def get_likelihood(self, uni_matrix): """Compute likelihood given a U matrix. Args: uni_matrix (numpy.array): Matrix to compute the likelihood. Return: tuple (np.ndarray, np.ndarray, np.array): likelihood and conditional values. """ if self.parents is None: left_u = uni_matrix[:, self.L] right_u = uni_matrix[:, self.R] else: left_ing = list(self.D - self.parents[0].D)[0] right_ing = list(self.D - self.parents[1].D)[0] left_u = uni_matrix[self.L, left_ing] right_u = uni_matrix[self.R, right_ing] copula = Bivariate(copula_type=self.name) copula.theta = self.theta X_left_right = np.array([[left_u, right_u]]) X_right_left = np.array([[right_u, left_u]]) value = np.sum(copula.probability_density(X_left_right)) left_given_right = copula.partial_derivative(X_left_right) right_given_left = copula.partial_derivative(X_right_left) return value, left_given_right, right_given_left
def test_sample(self, uniform_mock): """Sample use the inverse-transform method to generate new samples.""" # Setup instance = Bivariate(CopulaTypes.FRANK) instance.tau = 0.5 instance.theta = instance.compute_theta() uniform_mock.return_value = np.array([0.1, 0.2, 0.4, 0.6, 0.8]) expected_result = np.array([[6.080069565509917e-06, 0.1], [6.080069565509917e-06, 0.2], [6.080069565509917e-06, 0.4], [6.080069565509917e-06, 0.6], [4.500185268624483e-06, 0.8]]) expected_uniform_call_args_list = [((0, 1, 5), {}), ((0, 1, 5), {})] # Run result = instance.sample(5) # Check assert isinstance(result, np.ndarray) assert result.shape == (5, 2) compare_nested_iterables(result, expected_result) assert uniform_mock.call_args_list == expected_uniform_call_args_list
def prepare_next_tree(self): """Prepare conditional U matrix for next tree.""" for edge in self.edges: copula_theta = edge.theta if self.level == 1: left_u = self.u_matrix[:, edge.L] right_u = self.u_matrix[:, edge.R] else: left_parent, right_parent = edge.parents left_u, right_u = Edge.get_conditional_uni(left_parent, right_parent) # compute conditional cdfs C(i|j) = dC(i,j)/duj and dC(i,j)/du left_u = [x for x in left_u if x is not None] right_u = [x for x in right_u if x is not None] X_left_right = np.array([[x, y] for x, y in zip(left_u, right_u)]) X_right_left = np.array([[x, y] for x, y in zip(right_u, left_u)]) copula = Bivariate(copula_type=edge.name) copula.theta = copula_theta left_given_right = copula.partial_derivative(X_left_right) right_given_left = copula.partial_derivative(X_right_left) # correction of 0 or 1 left_given_right[left_given_right == 0] = EPSILON right_given_left[right_given_left == 0] = EPSILON left_given_right[left_given_right == 1] = 1 - EPSILON right_given_left[right_given_left == 1] = 1 - EPSILON edge.U = np.array([left_given_right, right_given_left])
def test_cdf_value_if_all_other_arg_are_one(self): """Test of the analytical properties of copulas on a range of values of theta.""" # Setup instance = Bivariate(CopulaTypes.FRANK) tau_values = np.linspace(-1.0, 1.0, 20)[1:-1] # Run/Check for tau in tau_values: instance.tau = tau instance.theta = instance.compute_theta() copula_single_arg_not_one(instance, tolerance=1E-03)
def test_cdf_zero_if_single_arg_is_zero(self): """Test of the analytical properties of copulas on a range of values of theta.""" # Setup instance = Bivariate(CopulaTypes.FRANK) tau_values = np.linspace(-1.0, 1.0, 20)[1:-1] # Run/Check for tau in tau_values: instance.tau = tau instance.theta = instance.compute_theta() copula_zero_if_arg_zero(instance)
def test_sample_random_state(self): """If random_state is set, the samples are the same.""" # Setup instance = Bivariate(CopulaTypes.FRANK, random_seed=0) instance.tau = 0.5 instance.theta = instance.compute_theta() expected_result = np.array([[3.66330927e-06, 5.48813504e-01], [6.08006957e-06, 7.15189366e-01], [5.27582646e-06, 6.02763376e-01], [5.58315848e-06, 5.44883183e-01], [6.08006957e-06, 4.23654799e-01]]) # Run result = instance.sample(5) # Check compare_nested_iterables(result, expected_result)
def test_sample_random_state(self): """If random_state is set, the samples are the same.""" # Setup instance = Bivariate(CopulaTypes.CLAYTON, random_seed=0) instance.tau = 0.5 instance.theta = instance.compute_theta() expected_result = np.array([[0.68627770, 0.54881350], [0.64059280, 0.71518937], [0.90594782, 0.60276338], [0.96040856, 0.54488318], [0.40876969, 0.42365480]]) # Run result = instance.sample(5) # Check compare_nested_iterables(result, expected_result)
def get_likelihood(self, uni_matrix): """Compute likelihood given a U matrix.""" if self.parents is None: left_u = uni_matrix[:, self.L] right_u = uni_matrix[:, self.R] else: left_ing = list(self.D - self.parents[0].D)[0] right_ing = list(self.D - self.parents[1].D)[0] left_u = uni_matrix[self.L, left_ing] right_u = uni_matrix[self.R, right_ing] copula = Bivariate(self.name) copula.theta = self.theta X_left_right = np.array([[left_u, right_u]]) X_right_left = np.array([[right_u, left_u]]) value = np.sum(copula.probability_density(X_left_right)) left_given_right = copula.partial_derivative(X_left_right) right_given_left = copula.partial_derivative(X_right_left) return value, left_given_right, right_given_left
def test_sample(self, uniform_mock): """Sample use the inverse-transform method to generate new samples.""" # Setup instance = Bivariate(CopulaTypes.CLAYTON) instance.tau = 0.5 instance.theta = instance.compute_theta() uniform_mock.return_value = np.array([0.1, 0.2, 0.4, 0.6, 0.8]) expected_result = np.array([[0.05233100, 0.1], [0.14271095, 0.2], [0.39959746, 0.4], [0.68567125, 0.6], [0.89420523, 0.8]]) expected_uniform_call_args_list = [((0, 1, 5), {}), ((0, 1, 5), {})] # Run result = instance.sample(5) # Check assert isinstance(result, np.ndarray) assert result.shape == (5, 2) compare_nested_iterables(result, expected_result) assert uniform_mock.call_args_list == expected_uniform_call_args_list
def _sample_row(self): """Generate a single sampled row from vine model. Returns: numpy.ndarray """ unis = np.random.uniform(0, 1, self.n_var) # randomly select a node to start with first_ind = np.random.randint(0, self.n_var) adj = self.trees[0].get_adjacent_matrix() visited = [] explore = [first_ind] sampled = np.zeros(self.n_var) itr = 0 while explore: current = explore.pop(0) neighbors = np.where(adj[current, :] == 1)[0].tolist() if itr == 0: new_x = self.ppfs[current](unis[current]) else: for i in range(itr - 1, -1, -1): current_ind = -1 if i >= self.truncated: continue current_tree = self.trees[i].edges # get index of edge to retrieve for edge in current_tree: if i == 0: if (edge.L == current and edge.R == visited[0]) or\ (edge.R == current and edge.L == visited[0]): current_ind = edge.index break else: if edge.L == current or edge.R == current: condition = set(edge.D) condition.add(edge.L) condition.add(edge.R) visit_set = set(visited) visit_set.add(current) if condition.issubset(visit_set): current_ind = edge.index break if current_ind != -1: # the node is not indepedent contional on visited node copula_type = current_tree[current_ind].name copula = Bivariate( copula_type=CopulaTypes(copula_type)) copula.theta = current_tree[current_ind].theta U = np.array([unis[visited[0]]]) if i == itr - 1: tmp = copula.percent_point( np.array([unis[current]]), U)[0] else: tmp = copula.percent_point(np.array([tmp]), U)[0] tmp = min(max(tmp, EPSILON), 0.99) new_x = self.ppfs[current](np.array([tmp])) sampled[current] = new_x for s in neighbors: if s not in visited: explore.insert(0, s) itr += 1 visited.insert(0, current) return sampled
def sample(self, num_rows=1): """Generating samples from vine model.""" unis = np.random.uniform(0, 1, self.n_var) # randomly select a node to start with first_ind = randint(0, self.n_var - 1) adj = self.trees[0].get_adjacent_matrix() visited = [] explore = [first_ind] sampled = np.zeros(self.n_var) itr = 0 while explore: current = explore.pop(0) neighbors = np.where(adj[current, :] == 1)[0].tolist() if itr == 0: new_x = self.ppfs[current](unis[current]) else: for i in range(itr - 1, -1, -1): current_ind = -1 if i >= self.truncated: continue current_tree = self.trees[i].edges # get index of edge to retrieve for edge in current_tree: if i == 0: if (edge.L == current and edge.R == visited[0]) or\ (edge.R == current and edge.L == visited[0]): current_ind = edge.index break else: if edge.L == current or edge.R == current: condition = set(edge.D) condition.add(edge.L) condition.add(edge.R) visit_set = set(visited) visit_set.add(current) if condition.issubset(visit_set): current_ind = edge.index break if current_ind != -1: # the node is not indepedent contional on visited node copula_type = current_tree[current_ind].name copula = Bivariate(CopulaTypes(copula_type)) copula.theta = current_tree[current_ind].theta derivative = copula.partial_derivative_scalar if i == itr - 1: tmp = optimize.fminbound( derivative, EPSILON, 1.0, args=(unis[visited[0]], unis[current]) ) else: tmp = optimize.fminbound( derivative, EPSILON, 1.0, args=(unis[visited[0]], tmp) ) tmp = min(max(tmp, EPSILON), 0.99) new_x = self.ppfs[current](tmp) sampled[current] = new_x for s in neighbors: if s not in visited: explore.insert(0, s) itr += 1 visited.insert(0, current) return sampled