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dirichlet.c
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dirichlet.c
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#include <stdio.h>
#include <math.h>
#include <assert.h>
#include <stdlib.h>
double *dirichlet_alphas;
double *dirichlet_counts;
int dirichlet_num_bags; /* e.g. the number of document classes */
int dirichlet_num_dims; /* e.g. the vocabulary size */
#define COUNTS(BI,DI) (counts[(BI * num_dims) + DI])
/* Read NUM_BAGS, NUM_DIMS, allocate COUNTS and read them from FP */
void
dirichlet_read_counts (FILE *fp,
double **counts_ptr,
int *num_bags_ptr, int *num_dims_ptr)
{
int i, j, num_bags, num_bags_capacity, num_dims;
double *counts;
fscanf (fp, "%d", &num_dims);
assert (num_dims > 1);
num_bags_capacity = 32;
counts = malloc (num_bags_capacity * num_dims * sizeof (double));
for (i = 0; fscanf (fp, "%lf", counts+i) == 1; i++)
{
if (i+1 >= num_bags_capacity * num_dims)
{
num_bags_capacity *= 2;
counts = realloc (counts, num_bags_capacity * num_dims
* sizeof (double));
}
//printf ("count[%d][%d] = %g\n", i/num_dims, i%num_dims, counts[i]);
}
if (i % num_dims)
{
fprintf (stderr, "Counts must be input in groups of %d\n", num_dims);
exit (1);
}
num_bags = i / num_dims;
*num_bags_ptr = num_bags;
*num_dims_ptr = num_dims;
*counts_ptr = counts;
}
/* Calculate the alpha parameters of a Dirichlet by moment matching
and place them in ALPHAS. Return the sum of the alphas. */
double
dirichlet_moment_match (int num_dims, int num_bags, double *counts,
double *alphas)
{
/* The "sample" we will calculate mean and variance for is the
"proportion" of each token type */
double *sample_mean = alloca (num_dims * sizeof (double));
double *sample_variance = alloca (num_dims * sizeof (double));
double *bag_total = alloca (num_bags * sizeof (double));
double x, y, alphas_sum;
int i, j;
/* Count the total number of words in each bag */
for (i = 0; i < num_bags; i++)
{
bag_total[i] = 0;
for (j = 0; j < num_dims; j++)
bag_total[i] += COUNTS(i,j);
assert (bag_total[i]);
}
/* Calculate the sample mean for each dimension, j. This is
= (1/#bags) * Sum_bags (count[bag][j]/total[bag]) */
for (j = 0; j < num_dims; j++)
{
sample_mean[j] = 0;
for (i = 0; i < num_bags; i++)
sample_mean[j] += COUNTS(i,j) / (bag_total[i] * num_bags);
assert (sample_mean[j] == sample_mean[j]);
}
#if 0
for (j = 0; j < num_dims; j++)
printf ("sample mean alpha[%d] = %g\n", j, sample_mean[j]);
#endif
/* Calculate the sample variance for each dimension, j. This is
= E[x^2] - E[x]^2
= [(1/(#bags-1)) * Sum_bags (COUNTS(i,j) / bag_total[i])^2]
- sample_mean[j]^2 */
for (j = 0; j < num_dims; j++)
{
sample_variance[j] = 0;
for (i = 0; i < num_bags; i++)
{
x = COUNTS(i,j) / bag_total[i];
sample_variance[j] += x * x;
}
sample_variance[j] /= num_bags;
/* We now have E[x^2] */
sample_variance[j] -= (sample_mean[j] * sample_mean[j]);
/* We now have E[x^2] - E[x]^2 */
assert (sample_variance[j] == sample_variance[j]);
}
/* Calculate the sum of the alphas */
x = 0;
for (j = 0; j < num_dims - 1; j++)
{
assert (sample_variance[j] > 0);
y = ((sample_mean[j] * (1 - sample_mean[j])) / sample_variance[j]) - 1;
assert (y > 0);
x += log (y);
assert (x == x);
}
x *= 1.0 / (num_dims - 1.0);
alphas_sum = exp (x);
assert (alphas_sum == alphas_sum);
for (j = 0; j < num_dims; j++)
alphas[j] = sample_mean[j] * alphas_sum;
return alphas_sum;
}
double log_gamma(double x)
{
double result, y, xnum, xden;
int i;
static double d1 = -5.772156649015328605195174e-1;
static double p1[] = {
4.945235359296727046734888e0, 2.018112620856775083915565e2,
2.290838373831346393026739e3, 1.131967205903380828685045e4,
2.855724635671635335736389e4, 3.848496228443793359990269e4,
2.637748787624195437963534e4, 7.225813979700288197698961e3
};
static double q1[] = {
6.748212550303777196073036e1, 1.113332393857199323513008e3,
7.738757056935398733233834e3, 2.763987074403340708898585e4,
5.499310206226157329794414e4, 6.161122180066002127833352e4,
3.635127591501940507276287e4, 8.785536302431013170870835e3
};
static double d2 = 4.227843350984671393993777e-1;
static double p2[] = {
4.974607845568932035012064e0, 5.424138599891070494101986e2,
1.550693864978364947665077e4, 1.847932904445632425417223e5,
1.088204769468828767498470e6, 3.338152967987029735917223e6,
5.106661678927352456275255e6, 3.074109054850539556250927e6
};
static double q2[] = {
1.830328399370592604055942e2, 7.765049321445005871323047e3,
1.331903827966074194402448e5, 1.136705821321969608938755e6,
5.267964117437946917577538e6, 1.346701454311101692290052e7,
1.782736530353274213975932e7, 9.533095591844353613395747e6
};
static double d4 = 1.791759469228055000094023e0;
static double p4[] = {
1.474502166059939948905062e4, 2.426813369486704502836312e6,
1.214755574045093227939592e8, 2.663432449630976949898078e9,
2.940378956634553899906876e10, 1.702665737765398868392998e11,
4.926125793377430887588120e11, 5.606251856223951465078242e11
};
static double q4[] = {
2.690530175870899333379843e3, 6.393885654300092398984238e5,
4.135599930241388052042842e7, 1.120872109616147941376570e9,
1.488613728678813811542398e10, 1.016803586272438228077304e11,
3.417476345507377132798597e11, 4.463158187419713286462081e11
};
static double c[] = {
-1.910444077728e-03, 8.4171387781295e-04,
-5.952379913043012e-04, 7.93650793500350248e-04,
-2.777777777777681622553e-03, 8.333333333333333331554247e-02,
5.7083835261e-03
};
static double a = 0.6796875;
if((x <= 0.5) || ((x > a) && (x <= 1.5))) {
if(x <= 0.5) {
result = -log(x);
/* Test whether X < machine epsilon. */
if(x+1 == 1) {
return result;
}
}
else {
result = 0;
x = (x - 0.5) - 0.5;
}
xnum = 0;
xden = 1;
for(i=0;i<8;i++) {
xnum = xnum * x + p1[i];
xden = xden * x + q1[i];
}
result += x*(d1 + x*(xnum/xden));
}
else if((x <= a) || ((x > 1.5) && (x <= 4))) {
if(x <= a) {
result = -log(x);
x = (x - 0.5) - 0.5;
}
else {
result = 0;
x -= 2;
}
xnum = 0;
xden = 1;
for(i=0;i<8;i++) {
xnum = xnum * x + p2[i];
xden = xden * x + q2[i];
}
result += x*(d2 + x*(xnum/xden));
}
else if(x <= 12) {
x -= 4;
xnum = 0;
xden = -1;
for(i=0;i<8;i++) {
xnum = xnum * x + p4[i];
xden = xden * x + q4[i];
}
result = d4 + x*(xnum/xden);
}
/* X > 12 */
else {
y = log(x);
result = x*(y - 1) - y*0.5 + .9189385332046727417803297;
x = 1/x;
y = x*x;
xnum = c[6];
for(i=0;i<6;i++) {
xnum = xnum * y + c[i];
}
xnum *= x;
result += xnum;
}
return result;
}
double
dirichlet_multinomial_log_evidence (int num_dims, int num_bags,
double *counts,
double *alphas)
{
double evidence, alphas_sum;
double *bag_total = alloca (num_bags * sizeof (double));
int i, j;
/* Calculate the sum of the alphas */
alphas_sum = 0;
for (j = 0; j < num_dims; j++)
alphas_sum += alphas[j];
/* Calculate the bag totals */
for (i = 0; i < num_bags; i++)
{
bag_total[i] = 0;
for (j = 0; j < num_dims; j++)
bag_total[i] += COUNTS(i,j);
}
evidence = 0;
for (i = 0; i < num_bags; i++)
{
evidence += (log_gamma (alphas_sum)
- log_gamma (bag_total[i] + alphas_sum));
for (j = 0; j < num_dims; j++)
evidence += log_gamma(COUNTS(i,j) + alphas[j]) - log_gamma(alphas[j]);
}
return evidence;
}
void
print_usage (const char *argv[])
{
fprintf (stderr, "usage: \n");
}
int
main (int argc, const char *argv[])
{
double sum;
int i, j, argi, num_classes;
/* Can be difference from num_dims when there are multiple classes */
int num_alphas;
int index_of_correct_class = -1;
num_classes = 0;
for (argi = 1; argi < argc; argi++)
{
if (argv[argi][0] != '-')
break;
switch (argv[argi][1])
{
case 'c':
/* Do classification of bags according to evidence from
several different dirichlets */
num_classes = atoi (argv[++argi]);
break;
case 'I':
index_of_correct_class = atoi (argv[++argi]);
break;
default:
fprintf (stderr, "%s: unrecognized option `%s'\n",
argv[0], argv[argi]);
print_usage (argv);
exit (-1);
}
}
if (argi < argc)
{
/* Get the alphas from the command line and then calculate the
evidence of the counts read in on stdin */
int dirichlet_num_dims_capacity = 32;
double evidence;
dirichlet_alphas = malloc (dirichlet_num_dims_capacity * sizeof(double));
for (num_alphas = 0; argi < argc; argi++, num_alphas++)
{
if (num_alphas >= dirichlet_num_dims_capacity)
{
dirichlet_num_dims_capacity *= 2;
dirichlet_alphas =
realloc (dirichlet_alphas,
dirichlet_num_dims_capacity * sizeof(double));
}
dirichlet_alphas[num_alphas] = atof (argv[argi]);
//printf("alpha[%d] = %g\n",num_alphas,dirichlet_alphas[num_alphas]);
}
dirichlet_read_counts (stdin, &dirichlet_counts,
&dirichlet_num_bags, &dirichlet_num_dims);
assert ((num_classes && num_alphas % dirichlet_num_dims == 0)
|| num_alphas == dirichlet_num_dims);
if (num_classes)
{
double *ev = alloca (num_classes * sizeof (double));
double max_ev;
int c, max_c, num_bags_correct;
assert (num_alphas == dirichlet_num_dims * num_classes);
num_bags_correct = 0;
for (i = 0; i < dirichlet_num_bags; i++)
{
max_c = -1;
max_ev = -DBL_MAX;
for (c = 0; c < num_classes; c++)
{
ev[c] = dirichlet_multinomial_log_evidence
(dirichlet_num_dims, 1,
dirichlet_counts + (i * dirichlet_num_dims),
dirichlet_alphas + (c * dirichlet_num_dims));
if (ev[c] > max_ev)
{
max_ev = ev[c];
max_c = c;
}
}
if (index_of_correct_class != -1
&& max_c == index_of_correct_class)
num_bags_correct++;
printf ("bag[%d] class=%d ", i, max_c);
for (c = 0; c < num_classes; c++)
printf ("class[%d]=%g ", c, ev[c]);
printf ("\n");
}
if (index_of_correct_class != -1)
printf ("Correct %d/%d = %g\n",
num_bags_correct, dirichlet_num_bags,
((float)num_bags_correct)/dirichlet_num_bags);
}
else
{
evidence = dirichlet_multinomial_log_evidence
(dirichlet_num_dims, dirichlet_num_bags,
dirichlet_counts, dirichlet_alphas);
printf ("log(evidence) = %g\n", evidence);
}
}
else
{
/* Read the counts on stdin, then calculate the alphas by
moment matching */
dirichlet_read_counts (stdin, &dirichlet_counts,
&dirichlet_num_bags, &dirichlet_num_dims);
dirichlet_alphas = malloc (dirichlet_num_dims * sizeof (double));
sum = dirichlet_moment_match (dirichlet_num_dims, dirichlet_num_bags,
dirichlet_counts, dirichlet_alphas);
fprintf (stderr, "n = %d\n", dirichlet_num_bags);
fprintf (stderr, "sum = %g\np = ", sum);
for (j = 0; j < dirichlet_num_dims; j++)
fprintf (stderr, "%9g ", dirichlet_alphas[j] / sum);
fprintf (stderr, "\nalphas =\n ");
for (j = 0; j < dirichlet_num_dims; j++)
printf ("%15f\n", dirichlet_alphas[j]);
}
exit (0);
}