220 lines
8.0 KiB
Python
220 lines
8.0 KiB
Python
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import warnings
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import numpy as np
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from scipy.sparse import csr_matrix
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class DensityRatioEstimator:
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"""
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Class to accomplish direct density estimation implementing the original KLIEP
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algorithm from Direct Importance Estimation with Model Selection
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and Its Application to Covariate Shift Adaptation by Sugiyama et al.
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The training set is distributed via
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train ~ p(x)
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and the test set is distributed via
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test ~ q(x).
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The KLIEP algorithm and its variants approximate w(x) = q(x) / p(x) directly. The predict function returns the
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estimate of w(x). The function w(x) can serve as sample weights for the training set during
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training to modify the expectation function that the model's loss function is optimized via,
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i.e.
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E_{x ~ w(x)p(x)} loss(x) = E_{x ~ q(x)} loss(x).
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Usage :
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The fit method is used to run the KLIEP algorithm using LCV and returns value of J
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trained on the entire training/test set with the best sigma found.
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Use the predict method on the training set to determine the sample weights from the KLIEP algorithm.
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"""
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def __init__(
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self,
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max_iter=5000,
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num_params=[0.1, 0.2],
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epsilon=1e-4,
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cv=3,
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sigmas=[0.01, 0.1, 0.25, 0.5, 0.75, 1],
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random_state=None,
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verbose=0,
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):
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"""
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Direct density estimation using an inner LCV loop to estimate the proper model. Can be used with sklearn
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cross validation methods with or without storing the inner CV. To use a standard grid search.
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max_iter : Number of iterations to perform
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num_params : List of number of test set vectors used to construct the approximation for inner LCV.
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Must be a float. Original paper used 10%, i.e. =.1
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sigmas : List of sigmas to be used in inner LCV loop.
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epsilon : Additive factor in the iterative algorithm for numerical stability.
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"""
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self.max_iter = max_iter
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self.num_params = num_params
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self.epsilon = epsilon
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self.verbose = verbose
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self.sigmas = sigmas
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self.cv = cv
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self.random_state = 0
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def fit(self, X_train, X_test, alpha_0=None):
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"""Uses cross validation to select sigma as in the original paper (LCV).
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In a break from sklearn convention, y=X_test.
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The parameter cv corresponds to R in the original paper.
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Once found, the best sigma is used to train on the full set."""
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# LCV loop, shuffle a copy in place for performance.
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cv = self.cv
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chunk = int(X_test.shape[0] / float(cv))
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if self.random_state is not None:
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np.random.seed(self.random_state)
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# if isinstance(X_test, csr_matrix):
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# X_test_shuffled = X_test.toarray()
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# else:
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# X_test_shuffled = X_test.copy()
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X_test_shuffled = X_test.copy()
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np.random.shuffle(X_test_shuffled)
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j_scores = {}
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if type(self.sigmas) != list:
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self.sigmas = [self.sigmas]
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if type(self.num_params) != list:
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self.num_params = [self.num_params]
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if len(self.sigmas) * len(self.num_params) > 1:
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# Inner LCV loop
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for num_param in self.num_params:
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for sigma in self.sigmas:
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j_scores[(num_param, sigma)] = np.zeros(cv)
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for k in range(1, cv + 1):
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if self.verbose > 0:
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print("Training: sigma: %s R: %s" % (sigma, k))
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X_test_fold = X_test_shuffled[(k - 1) * chunk : k * chunk, :]
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j_scores[(num_param, sigma)][k - 1] = self._fit(
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X_train=X_train,
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X_test=X_test_fold,
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num_parameters=num_param,
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sigma=sigma,
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)
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j_scores[(num_param, sigma)] = np.mean(j_scores[(num_param, sigma)])
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sorted_scores = sorted(
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[x for x in j_scores.items() if np.isfinite(x[1])],
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key=lambda x: x[1],
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reverse=True,
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)
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if len(sorted_scores) == 0:
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warnings.warn("LCV failed to converge for all values of sigma.")
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return self
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self._sigma = sorted_scores[0][0][1]
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self._num_parameters = sorted_scores[0][0][0]
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self._j_scores = sorted_scores
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else:
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self._sigma = self.sigmas[0]
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self._num_parameters = self.num_params[0]
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# best sigma
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self._j = self._fit(
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X_train=X_train,
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X_test=X_test_shuffled,
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num_parameters=self._num_parameters,
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sigma=self._sigma,
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)
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return self # Compatibility with sklearn
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def _fit(self, X_train, X_test, num_parameters, sigma, alpha_0=None):
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"""Fits the estimator with the given parameters w-hat and returns J"""
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num_parameters = num_parameters
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if type(num_parameters) == float:
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num_parameters = int(X_test.shape[0] * num_parameters)
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self._select_param_vectors(
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X_test=X_test, sigma=sigma, num_parameters=num_parameters
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)
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# if isinstance(X_train, csr_matrix):
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# X_train = X_train.toarray()
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X_train = self._reshape_X(X_train)
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X_test = self._reshape_X(X_test)
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if alpha_0 is None:
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alpha_0 = np.ones(shape=(num_parameters, 1)) / float(num_parameters)
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self._find_alpha(
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X_train=X_train,
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X_test=X_test,
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num_parameters=num_parameters,
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epsilon=self.epsilon,
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alpha_0=alpha_0,
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sigma=sigma,
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)
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return self._calculate_j(X_test, sigma=sigma)
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def _calculate_j(self, X_test, sigma):
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pred = self.predict(X_test, sigma=sigma) + 0.0000001
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log = np.log(pred).sum()
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return log / (X_test.shape[0])
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def score(self, X_test):
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"""Return the J score, similar to sklearn's API"""
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return self._calculate_j(X_test=X_test, sigma=self._sigma)
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@staticmethod
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def _reshape_X(X):
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"""Reshape input from mxn to mx1xn to take advantage of numpy broadcasting."""
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if len(X.shape) != 3:
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return X.reshape((X.shape[0], 1, X.shape[1]))
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return X
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def _select_param_vectors(self, X_test, sigma, num_parameters):
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"""X_test is the test set. b is the number of parameters."""
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indices = np.random.choice(X_test.shape[0], size=num_parameters, replace=False)
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self._test_vectors = X_test[indices, :].copy()
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self._phi_fitted = True
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def _phi(self, X, sigma=None):
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if sigma is None:
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sigma = self._sigma
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if self._phi_fitted:
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return np.exp(
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-np.sum((X - self._test_vectors) ** 2, axis=-1) / (2 * sigma**2)
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)
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raise Exception("Phi not fitted.")
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def _find_alpha(self, alpha_0, X_train, X_test, num_parameters, sigma, epsilon):
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A = np.zeros(shape=(X_test.shape[0], num_parameters))
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b = np.zeros(shape=(num_parameters, 1))
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A = self._phi(X_test, sigma)
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b = self._phi(X_train, sigma).sum(axis=0) / X_train.shape[0]
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b = b.reshape((num_parameters, 1))
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out = alpha_0.copy()
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for k in range(self.max_iter):
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mat = np.dot(A, out)
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mat += 0.000000001
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out += epsilon * np.dot(np.transpose(A), 1.0 / mat)
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out += b * (
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((1 - np.dot(np.transpose(b), out)) / np.dot(np.transpose(b), b))
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)
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out = np.maximum(0, out)
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out /= np.dot(np.transpose(b), out)
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self._alpha = out
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self._fitted = True
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def predict(self, X, sigma=None):
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"""Equivalent of w(X) from the original paper."""
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X = self._reshape_X(X)
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if not self._fitted:
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raise Exception("Not fitted!")
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return np.dot(self._phi(X, sigma=sigma), self._alpha).reshape((X.shape[0],))
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