#!/usr/bin/env python # This code is part of the Biopython distribution and governed by its # license. Please see the LICENSE file that should have been included # as part of this package. """ This module provides code for doing logistic regressions. Classes: LogisticRegression Holds information for a LogisticRegression classifier. Functions: train Train a new classifier. calculate Calculate the probabilities of each class, given an observation. classify Classify an observation into a class. """ import numpy import numpy.linalg 00022 class LogisticRegression: """Holds information necessary to do logistic regression classification. Members: beta List of the weights for each dimension. """ 00030 def __init__(self): """LogisticRegression()""" self.beta = [] def train(xs, ys, update_fn=None, typecode=None): """train(xs, ys[, update_fn]) -> LogisticRegression Train a logistic regression classifier on a training set. xs is a list of observations and ys is a list of the class assignments, which should be 0 or 1. xs and ys should contain the same number of elements. update_fn is an optional callback function that takes as parameters that iteration number and log likelihood. """ if len(xs) != len(ys): raise ValueError("xs and ys should be the same length.") classes = set(ys) if classes != set([0, 1]): raise ValueError("Classes should be 0's and 1's") if typecode is None: typecode = 'd' # Dimensionality of the data is the dimensionality of the # observations plus a constant dimension. N, ndims = len(xs), len(xs[0]) + 1 if N==0 or ndims==1: raise ValueError("No observations or observation of 0 dimension.") # Make an X array, with a constant first dimension. X = numpy.ones((N, ndims), typecode) X[:, 1:] = xs Xt = numpy.transpose(X) y = numpy.asarray(ys, typecode) # Initialize the beta parameter to 0. beta = numpy.zeros(ndims, typecode) MAX_ITERATIONS = 500 CONVERGE_THRESHOLD = 0.01 stepsize = 1.0 # Now iterate using Newton-Raphson until the log-likelihoods # converge. i = 0 old_beta = old_llik = None while i < MAX_ITERATIONS: # Calculate the probabilities. p = e^(beta X) / (1+e^(beta X)) ebetaX = numpy.exp(numpy.dot(beta, Xt)) p = ebetaX / (1+ebetaX) # Find the log likelihood score and see if I've converged. logp = y*numpy.log(p) + (1-y)*numpy.log(1-p) llik = sum(logp) if update_fn is not None: update_fn(iter, llik) if old_llik is not None: # Check to see if the likelihood decreased. If it did, then # restore the old beta parameters and half the step size. if llik < old_llik: stepsize = stepsize / 2.0 beta = old_beta # If I've converged, then stop. if numpy.fabs(llik-old_llik) <= CONVERGE_THRESHOLD: break old_llik, old_beta = llik, beta i += 1 W = numpy.identity(N) * p Xtyp = numpy.dot(Xt, y-p) # Calculate the first derivative. XtWX = numpy.dot(numpy.dot(Xt, W), X) # Calculate the second derivative. #u, s, vt = singular_value_decomposition(XtWX) #print "U", u #print "S", s delta = numpy.linalg.solve(XtWX, Xtyp) if numpy.fabs(stepsize-1.0) > 0.001: delta = delta * stepsize beta = beta + delta # Update beta. else: raise RuntimeError("Didn't converge.") lr = LogisticRegression() lr.beta = map(float, beta) # Convert back to regular array. return lr def calculate(lr, x): """calculate(lr, x) -> list of probabilities Calculate the probability for each class. lr is a LogisticRegression object. x is the observed data. Returns a list of the probability that it fits each class. """ # Insert a constant term for x. x = numpy.asarray([1.0] + x) # Calculate the probability. p = e^(beta X) / (1+e^(beta X)) ebetaX = numpy.exp(numpy.dot(lr.beta, x)) p = ebetaX / (1+ebetaX) return [1-p, p] def classify(lr, x): """classify(lr, x) -> 1 or 0 Classify an observation into a class. """ probs = calculate(lr, x) if probs[0] > probs[1]: return 0 return 1

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