Created
March 12, 2024 22:44
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Manually sampling from any given 1D histogram
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| """ | |
| Script discussed in the video: | |
| https://youtu.be/ndAmT8CYGDM | |
| Links: | |
| * https://en.wikipedia.org/wiki/Energy-based_model | |
| * https://en.wikipedia.org/wiki/Brownian_motion | |
| * https://www.extropic.ai/future | |
| """ | |
| import random | |
| import time | |
| def sample_digit_from_time(): | |
| t = time.time() | |
| _secs, subsecs = str(t).split(".") | |
| ms_digit = int(subsecs[2]) | |
| bin_digit = ms_digit % 2 | |
| print(f"t={t}, ms_digit={ms_digit}, bin_digit={bin_digit}") | |
| return bin_digit | |
| def sample_digit_list(num_digits, use_random_lib): | |
| bin_digits = [] | |
| for _ in range(num_digits): | |
| if use_random_lib: | |
| bin_digits.append(random.choice([0, 1])) | |
| else: | |
| bin_digits.append(sample_digit_from_time()) | |
| print(f"(digit sum = {sum(bin_digits)} of {num_digits})") | |
| input() | |
| return bin_digits | |
| def unit_interval_real(bin_digits): | |
| x = 0 | |
| for n, digit in enumerate(bin_digits): | |
| power_of_two = 2 ** (n + 1) | |
| x_summand = digit / power_of_two | |
| x += x_summand | |
| print(f"Level {n}, power={power_of_two}, digit={digit}: add {x_summand}, get x={x}") | |
| return x | |
| def draw_sample(hist, x): | |
| cdf = [sum(hist[:n+1]) / sum(hist) for n in range(len(hist))] # Normalized cdf | |
| lb = 0 # lower bound | |
| for n, ub in enumerate(cdf): # loop over upper bounds | |
| if lb < x < ub: | |
| return n # r was in interval with index n | |
| lb = ub | |
| if __name__=='__main__': | |
| HIST = [17, 3, 4, 20, 1, 13, 2, 30] # Sample from this distribution (0 and 3 nd 7 will come up often) | |
| bin_digits_list = [sample_digit_list(15, False)] | |
| #bin_digits_list = [sample_digit_list(10, True) for _ in range(20)] | |
| drawn_samples = [] | |
| for bin_digits in bin_digits_list: | |
| x = unit_interval_real(bin_digits) | |
| print(f"\nRun bin_digits={bin_digits}\nx={x}\n\n" + \ | |
| "Sample from histogram:\nindex->weight (chance)\n" + \ | |
| "\n".join(f"{idx}->{h} ({p} %)" | |
| for idx, (h, p) in enumerate([(h, round(100 * h / sum(HIST), 1)) for h in HIST])) + "\n") | |
| drawn_samples.append(draw_sample(HIST, x)) | |
| print(f"\nDrew {drawn_samples}") |
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