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class AddSign(optimizer.Optimizer):
    """Implementation of AddSign.
    See [Bello et. al., 2017](https://arxiv.org/abs/1709.07417)
    @@__init__
    """

    def __init__(self, learning_rate=1.001,alpha=0.01,beta=0.5, use_locking=False, name="AddSign"):
        super(AddSign, self).__init__(use_locking, name)
        self._lr = learning_rate

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class PowerSign(optimizer.Optimizer):
    """Implementation of PowerSign.
    See [Bello et. al., 2017](https://arxiv.org/abs/1709.07417)
    @@__init__
    """
    def __init__(self, learning_rate=0.001,alpha=0.01,beta=0.5, use_locking=False, name="PowerSign"):
        super(PowerSign, self).__init__(use_locking, name)
        self._lr = learning_rate
        self._alpha = alpha
        self._beta = beta

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# This class defines the API to add Ops to train a model. 
from tensorflow.python.ops import control_flow_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import state_ops
from tensorflow.python.framework import ops
from tensorflow.python.training import optimizer
import tensorflow as tf

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 def _create_slots(self, var_list):
     # Create slots for allocation and later management of additional 
     # variables associated with the variables to train.
     # for example: the first and second moments.
     '''
     for v in var_list:
     self._zeros_slot(v, "m", self._name)
     self._zeros_slot(v, "v", self._name)
     '''
 def _apply_dense(self, grad, var):

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# Gradient Descent
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(cost)

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class SoftDecisionTree(object):
    def __init__(self, *args,**kwargs):
        self.params = TreeProperties(*args,**kwargs)

        self.loss = 0.0

        self.output = list()
        self.leafs_distribution = list()
    def build_tree(self):
        self.tf_X = tf.placeholder(tf.float32, [None, self.params.n_features])

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class Node(object):
    def __init__(self,id,depth,pathprob,tree):
        self.id = id
        self.depth = depth
        self.prune(tree)
        if self.isLeaf:
            self.W = tf.get_variable(...)
            self.b = tf.get_variable(...)
        else:
            self.W = tf.get_variable(...)

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class TreeProperties(object):
    '''
    :param max_leafs: maximum number of leafs
    :param n_features: maximum number of feature available within the data
    :param n_classes: number of classes
    '''
    def __init__(self,max_depth,max_leafs,n_features,n_classes,regularisation_penality=10.,decay_penality=0.9):
        self.max_depth = max_depth
        self.max_leafs = max_leafs
        self.n_features = n_features

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import numpy as np

np.random.seed(1)
def f(x):
"""The function to predict."""
return x *np.sin(x)

#----------------------------------------------------------------------
# First the noiseless case
X = np.atleast_2d(np.random.uniform(0, 10.0, size=100)).T

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class XGBQuantile(XGBRegressor):
  def __init__(self,quant_alpha=0.95,quant_delta = 1.0,quant_thres=1.0,quant_var =1.0,base_score=0.5, booster='gbtree', colsample_bylevel=1,
                colsample_bytree=1, gamma=0, learning_rate=0.1, max_delta_step=0,max_depth=3, min_child_weight=1, missing=None, n_estimators=100,
                n_jobs=1, nthread=None, objective='reg:linear', random_state=0,reg_alpha=0, reg_lambda=1, scale_pos_weight=1, seed=None,silent=True, subsample=1):
    self.quant_alpha = quant_alpha
    self.quant_delta = quant_delta
    self.quant_thres = quant_thres
    self.quant_var = quant_var
    
    super().__init__(base_score=base_score, booster=booster, colsample_bylevel=colsample_bylevel,