(i) = gamma(0,i) */
if (0 == t)
vec_pi[i] = gamma;
/* n_b(i,c) = sum[t, hist(t)=c | gamma(t,i)] / sum[t | gamma(t,i)] */
e_index = get_emission_index (mo, i, seq[t], t);
if (-1 != e_index)
matrix_b[i][e_index] += gamma;
}
/* updating history, xi needs the right e_index for the next state */
update_emission_history (mo, seq[t]);
for (i = 0; i < mo->N; i++) {
/* n_a(i,j) = sum[t=0..T-2 | xi(t,i,j)] / sum[t=0..T-2 | gamma(t,i)] */
/* compute xi only till the state before the last */
for (j = 0; (j < mo->s[i].out_states) && (t < seq_len - 1); j++) {
j_id = mo->s[i].out_id[j];
/* compute xi implicit */
xi = 0;
e_index = get_emission_index (mo, j_id, seq[t + 1], t + 1);
if (e_index != -1)
xi = alpha[t][i] * beta[t + 1][j_id] * mo->s[i].out_a[j]
* mo->s[j_id].b[e_index] / (scale[t + 1] * foba_sum);
matrix_a[i * mo->N + j_id] += xi;
}
}
}
return 0;
#undef CUR_PROC
}
/*============================================================================*/
int *ghmm_dmodel_label_kbest (ghmm_dmodel * mo, int *o_seq, int seq_len, int k, double *log_p)
{
#define CUR_PROC "ghmm_dl_kbest"
int i, t, c, l, m; /* counters */
int no_oldHyps; /* number of hypotheses until position t-1 */
int b_index, i_id; /* index for addressing states' b arrays */
int no_labels = 0;
int exists, g_nr;
int *states_wlabel;
int *label_max_out;
char *str;
/* logarithmized transition matrix A, log(a(i,j)) => log_a[i*N+j],
1.0 for zero probability */
double **log_a;
/* matrix of hypotheses, holds for every position in the sequence a list
of hypotheses */
hypoList **h;
hypoList *hP;
/* vectors for rows in the matrices */
int *hypothesis;
/* pointer & prob. of the k most probable hypotheses for each state
- matrices of dimensions #states x k: argm(i,l) => argmaxs[i*k+l] */
double *maxima;
hypoList **argmaxs;
/* pointer to & probability of most probable hypothesis in a certain state */
hypoList *argmax;
double sum;
/* break if sequence empty or k<1: */
if (seq_len <= 0 || k <= 0)
return NULL;
ARRAY_CALLOC (h, seq_len);
/* 1. Initialization (extend empty hypothesis to #labels hypotheses of
length 1): */
/* get number of labels (= maximum label + 1)
and number of states with those labels */
ARRAY_CALLOC (states_wlabel, mo->N);
ARRAY_CALLOC (label_max_out, mo->N);
for (i = 0; i < mo->N; i++) {
c = mo->label[i];
states_wlabel[c]++;
if (c > no_labels)
no_labels = c;
if (mo->s[i].out_states > label_max_out[c])
label_max_out[c] = mo->s[i].out_states;
}
/* add one to the maximum label to get the number of labels */
no_labels++;
ARRAY_REALLOC (states_wlabel, no_labels);
ARRAY_REALLOC (label_max_out, no_labels);
/* initialize h: */
hP = h[0];
for (i = 0; i < mo->N; i++) {
if (mo->s[i].pi > KBEST_EPS) {
/* printf("Found State %d with initial probability %f\n", i, mo->s[i].pi); */
exists = 0;
while (hP != NULL) {
if (hP->hyp_c == mo->label[i]) {
/* add entry to the gamma list */
g_nr = hP->gamma_states;
hP->gamma_id[g_nr] = i;
hP->gamma_a[g_nr] =
log (mo->s[i].pi) +
log (mo->s[i].b[get_emission_index (mo, i, o_seq[0], 0)]);
hP->gamma_states = g_nr + 1;
exists = 1;
break;
}
else
hP = hP->next;
}
if (!exists) {
ighmm_hlist_insert (&(h[0]), mo->label[i], NULL);
/* initiallize gamma-array with safe size (number of states) and add the first entry */
ARRAY_MALLOC (h[0]->gamma_a, states_wlabel[mo->label[i]]);
ARRAY_MALLOC (h[0]->gamma_id, states_wlabel[mo->label[i]]);
h[0]->gamma_id[0] = i;
h[0]->gamma_a[0] =
log (mo->s[i].pi) +
log (mo->s[i].b[get_emission_index (mo, i, o_seq[0], 0)]);
h[0]->gamma_states = 1;
h[0]->chosen = 1;
}
hP = h[0];
}
}
/* reallocating the gamma list to the real size */
hP = h[0];
while (hP != NULL) {
ARRAY_REALLOC (hP->gamma_a, hP->gamma_states);
ARRAY_REALLOC (hP->gamma_id, hP->gamma_states);
hP = hP->next;
}
/* calculate transition matrix with logarithmic values: */
log_a = kbest_buildLogMatrix (mo->s, mo->N);
/* initialize temporary arrays: */
ARRAY_MALLOC (maxima, mo->N * k); /* for each state save k */
ARRAY_MALLOC (argmaxs, mo->N * k);
/*------ Main loop: Cycle through the sequence: ------*/
for (t = 1; t < seq_len; t++) {
/* put o_seq[t-1] in emission history: */
update_emission_history (mo, o_seq[t - 1]);
/* 2. Propagate hypotheses forward and update gamma: */
no_oldHyps =
ighmm_hlist_prop_forward (mo, h[t - 1], &(h[t]), no_labels, states_wlabel,
label_max_out);
/* printf("t = %d (%d), no of old hypotheses = %d\n", t, seq_len, no_oldHyps); */
/*-- calculate new gamma: --*/
hP = h[t];
/* cycle through list of hypotheses */
while (hP != NULL) {
for (i = 0; i < hP->gamma_states; i++) {
/* if hypothesis hP ends with label of state i:
gamma(i,c):= log(sum(exp(a(j,i)*exp(oldgamma(j,old_c)))))
+ log(b[i](o_seq[t]))
else: gamma(i,c):= -INF (represented by 1.0) */
i_id = hP->gamma_id[i];
hP->gamma_a[i] = ighmm_log_gamma_sum (log_a[i_id], &mo->s[i_id], hP->parent);
b_index = get_emission_index (mo, i_id, o_seq[t], t);
if (b_index < 0) {
hP->gamma_a[i] = 1.0;
if (mo->order[i_id] > t)
continue;
else {
str = ighmm_mprintf (NULL, 0,
"i_id: %d, o_seq[%d]=%d\ninvalid emission index!\n",
i_id, t, o_seq[t]);
GHMM_LOG(LCONVERTED, str);
m_free (str);
}
}
else
hP->gamma_a[i] += log (mo->s[i_id].b[b_index]);
/*printf("%g = %g\n", log(mo->s[i_id].b[b_index]), hP->gamma_a[i]); */
if (hP->gamma_a[i] > 0.0) {
GHMM_LOG(LCONVERTED, "gamma to large. ghmm_dl_kbest failed\n");
exit (1);
}
}
hP = hP->next;
}
/* 3. Choose the k most probable hypotheses for each state and discard all
hypotheses that were not chosen: */
/* initialize temporary arrays: */
for (i = 0; i < mo->N * k; i++) {
maxima[i] = 1.0;
argmaxs[i] = NULL;
}
/* cycle through hypotheses & calculate the k most probable hypotheses for
each state: */
hP = h[t];
while (hP != NULL) {
for (i = 0; i < hP->gamma_states; i++) {
i_id = hP->gamma_id[i];
if (hP->gamma_a[i] > KBEST_EPS)
continue;
/* find first best hypothesis that is worse than current hypothesis: */
for (l = 0;
l < k && maxima[i_id * k + l] < KBEST_EPS
&& maxima[i_id * k + l] > hP->gamma_a[i]; l++);
if (l < k) {
/* for each m>l: m'th best hypothesis becomes (m+1)'th best */
for (m = k - 1; m > l; m--) {
argmaxs[i_id * k + m] = argmaxs[i_id * k + m - 1];
maxima[i_id * k + m] = maxima[i_id * k + m - 1];
}
/* save new l'th best hypothesis: */
maxima[i_id * k + l] = hP->gamma_a[i];
argmaxs[i_id * k + l] = hP;
}
}
hP = hP->next;
}
/* set 'chosen' for all hypotheses from argmaxs array: */
for (i = 0; i < mo->N * k; i++)
/* only choose hypotheses whose prob. is at least threshold*max_prob */
if (maxima[i] != 1.0
&& maxima[i] >= KBEST_THRESHOLD + maxima[(i % mo->N) * k])
argmaxs[i]->chosen = 1;
/* remove hypotheses that were not chosen from the lists: */
/* remove all hypotheses till the first chosen one */
while (h[t] != NULL && 0 == h[t]->chosen)
ighmm_hlist_remove (&(h[t]));
/* remove all other not chosen hypotheses */
if (!h[t]) {
GHMM_LOG(LCONVERTED, "No chosen hypothesis. ghmm_dl_kbest failed\n");
exit (1);
}
hP = h[t];
while (hP->next != NULL) {
if (1 == hP->next->chosen)
hP = hP->next;
else
ighmm_hlist_remove (&(hP->next));
}
}
/* dispose of temporary arrays: */
m_free(states_wlabel);
m_free(label_max_out);
m_free(argmaxs);
m_free(maxima);
/* transition matrix is no longer needed from here on */
for (i=0; i<mo->N; i++)
m_free(log_a[i]);
m_free(log_a);
/* 4. Save the hypothesis with the highest probability over all states: */
hP = h[seq_len - 1];
argmax = NULL;
*log_p = 1.0; /* log_p will store log of maximum summed probability */
while (hP != NULL) {
/* sum probabilities for each hypothesis over all states: */
sum = ighmm_cvector_log_sum (hP->gamma_a, hP->gamma_states);
/* and select maximum sum */
if (sum < KBEST_EPS && (*log_p == 1.0 || sum > *log_p)) {
*log_p = sum;
argmax = hP;
}
hP = hP->next;
}
/* found a valid path? */
if (*log_p < KBEST_EPS) {
/* yes: extract chosen hypothesis: */
ARRAY_MALLOC (hypothesis, seq_len);
for (i = seq_len - 1; i >= 0; i--) {
hypothesis[i] = argmax->hyp_c;
argmax = argmax->parent;
}
}
else
/* no: return 1.0 representing -INF and an empty hypothesis */
hypothesis = NULL;
/* dispose of calculation matrices: */
hP = h[seq_len - 1];
while (hP != NULL)
ighmm_hlist_remove (&hP);
free (h);
return hypothesis;
STOP: /* Label STOP from ARRAY_[CM]ALLOC */
GHMM_LOG(LCONVERTED, "ghmm_dl_kbest failed\n");
exit (1);
#undef CUR_PROC
}
