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###############################################################
# PyNLPp - Statistics & Information Theory Library
# by Maarten van Gompel (proycon)
# http://ilk.uvt.nl/~mvgompel
# Induction for Linguistic Knowledge Research Group
# Universiteit van Tilburg
#
# Also contains MIT licensed code from
# AI: A Modern Appproach : http://aima.cs.berkeley.edu/python/utils.html
# Peter Norvig
#
# Licensed under GPLv3
#
###############################################################
"""This is a Python library containing classes for Statistic and Information Theoretical computations. It also contains some code from Peter Norvig, AI: A Modern Appproach : http://aima.cs.berkeley.edu/python/utils.html"""
import math
import codecs
import random
import operator
class FrequencyList:
"""A frequency list (implemented using dictionaries)"""
def __init__(self, tokens = None, casesensitive = True, dovalidation = True):
self._count = {}
self._ranked = {}
self.total = 0 #number of tokens
self.casesensitive = casesensitive
self.dovalidation = dovalidation
if tokens: self.append(tokens)
def load(self, filename):
"""Load a frequency list from file (in the format produced by the save method)"""
f = codecs.open(filename,'r','utf-8')
for line in self.readline():
type, count = line.split("\t")
self.count(type,count)
f.close()
def save(self, filename):
"""Save a frequency list to file, can be loaded later using the load method"""
f = codecs.open(filename,'w','utf-8')
for line in self.output():
f.write(line + '\n')
f.close()
def _validate(self,type):
if isinstance(type,list):
type = tuple(type)
if isinstance(type,tuple):
if not self.casesensitive:
return tuple([x.lower() for x in type])
else:
return type
else:
if not self.casesensitive:
return type.lower()
else:
return type
def append(self,tokens):
"""Add a list of tokens to the frequencylist. This method will count them for you."""
for token in tokens:
self.count(token)
def count(self, type, amount = 1):
"""Count a certain type. The counter will increase by the amount specified (defaults to one)"""
if self.dovalidation: type = self._validate(type)
if self._ranked: self._ranked = None
if type in self._count:
self._count[type] += amount
else:
self._count[type] = amount
self.total += amount
def sum(self):
"""Returns the total amount of tokens"""
return self.total
def _rank(self):
if not self._ranked: self._ranked = sorted(self._count.items(),key=lambda x: x[1], reverse=True )
def __iter__(self):
"""Iterate over the frequency lists, in order (frequent to rare). This is a generator that yields (type, count) pairs. The first time you iterate over the FrequencyList, the ranking will be computed. For subsequent calls it will be available immediately, unless the frequency list changed in the meantime."""
self._rank()
for type, count in self._ranked:
yield type, count
def items(self):
"""Returns an *unranked* list of (type, count) pairs. Use this only if you are not interested in the order."""
for type, count in self._count.items():
yield type, count
def __getitem__(self, type):
if self.dovalidation: type = self._validate(type)
return self._count[type]
def __setitem__(self, type, value):
"""alias for count, but can only be called once"""
if self.dovalidation: type = self._validate(type)
if not type in self._count:
self.count(type,value)
else:
raise ValueError("This type is already set!")
def __delitem__(self, type):
if self.dovalidation: type = self._validate(type)
del self._count[type]
if self._ranked: self._ranked = None
def typetokenratio(self):
"""Computes the type/token ratio"""
return len(self._count) / float(self.total)
def __len__(self):
"""Returns the total amount of types"""
return len(self._count)
def tokens(self):
"""Returns the total amount of tokens"""
return self.total
def mode(self):
"""Returns the type that occurs the most frequently in the frequency list"""
self._rank()
return self._ranked[0][0]
def p(self, type):
"""Returns the probability (relative frequency) of the token"""
if self.dovalidation: type = self._validate(type)
return self._count[type] / float(self.total)
def __eq__(self, otherfreqlist):
return (self.total == otherfreqlist.total and self._count == otherfreqlist._count)
def __contains__(self, type):
"""Checks if the specified type is in the frequency list"""
if self.dovalidation: type = self._validate(type)
return type in self._count
def __add__(self, otherfreqlist):
"""Multiple frequency lists can be added together"""
product = FrequencyList(None, )
for type, count in self.items():
product.count(type,count)
for type, count in otherfreqlist.items():
product.count(type,count)
return product
def output(self,delimiter = '\t'):
"""Print a representation of the frequency list"""
for type, count in self:
if isinstance(type,tuple) or isinstance(type,list):
yield u" ".join(type) + delimiter + str(count)
elif isinstance(type,str) or isinstance(type,unicode):
yield type + delimiter + str(count)
else:
yield str(type) + delimiter + str(count)
def __repr__(self):
return repr(self._count)
def __unicode__(self):
return u"\n".join(self.output())
def __str__(self):
return "\n".join(self.output())
def values(self):
return self._count.values()
def dict(self):
return self._count
#class FrequencyTrie:
# def __init__(self):
# self.data = Tree()
#
# def count(self, sequence):
#
#
# self.data.append( Tree(item) )
class Distribution:
"""A distribution can be created over a FrequencyList or a plain dictionary with numeric values. It will be normalized automatically. This implemtation uses dictionaries/hashing"""
def __init__(self, data, base = 2):
self.base = base #logarithmic base: can be set to 2, 10 or math.e (or anything else). when set to None, it's set to e automatically
self._dist = {}
if isinstance(data, FrequencyList):
for type, count in data.items():
self._dist[type] = count / float(data.total)
elif isinstance(data, dict) or isinstance(data, list):
if isinstance(data, list):
self._dist = {}
for key,value in data:
self._dist[key] = float(value)
else:
self._dist = data
total = float(sum(self._dist.values()))
if total < 0.999 or total > 1.000:
#normalize again
for key, value in self._dist.items():
self._dist[key] = value / total
else:
raise Exception("Can't create distribution")
self._ranked = None
def _rank(self):
if not self._ranked: self._ranked = sorted(self._dist.items(),key=lambda x: x[1], reverse=True )
def information(self, type):
"""Computes the information content of the specified type: -log_e(p(X))"""
if not self.base:
return -math.log(self._dist[type])
else:
return -math.log(self._dist[type], self.base)
def poslog(self, type):
"""alias for information content"""
return self.information(type)
def entropy(self, base = 2):
"""Compute the entropy of the distribution"""
entropy = 0
if not base and self.base: base = self.base
for type in self._dist:
if not base:
entropy += self._dist[type] * -math.log(self._dist[type])
else:
entropy += self._dist[type] * -math.log(self._dist[type], base)
return entropy
def perplexity(self, base=2):
return base ** self.entropy(base)
def mode(self):
"""Returns the type that occurs the most frequently in the probability distribution"""
self._rank()
return self._ranked[0][0]
def maxentropy(self, base = 2):
"""Compute the maximum entropy of the distribution: log_e(N)"""
if not base and self.base: base = self.base
if not base:
return math.log(len(self._dist))
else:
return math.log(len(self._dist), base)
def __len__(self):
"""Returns the number of types"""
return len(self._dist)
def __getitem__(self, type):
"""Return the probability for this type"""
return self._dist[type]
def __iter__(self):
"""Iterate over the *ranked* distribution, returns (type, probability) pairs"""
self._rank()
for type, p in self._ranked:
yield type, p
def items(self):
"""Returns an *unranked* list of (type, prob) pairs. Use this only if you are not interested in the order."""
for type, count in self._dist.items():
yield type, count
def output(self,delimiter = '\t', freqlist = None):
for type, prob in self:
if freqlist:
if isinstance(type,list) or isinstance(type, tuple):
yield u" ".join(type) + delimiter + str(freqlist[type]) + delimiter + str(prob)
else:
yield type + delimiter + str(freqlist[type]) + delimiter + str(prob)
else:
if isinstance(type,list) or isinstance(type, tuple):
yield u" ".join(type) + delimiter + str(prob)
else:
yield type + delimiter + str(prob)
def __unicode__(self):
return u"\n".join(self.output())
def __str__(self):
return "\n".join(self.output())
def __repr__(self):
return repr(self._dist)
def keys(self):
return self._dist.keys()
def values(self):
return self._dist.values()
class MarkovChain(object):
def __init__(self, startstate, endstate = None):
self.nodes = set()
self.edges_out = {}
self.startstate = startstate
self.endstate = endstate
def settransitions(self, state, distribution):
self.nodes.add(state)
if not isinstance(distribution, Distribution):
distribution = Distribution(distribution)
self.edges_out[state] = distribution
self.nodes.update(distribution.keys())
def __iter__(self):
for state, distribution in self.edges_out.items():
yield state, distribution
def __getitem__(self, state):
for distribution in self.edges_out[state]:
yield distribution
def size(self):
return len(self.nodes)
def accessible(self,fromstate, tostate):
"""Is state tonode directly accessible (in one step) from state fromnode? (i.e. is there an edge between the nodes). If so, return the probability, else zero"""
if (not (fromstate in self.nodes)) or (not (tostate in self.nodes)) or not (fromstate in self.edges_out):
return 0
if tostate in self.edges_out[fromstate]:
return self.edges_out[fromstate][tostate]
else:
return 0
def communicates(self,fromstate, tostate, maxlength=999999):
"""See if a node communicates (directly or indirectly) with another. Returns the probability of the *shortest* path (probably, but not necessarily the highest probability)"""
if (not (fromstate in self.nodes)) or (not (tostate in self.nodes)):
return 0
assert (fromstate != tostate)
def _test(node,length,prob):
if length > maxlength:
return 0
if node == tostate:
prob *= self.edges_out[node][tostate]
return True
for child in self.edges_out[node].keys():
if not child in visited:
visited.add(child)
if child == tostate:
return prob * self.edges_out[node][tostate]
else:
r = _test(child, length+1, prob * self.edges_out[node][tostate])
if r:
return r
return 0
visited = set(fromstate)
return _test(fromstate,1,1)
def p(self, sequence, subsequence=True):
"""Returns the probability of the given sequence or subsequence (if subsequence=True, default)."""
if sequence[0] != self.startstate:
if isinstance(sequence, tuple):
sequence = (self.startstate,) + sequence
else:
sequence = (self.startstate,) + tuple(sequence)
if self.endstate:
if sequence[-1] != self.endstate:
if isinstance(sequence, tuple):
sequence = sequence + (self.endstate,)
else:
sequence = tuple(sequence) + (self.endstate,)
prevnode = None
prob = 1
for node in sequence:
if prevnode:
try:
prob *= self.edges_out[prevnode][node]
except:
return 0
return prob
def __contains__(self, sequence):
"""Is the given sequence generated by the markov model? Does not work for subsequences!"""
return bool(self.p(sequence,False))
def reducible(self):
#TODO: implement
raise NotImplementedError
class HiddenMarkovModel(MarkovChain):
def __init__(self, startstate, endstate = None):
self.observablenodes = set()
self.edges_toobservables = {}
super(HiddenMarkovModel, self).__init__(startstate,endstate)
def setemission(self, state, distribution):
self.nodes.add(state)
if not isinstance(distribution, Distribution):
distribution = Distribution(distribution)
self.edges_toobservables[state] = distribution
self.observablenodes.update(distribution.keys())
def print_dptable(self, V):
print " ",
for i in range(len(V)): print "%7s" % ("%d" % i),
print
for y in V[0].keys():
print "%.5s: " % y,
for t in range(len(V)):
print "%.7s" % ("%f" % V[t][y]),
print
#Adapted from: http://en.wikipedia.org/wiki/Viterbi_algorithm
def viterbi(self,observations, doprint=False):
#states, start_p, trans_p, emit_p):
V = [{}] #Viterbi matrix
path = {}
# Initialize base cases (t == 0)
for node in self.edges_out[self.startstate].keys():
try:
V[0][node] = self.edges_out[self.startstate][node] * self.edges_toobservables[node][observations[0]]
path[node] = [node]
except KeyError:
pass #will be 0, don't store
# Run Viterbi for t > 0
for t in range(1,len(observations)):
V.append({})
newpath = {}
for node in self.nodes:
column = []
for prevnode in V[t-1].keys():
try:
column.append( (V[t-1][prevnode] * self.edges_out[prevnode][node] * self.edges_toobservables[node][observations[t]], prevnode ) )
except KeyError:
pass #will be 0
if column:
(prob, state) = max(column)
V[t][node] = prob
newpath[node] = path[state] + [node]
# Don't need to remember the old paths
path = newpath
if doprint: print_dptable(V)
if not V[len(observations) - 1]:
return (0,[])
else:
(prob, state) = max([(V[len(observations) - 1][node], node) for node in V[len(observations) - 1].keys()])
return (prob, path[state])
# ********************* Common Functions ******************************
def product(seq):
"""Return the product of a sequence of numerical values.
>>> product([1,2,6])
12
"""
if len(seq) == 0:
return 0
else:
product = 1
for x in seq:
product *= x
return product
# All below functions are mathematical functions from AI: A Modern Approach, see: http://aima.cs.berkeley.edu/python/utils.html
def histogram(values, mode=0, bin_function=None): #from AI: A Modern Appproach
"""Return a list of (value, count) pairs, summarizing the input values.
Sorted by increasing value, or if mode=1, by decreasing count.
If bin_function is given, map it over values first."""
if bin_function: values = map(bin_function, values)
bins = {}
for val in values:
bins[val] = bins.get(val, 0) + 1
if mode:
return sorted(bins.items(), key=lambda v: v[1], reverse=True)
else:
return sorted(bins.items())
def log2(x): #from AI: A Modern Appproach
"""Base 2 logarithm.
>>> log2(1024)
10.0
"""
return math.log(x, 2)
def mode(values): #from AI: A Modern Appproach
"""Return the most common value in the list of values.
>>> mode([1, 2, 3, 2])
2
"""
return histogram(values, mode=1)[0][0]
def median(values): #from AI: A Modern Appproach
"""Return the middle value, when the values are sorted.
If there are an odd number of elements, try to average the middle two.
If they can't be averaged (e.g. they are strings), choose one at random.
>>> median([10, 100, 11])
11
>>> median([1, 2, 3, 4])
2.5
"""
n = len(values)
values = sorted(values)
if n % 2 == 1:
return values[n/2]
else:
middle2 = values[(n/2)-1:(n/2)+1]
try:
return mean(middle2)
except TypeError:
return random.choice(middle2)
def mean(values): #from AI: A Modern Appproach
"""Return the arithmetic average of the values."""
return sum(values) / float(len(values))
def stddev(values, meanval=None): #from AI: A Modern Appproach
"""The standard deviation of a set of values.
Pass in the mean if you already know it."""
if meanval == None: meanval = mean(values)
return math.sqrt( sum([(x - meanval)**2 for x in values]) / (len(values)-1) )
def dotproduct(X, Y): #from AI: A Modern Appproach
"""Return the sum of the element-wise product of vectors x and y.
>>> dotproduct([1, 2, 3], [1000, 100, 10])
1230
"""
return sum([x * y for x, y in zip(X, Y)])
def vector_add(a, b): #from AI: A Modern Appproach
"""Component-wise addition of two vectors.
>>> vector_add((0, 1), (8, 9))
(8, 10)
"""
return tuple(map(operator.add, a, b))
def normalize(numbers, total=1.0): #from AI: A Modern Appproach
"""Multiply each number by a constant such that the sum is 1.0 (or total).
>>> normalize([1,2,1])
[0.25, 0.5, 0.25]
"""
k = total / sum(numbers)
return [k * n for n in numbers]
###########################################################################################
def levenshtein(s1, s2):
"""Computes the levenshtein distance between to strings. From: http://en.wikibooks.org/wiki/Algorithm_Implementation/Strings/Levenshtein_distance#Python"""
if len(s1) < len(s2):
return levenshtein(s2, s1)
if not s1:
return len(s2)
previous_row = xrange(len(s2) + 1)
for i, c1 in enumerate(s1):
current_row = [i + 1]
for j, c2 in enumerate(s2):
insertions = previous_row[j + 1] + 1 # j+1 instead of j since previous_row and current_row are one character longer
deletions = current_row[j] + 1 # than s2
substitutions = previous_row[j] + (c1 != c2)
current_row.append(min(insertions, deletions, substitutions))
previous_row = current_row
return previous_row[-1]