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/* These are tests of distributions. The basic idea is to
--assume a true set of parameters
--generate a fake data set via a few thousand draws from your preferred model.
--estimate the parameters of a new model using the fake data
--assert that the estimated parameters are within epsilon of the true parameters.
*/
#include <apop.h>
#include <unistd.h>
#ifdef _OPENMP
#include <omp.h>
#endif
#define Diff(L, R, eps) Apop_assert(fabs((L)-(R))<(eps), "%g is too different from %g (abitrary limit=%g).", (double)(L), (double)(R), eps);
#define Print_dot if(verbose){printf(".");fflush(NULL);}
#define is_t(d) !strcmp((d)->name, "t distribution")
#define is_bernie(d) !strcmp((d)->name, "Bernoulli distribution")
#define is_binom(d) !strcmp((d)->name, "Binomial distribution")
#define is_beta(d) !strcmp((d)->name, "Beta distribution")
#define is_poisson(d) !strcmp((d)->name, "Poisson distribution")
int verbose = 1;
//The MLE of the t distribution may have non-integer value (why not?)
//Because we started with an integer value, we have to find the floor.
void tfloor(apop_model *dce){
if (is_t(dce)) dce->parameters->vector->data[2] = floor(dce->parameters->vector->data[2]);
}
int estimate_model(apop_data *data, apop_model *dist, char *method, apop_data *true_params){
double *starting_pt;
if(is_bernie(dist))
starting_pt = (double[]){.5};
else starting_pt = (double[]) {1.6, 1.4, 10};
Apop_settings_add_group(dist, apop_mle,
.starting_pt = starting_pt,
.method = method, .verbose =0,
.step_size = 1e-1,
.tolerance = 1e-4, .k = 1.8,
.t_initial = 1, .t_min = .5
);
//Apop_model_add_group(dist, apop_parts_wanted);
if((is_bernie(dist) || is_beta(dist))
&& !strcasecmp(method, "Newton hybrid"))
return 0;
apop_model *e = apop_estimate(data, dist);
tfloor(e);
Diff(0.0, apop_vector_distance(apop_data_pack(true_params), apop_data_pack(e->parameters)), 1e-1);
//if (is_poisson(dist)) Apop_settings_add(dist, apop_parts_wanted, covariance, 'y');
Print_dot
e = apop_estimate_restart(e);
tfloor(e);
Diff(0.0, apop_vector_distance(apop_data_pack(true_params),apop_data_pack(e->parameters)), 1e-1);
if (!strcmp(e->name, "Dirichlet distribution")
|| !strcmp(e->name, "Gamma distribution") //just doesn't work.
||(is_bernie(e) && !strcasecmp(method, "Newton hybrid"))
||(is_t(e)) //requires several restarts to work.
||(!strcmp(e->name, "Exponential distribution")) //imprecise
|| !strcmp(e->name, "Yule distribution")){
//cycle takes all day.
return 0;
}
apop_model *dc = apop_model_copy(dist);
Apop_settings_add(dc, apop_mle, tolerance, 1e-4);
Apop_settings_add(dc, apop_mle, dim_cycle_tolerance, fabs(apop_log_likelihood(data, e))/200.); //within .5%.
Print_dot
apop_model *dce = apop_estimate(data, dc);
Print_dot
Diff(0.0, apop_vector_distance(apop_data_pack(true_params),apop_data_pack(dce->parameters)), 1e-2);
return 0;
}
/*Produce random data, then try to recover the original params */
void test_one_distribution(gsl_rng *r, apop_model *model, apop_model *true_params){
long int runsize = 1e5;
//generate.
apop_data *data = apop_data_calloc(runsize, model->dsize);
if (!strcmp(model->name, "Wishart distribution")){
data = apop_data_calloc(runsize,4);
true_params->parameters->vector->data[0] = runsize-4;
//Use Apop_r to get one row's data and fill it with a draw
for (size_t i=0; i< runsize; i++){
gsl_vector *v = Apop_rv(data, i);
true_params->draw(v->data, r, true_params);
assert(!isnan(apop_sum(v)));
}
} else {
for (size_t i=0; i< runsize; i++){
gsl_vector *v = Apop_rv(data, i);
true_params->draw(v->data, r, true_params);
assert(!isnan(apop_sum(v)));
}
}
if (model->estimate) estimate_model(data, model, "", true_params->parameters);
else { //try all the MLEs.
estimate_model(data, model, "NM simplex", true_params->parameters);
if(is_t(model)) return; //t distribution still v. slow to converge.
estimate_model(data, model, "PR cg", true_params->parameters);
estimate_model(data, model, "Newton Hybrid", true_params->parameters);
}
apop_data_free(data);
}
void test_cdf(gsl_rng *r, apop_model *m){//m is parameterized
//Make random draws from the dist, then find the CDF at that draw
//That should generate a uniform distribution.
if (!m->cdf || is_bernie(m) || is_binom(m))
return;
int drawct = 1e4;
apop_data *draws = apop_data_alloc(drawct, m->dsize);
apop_data *cdfs = apop_data_alloc(drawct);
for (int i=0; i< drawct; i++){
Apop_stopif(apop_draw(Apop_r(draws, i)->matrix->data, r, m), abort(), 0, "bad draw.");
apop_data_set(cdfs, i, -1, apop_cdf(Apop_r(draws, i), m));
}
apop_model *cdf = apop_estimate(apop_data_sort(cdfs), apop_pmf);
apop_model *u01 = apop_model_set_parameters(apop_uniform, 0, 1);
apop_data *ktest = apop_test_kolmogorov(cdf, u01);
//apop_data_show(ktest);
double maxdist = apop_data_get(ktest, .rowname="max distance");
assert(maxdist < .03); //the K-S test has high confidence of rejection with large N
apop_data_free(ktest); apop_data_free(draws); apop_data_free(cdfs);
apop_model_free(u01); apop_model_free(cdf);
}
double true_parameter_v[] = {1.82,2.1};
void test_distributions(gsl_rng *r){
if (verbose) printf("\n");
apop_model* true_params;
apop_model *null_model = &(apop_model){"the null model"};
#define model_no_est(base) \
apop_model * base ## _no_est = apop_model_copy(apop_##base);\
base ## _no_est->estimate=NULL;
model_no_est(beta);
model_no_est(bernoulli);
model_no_est(gamma);
model_no_est(exponential);
model_no_est(poisson);
apop_t_distribution->estimate=NULL; //find df by MLE, not observation count.
apop_model *dist[] = {
apop_bernoulli, bernoulli_no_est,
apop_beta, beta_no_est,
apop_binomial, apop_dirichlet,
apop_exponential, exponential_no_est,
apop_gamma, gamma_no_est,
apop_lognormal, apop_multinomial,
apop_multivariate_normal,
apop_normal, apop_poisson, poisson_no_est,
apop_t_distribution, apop_uniform,
apop_yule, apop_zipf, /*apop_wishart,*/
null_model};
for (int i=0; strcmp(dist[i]->name, "the null model"); i++){
if (verbose) {printf("%s: ", dist[i]->name); fflush(NULL);}
true_params = apop_model_copy(dist[i]);
true_params->parameters = apop_data_fill_base(apop_data_alloc(dist[i]->vsize==1 ? 1 : 2), true_parameter_v);
if (is_beta(dist[i]))
true_params->parameters = apop_data_falloc((2), .5, .2);
if (is_bernie(dist[i]))
true_params->parameters = apop_data_falloc((1), .1);
if (is_binom(dist[i])){
true_params->parameters = apop_data_falloc((2), 15, .2);
dist[i]->dsize=2;
}
if (!strcmp(dist[i]->name, "Dirichlet distribution"))
dist[i]->dsize=2;
if (!strcmp(dist[i]->name, "Multivariate normal distribution")){
true_params->parameters = apop_data_falloc((2, 2, 2), 15, .5, .2,
3, .2, .5);
dist[i]->dsize=2;
}
if (!strcmp(dist[i]->name, "Multinomial distribution")){
true_params->parameters = apop_data_falloc((4), 15, .5, .2, .1);
dist[i]->dsize=4;
}
if (apop_regex(dist[i]->name, "gamma distribution"))
true_params->parameters = apop_data_falloc((2), 1.5, 2.5);
if (is_t(dist[i]))
true_params->parameters = apop_data_falloc((3), 1, 3, 16);
if (!strcmp(dist[i]->name, "Wishart distribution")){
true_params->parameters = apop_data_falloc((2, 2, 2), 996, .2, .1,
0, .1, .2);
apop_vector_realloc(true_params->parameters->vector, 1);
}
test_one_distribution(r, dist[i], true_params);
test_cdf(r, true_params);
if (verbose) {printf("\nPASS. "); fflush(NULL);}
}
}
static void got_bored(){ exit(0); }
int main(int argc, char **argv){
#ifdef _OPENMP
if (omp_get_num_procs()==1) omp_set_num_threads(2); //always at least 2 threads
#endif
int c;
char opts[] = "sqt:";
if (argc==1)
printf("\tDistribution tests. Each dot is an optimization run, including some methods known to be inefficient.\n\tFor quieter output, use -q. Default is two threads; change with -t1, -t3, ...\n");
while((c = getopt(argc, argv, opts))!=-1)
if (c == 'q') verbose --;
#ifdef _OPENMP
else if (c == 't') omp_set_num_threads(atoi(optarg));
#endif
gsl_rng *r = apop_rng_alloc(213452);
signal(SIGINT, got_bored);
test_distributions(r);
}
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