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Input warping using Kumar warping
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5 changed files with 475 additions and 1 deletions
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@ -17,4 +17,4 @@ from . import multioutput
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from . import parallel
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from . import functions
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from . import cluster_with_offset
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from . import quad_integrate
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from . import input_warping_functions
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262
GPy/util/input_warping_functions.py
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262
GPy/util/input_warping_functions.py
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@ -0,0 +1,262 @@
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# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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import numpy as np
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from ..core.parameterization import Parameterized, Param
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from ..core.parameterization.priors import LogGaussian
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class InputWarpingFunction(Parameterized):
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"""Abstract class for input warping functions
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"""
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def __init__(self, name):
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super(InputWarpingFunction, self).__init__(name=name)
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def f(self, X, test=False):
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raise NotImplementedError
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def fgrad_x(self, X):
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raise NotImplementedError
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def update_grads(self, X, dL_dW):
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raise NotImplementedError
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class IdentifyWarping(InputWarpingFunction):
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"""The identity warping function, for testing"""
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def __init__(self):
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super(IdentifyWarping, self).__init__(name='input_warp_identity')
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def f(self, X, test_data=False):
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return X
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def fgrad_X(self, X):
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return np.zeros(X.shape)
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def update_grads(self, X, dL_dW):
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pass
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class InputWarpingTest(InputWarpingFunction):
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"""The identity warping function, for testing"""
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def __init__(self):
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super(InputWarpingTest, self).__init__(name='input_warp_test')
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self.a = Param('a', 1.0)
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self.set_prior(LogGaussian(0.0, 0.75))
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self.link_parameter(self.a)
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def f(self, X, test_data=False):
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return X * self.a
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def fgrad_X(self, X):
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return self.ones(X.shape) * self.a
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def update_grads(self, X, dL_dW):
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self.a.gradient[:] = np.sum(dL_dW * X)
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class KumarWarping(InputWarpingFunction):
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"""Kumar Warping for input data
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Parameters
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----------
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X : array_like, shape = (n_samples, n_features)
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The input data that is going to be warped
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warping_indices: list of int, optional
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The features that are going to be warped
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Default to warp all the features
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epsilon: float, optional
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Used to normalized input data to [0+e, 1-e]
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Default to 1e-6
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Xmin : list of float, Optional
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The min values for each feature defined by users
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Default to the train minimum
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Xmax : list of float, Optional
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The max values for each feature defined by users
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Default to the train maximum
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Attributes
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----------
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warping_indices: list of int
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The features that are going to be warped
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Default to warp all the features
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warping_dim: int
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The number of features to be warped
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Xmin : list of float
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The min values for each feature defined by users
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Default to the train minimum
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Xmax : list of float
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The max values for each feature defined by users
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Default to the train maximum
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epsilon: float
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Used to normalized input data to [0+e, 1-e]
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Default to 1e-6
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X_normalized : array_like, shape = (n_samples, n_features)
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The normalized training X
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scaling : list of float, length = n_features in X
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Defined as 1.0 / (self.Xmax - self.Xmin)
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params : list of Param
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The list of all the parameters used in Kumar Warping
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num_parameters: int
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The number of parameters used in Kumar Warping
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"""
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def __init__(self, X, warping_indices=None, epsilon=None, Xmin=None, Xmax=None):
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super(KumarWarping, self).__init__(name='input_warp_kumar')
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if warping_indices is not None and np.max(warping_indices) > X.shape[1] -1:
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raise ValueError("Kumar warping indices exceed feature dimension")
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if warping_indices is not None and np.min(warping_indices) < 0:
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raise ValueError("Kumar warping indices should be larger than 0")
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if warping_indices is not None and np.any(list(map(lambda x: not isinstance(x, int), warping_indices))):
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raise ValueError("Kumar warping indices should be integer")
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if Xmin is None and Xmax is None:
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Xmin = X.min(axis=0)
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Xmax = X.max(axis=0)
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else:
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if Xmin is None or Xmax is None:
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raise ValueError("Xmin and Xmax need to be provide at the same time!")
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if len(Xmin) != X.shape[1] or len(Xmax) != X.shape[1]:
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raise ValueError("Xmin and Xmax should have n_feature values!")
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if epsilon is None:
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epsilon = 1e-6
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self.epsilon = epsilon
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self.Xmin = Xmin - self.epsilon
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self.Xmax = Xmax + self.epsilon
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self.scaling = 1.0 / (self.Xmax - self.Xmin)
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self.X_normalized = (X - self.Xmin) / (self.Xmax - self.Xmin)
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if warping_indices is None:
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warping_indices = range(X.shape[1])
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self.warping_indices = warping_indices
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self.warping_dim = len(self.warping_indices)
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self.num_parameters = 2 * self.warping_dim
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# create parameters
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self.params = [[Param('a%d' % i, 1.0), Param('b%d' % i, 1.0)] for i in range(self.warping_dim)]
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# add constraints
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for i in range(self.warping_dim):
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self.params[i][0].constrain_bounded(0.0, 10.0)
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self.params[i][1].constrain_bounded(0.0, 10.0)
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# set priors and add them into handler
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for i in range(self.warping_dim):
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self.params[i][0].set_prior(LogGaussian(0.0, 0.75))
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self.params[i][1].set_prior(LogGaussian(0.0, 0.75))
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self.link_parameter(self.params[i][0])
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self.link_parameter(self.params[i][1])
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def f(self, X, test_data=False):
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"""Apply warping_function to some Input data
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Parameters:
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-----------
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X : array_like, shape = (n_samples, n_features)
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test_data: bool, optional
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Default to False, should set to True when transforming test data
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Returns
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-------
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X_warped : array_like, shape = (n_samples, n_features)
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The warped input data
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Math
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----
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f(x) = 1 - (1 - x^a)^b
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"""
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X_warped = X.copy()
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if test_data:
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X_normalized = (X - self.Xmin) / (self.Xmax - self.Xmin)
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else:
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X_normalized = self.X_normalized
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for i_seq, i_fea in enumerate(self.warping_indices):
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a, b = self.params[i_seq][0], self.params[i_seq][1]
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X_warped[:, i_fea] = 1 - np.power(1 - np.power(X_normalized[:, i_fea], a), b)
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return X_warped
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def fgrad_X(self, X):
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"""Compute the gradient of warping function with respect to X
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Parameters
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----------
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X : array_like, shape = (n_samples, n_features)
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The location to compute gradient
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Returns
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-------
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grad : array_like, shape = (n_samples, n_features)
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The gradient for every location at X
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Math
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----
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grad = a * b * x ^(a-1) * (1 - x^a)^(b-1)
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"""
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grad = np.zeros(X.shape)
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for i_seq, i_fea in enumerate(self.warping_indices):
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a, b = self.params[i_seq][0], self.params[i_seq][1]
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grad[:, i_fea] = a * b * np.power(self.X_normalized[:, i_fea], a-1) * \
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np.power(1 - np.power(self.X_normalized[:, i_fea], a), b-1) * self.scaling[i_fea]
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return grad
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def update_grads(self, X, dL_dW):
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"""Update the gradients of marginal log likelihood with respect to the parameters of warping function
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Parameters
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----------
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X : array_like, shape = (n_samples, n_features)
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The input BEFORE warping
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dL_dW : array_like, shape = (n_samples, n_features)
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The gradient of marginal log likelihood with respect to the Warped input
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Math
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----
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let w = f(x), the input after warping, then
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dW_da = b * (1 - x^a)^(b - 1) * x^a * ln(x)
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dW_db = - (1 - x^a)^b * ln(1 - x^a)
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dL_da = dL_dW * dW_da
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dL_db = dL_dW * dW_db
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"""
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for i_seq, i_fea in enumerate(self.warping_indices):
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ai, bi = self.params[i_seq][0], self.params[i_seq][1]
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# cache some value for save some computation
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x_pow_a = np.power(self.X_normalized[:, i_fea], ai)
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# compute gradient for ai, bi on all X
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dz_dai = bi * np.power(1 - x_pow_a, bi-1) * x_pow_a * np.log(self.X_normalized[:, i_fea])
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dz_dbi = - np.power(1 - x_pow_a, bi) * np.log(1 - x_pow_a)
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# sum gradients on all the data
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dL_dai = np.sum(dL_dW[:, i_fea] * dz_dai)
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dL_dbi = np.sum(dL_dW[:, i_fea] * dz_dbi)
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self.params[i_seq][0].gradient[:] = dL_dai
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self.params[i_seq][1].gradient[:] = dL_dbi
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