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#!/usr/bin/env python3 | |

# -*- coding: utf-8 -*- | |

"""This module implements the linear algorithm for computing the stochastic | |

complexity of a discrete sequence relative to a parametric family of | |

multinomial distributions. For more detail, please refer to | |

http://pgm08.cs.aau.dk/Papers/31_Paper.pdf | |

""" | |

from __future__ import division | |

from collections import Counter | |

from math import ceil, log, sqrt | |

def log2(n): | |

return log(n or 1, 2) | |

def model_cost(ndistinct_vals, n): | |

"""Computes the logarithm of the normalising term of multinomial | |

stochastic complexity. | |

Args: | |

ndistinct_vals (int): number of distinct values of a multinomial r.v. | |

n (int): number of trials | |

Returns: | |

float: the model cost of the parametric family of multinomials | |

""" | |

total = 1.0 | |

b = 1.0 | |

d = 10 | |

bound = int(ceil(2 + sqrt(2 * n * d * log(10)))) # using equation (38) | |

for k in range(1, bound + 1): | |

b = (n - k + 1) / n * b | |

total += b | |

log_old_sum = log2(1.0) | |

log_total = log2(total) | |

log_n = log2(n) | |

for j in range(3, ndistinct_vals + 1): | |

log_x = log_n + log_old_sum - log_total - log2(j - 2) | |

x = 2 ** log_x | |

# log_one_plus_x = (x + 8 * x / (2 + x) + x / (1 + x)) / 6 | |

log_one_plus_x = log2(1 + x) | |

# one_plus_x = 1 + n * 2 ** log_old_sum / (2 ** log_total * (j - 2)) | |

# log_one_plus_x = log2(one_plus_x) | |

log_new_sum = log_total + log_one_plus_x | |

log_old_sum = log_total | |

log_total = log_new_sum | |

# print log_total, | |

if ndistinct_vals == 1: | |

log_total = log2(1.0) | |

return log_total | |

def sc(X, ndistinct_vals=None): | |

"""Computes the stochastic complexity of a discrete sequence. | |

Args: | |

X (sequence): sequence of discrete outcomes | |

ndistinct_vals (int): number of distinct values of the multinomial | |

r.v. X. If not provided, we take it directly from X. | |

Returns: | |

float: the multinomial stochastic complexity of X | |

""" | |

freqs = Counter(X) | |

n = len(X) | |

ndistinct_vals = ndistinct_vals or len(freqs) | |

data_cost = 0.0 | |

for freq in freqs.values(): | |

data_cost += freq * (log2(n) - log2(freq)) | |

return data_cost + model_cost(ndistinct_vals, n) | |

if __name__ == "__main__": | |

print(sc([1, 2, 3, 2, 1, 2])) |