add example of getting confidence interval & misc changes

This commit is contained in:
NunoSempere 2023-07-23 19:11:25 +02:00
parent d531d5571f
commit e053a726ee
15 changed files with 142 additions and 16 deletions

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@ -11,7 +11,8 @@ A self-contained C99 library that provides a subset of [Squiggle](https://www.sq
- Because it can fit in my head
- Because if you can implement something in C, you can implement it anywhere else
- Because it can be made faster if need be
- e.g., with a multi-threading library like OpenMP, or by adding more algorithmic complexity
- e.g., with a multi-threading library like OpenMP,
- or by implementing faster but more complex algorithms
- or more simply, by inlining the sampling functions (adding an `inline` directive before their function declaration)
- **Because there are few abstractions between it and machine code** (C => assembly => machine code with gcc, or C => machine code, with tcc), leading to fewer errors beyond the programmer's control.
@ -184,16 +185,11 @@ int main(){
## To do list
- [ ] Test summary statistics for each of the distributions.
- [ ] Pontificate about lognormal tests
- [ ] Have some more complicated & realistic example
- [ ] Add summarization functions: 90% ci (or all c.i.?)
- [ ] Systematize references
- [ ] Publish online
- [ ] Add efficient sampling from a beta distribution
- https://dl.acm.org/doi/10.1145/358407.358414
- https://link.springer.com/article/10.1007/bf02293108
- https://stats.stackexchange.com/questions/502146/how-does-numpy-generate-samples-from-a-beta-distribution
- https://github.com/numpy/numpy/blob/5cae51e794d69dd553104099305e9f92db237c53/numpy/random/src/distributions/distributions.c
- [ ] Support all distribution functions in <https://www.squiggle-language.com/docs/Api/Dist>
- [ ] Support all distribution functions in <https://www.squiggle-language.com/docs/Api/Dist>, and do so efficiently
@ -224,3 +220,15 @@ int main(){
- https://dl.acm.org/doi/pdf/10.1145/358407.358414
- [x] Explain correlated samples
- [-] ~~Add tests in Stan?~~
- [x] Test summary statistics for each of the distributions.
- [x] For uniform
- [x] For normal
- [x] For lognormal
- [x] For lognormal (to syntax)
- [x] For beta distribution
- [x] Clarify gamma/standard gamma
- [x] Add efficient sampling from a beta distribution
- https://dl.acm.org/doi/10.1145/358407.358414
- https://link.springer.com/article/10.1007/bf02293108
- https://stats.stackexchange.com/questions/502146/how-does-numpy-generate-samples-from-a-beta-distribution
- https://github.com/numpy/numpy/blob/5cae51e794d69dd553104099305e9f92db237c53/numpy/random/src/distributions/distributions.c

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@ -87,9 +87,9 @@ int main()
printf("\nGetting some samples from sample_unit_normal\n");
clock_t begin_2 = clock();
double* normal_samples = malloc(NUM_SAMPLES * sizeof(double));
for (int i = 0; i < NUM_SAMPLES; i++) {
double normal_sample = sample_unit_normal(seed);
normal_samples[i] = sample_unit_normal(seed);
// printf("%f\n", normal_sample);
}

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@ -43,10 +43,3 @@ int main()
free(seed);
}
/*
Aggregation mechanisms:
- Quantiles (requires a sort)
- Sum
- Average
- Std
*/

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examples/07_ci_beta/example Executable file

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@ -0,0 +1,21 @@
#include "../../squiggle.h"
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
// Estimate functions
double beta_1_2_sampler(uint64_t* seed){
return sample_beta(1, 2.0, seed);
}
int main()
{
// set randomness seed
uint64_t* seed = malloc(sizeof(uint64_t));
*seed = 1000; // xorshift can't start with 0
struct c_i beta_1_2_ci_90 = get_90_confidence_interval(beta_1_2_sampler, seed);
printf("90%% confidence interval of beta(1,2) is [%f, %f]\n", beta_1_2_ci_90.low, beta_1_2_ci_90.high);
free(seed);
}

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@ -0,0 +1,53 @@
# Interface:
# make
# make build
# make format
# make run
# Compiler
CC=gcc
# CC=tcc # <= faster compilation
# Main file
SRC=example.c ../../squiggle.c
OUTPUT=example
## Dependencies
MATH=-lm
## Flags
DEBUG= #'-g'
STANDARD=-std=c99
WARNINGS=-Wall
OPTIMIZED=-O3 #-Ofast
# OPENMP=-fopenmp
## Formatter
STYLE_BLUEPRINT=webkit
FORMATTER=clang-format -i -style=$(STYLE_BLUEPRINT)
## make build
build: $(SRC)
$(CC) $(OPTIMIZED) $(DEBUG) $(SRC) $(MATH) -o $(OUTPUT)
format: $(SRC)
$(FORMATTER) $(SRC)
run: $(SRC) $(OUTPUT)
OMP_NUM_THREADS=1 ./$(OUTPUT) && echo
time-linux:
@echo "Requires /bin/time, found on GNU/Linux systems" && echo
@echo "Running 100x and taking avg time $(OUTPUT)"
@t=$$(/usr/bin/time -f "%e" -p bash -c 'for i in {1..100}; do $(OUTPUT); done' 2>&1 >/dev/null | grep real | awk '{print $$2}' ); echo "scale=2; 1000 * $$t / 100" | bc | sed "s|^|Time using 1 thread: |" | sed 's|$$|ms|' && echo
## Profiling
profile-linux:
echo "Requires perf, which depends on the kernel version, and might be in linux-tools package or similar"
echo "Must be run as sudo"
$(CC) $(SRC) $(MATH) -o $(OUTPUT)
sudo perf record ./$(OUTPUT)
sudo perf report
rm perf.data

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@ -11,6 +11,7 @@ all:
cd examples/04_sample_from_cdf_simple && make && echo
cd examples/05_sample_from_cdf_beta && make && echo
cd examples/06_gamma_beta && make && echo
cd examples/07_ci_beta && make && echo
format: squiggle.c squiggle.h
$(FORMATTER) squiggle.c

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@ -94,6 +94,12 @@ double sample_gamma(double alpha, uint64_t* seed)
// A Simple Method for Generating Gamma Variables, Marsaglia and Wan Tsang, 2001
// https://dl.acm.org/doi/pdf/10.1145/358407.358414
// see also the references/ folder
// Note that the Wikipedia page for the gamma distribution includes a scaling parameter
// k or beta
// https://en.wikipedia.org/wiki/Gamma_distribution
// such that gamma_k(alpha, k) = k * gamma(alpha)
// or gamma_beta(alpha, beta) = gamma(alpha) / beta
// So far I have not needed to use this, and thus the second parameter is by default 1.
if (alpha >= 1) {
double d, c, x, v, u;
d = alpha - 1.0 / 3.0;
@ -377,6 +383,43 @@ struct box sampler_cdf_double(double cdf(double), uint64_t* seed)
return result;
}
// Get confidence intervals, given a sampler
struct c_i {
float low;
float high;
};
int compare_doubles(const void *p, const void *q) {
// https://wikiless.esmailelbob.xyz/wiki/Qsort?lang=en
double x = *(const double *)p;
double y = *(const double *)q;
/* Avoid return x - y, which can cause undefined behaviour
because of signed integer overflow. */
if (x < y)
return -1; // Return -1 if you want ascending, 1 if you want descending order.
else if (x > y)
return 1; // Return 1 if you want ascending, -1 if you want descending order.
return 0;
}
struct c_i get_90_confidence_interval(double (*sampler)(uint64_t*), uint64_t* seed){
int n = 100 * 1000;
double* samples_array = malloc(n * sizeof(double));
for(int i=0; i<n; i++){
samples_array[i] = sampler(seed);
}
qsort(samples_array, n, sizeof(double), compare_doubles);
struct c_i result = {
.low = samples_array[5000],
.high =samples_array[94999],
};
free(samples_array);
return result;
}
/* Could also define other variations, e.g.,
double sampler_danger(struct box cdf(double), uint64_t* seed)
{

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@ -50,4 +50,11 @@ struct box inverse_cdf_box(struct box cdf_box(double), double p);
struct box sampler_cdf_double(double cdf(double), uint64_t* seed);
struct box sampler_cdf_box(struct box cdf(double), uint64_t* seed);
// Get 90% confidence interval
struct c_i {
float low;
float high;
};
struct c_i get_90_confidence_interval(double (*sampler)(uint64_t*), uint64_t* seed);
#endif