Pairwise CRF on a general graph.
Pairwise potentials the same for all edges, are symmetric by default (directed=False). This leads to n_classes parameters for unary potentials.
If directed=True, there are n_classes * n_classes parameters for pairwise potentials, if directed=False, there are only n_classes * (n_classes + 1) / 2 (for a symmetric matrix).
Examples, i.e. X, are given as an iterable of n_examples. An example, x, is represented as a tuple (features, edges) where features is a numpy array of shape (n_nodes, n_attributes), and edges is is an array of shape (n_edges, 2), representing the graph.
Labels, Y, are given as an iterable of n_examples. Each label, y, in Y is given by a numpy array of shape (n_nodes,).
There are n_states * n_features parameters for unary potentials. For edge potential parameters, there are n_state * n_states permutations, i.e.
state_1 state_2 state 3 state_1 1 2 3 state_2 4 5 6 state_3 7 8 9
The fitted parameters of this model will be returned as an array with the first n_states * n_features elements representing the unary potentials parameters, followed by the edge potential parameters.
Say we have two state, A and B, and two features 1 and 2. The unary potential parameters will be returned as [A1, A2, B1, B2].
If directed=True the edge potential parameters will return n_states * n_states parameters. The rows are senders and the columns are recievers, i.e. the edge potential state_2 -> state_1 is [2,1]; 4 in the above matrix.
The above edge potential parameters example would be returned as [1, 2, 3, 4, 5, 6, 7, 8, 9] (see numpy.ravel).
If edges are undirected, the edge potential parameter matrix is assumed to be symmetric and only the lower triangle is returned, i.e. [1, 4, 5, 7, 8, 9].
Parameters:n_states : int, default=None
Number of states for all variables. Inferred from data if not provided.
n_features : int, default=None
Number of features per node. Inferred from data if not provided.
inference_method : string or None, default=None
Function to call do do inference and loss-augmented inference. Possible values are:
- ‘max-product’ for max-product belief propagation.
Recommended for chains an trees. Loopy belief propagatin in case of a general graph.
‘lp’ for Linear Programming relaxation using cvxopt.
‘ad3’ for AD3 dual decomposition.
‘qpbo’ for QPBO + alpha expansion.
‘ogm’ for OpenGM inference algorithms.
If None, ad3 is used if installed, otherwise lp.
class_weight : None, or array-like
Class weights. If an array-like is passed, it must have length n_classes. None means equal class weights.
directed : boolean, default=False
Whether to model directed or undirected connections. In undirected models, interaction terms are symmetric, so an edge
a -> bhas the same energy asb -> a.
Methods
batch_inference(X, w[, relaxed]) batch_joint_feature(X, Y[, Y_true]) batch_loss(Y, Y_hat) batch_loss_augmented_inference(X, Y, w[, ...]) continuous_loss(y, y_hat) inference(x, w[, relaxed, return_energy]) Inference for x using parameters w. initialize(X, Y) joint_feature(x, y) Feature vector associated with instance (x, y). loss(y, y_hat) loss_augmented_inference(x, y, w[, relaxed, ...]) Loss-augmented Inference for x relative to y using parameters w. max_loss(y)
__init__(n_states=None, n_features=None, inference_method=None, class_weight=None, directed=False)[source]¶
inference(x, w, relaxed=False, return_energy=False)¶
Inference for x using parameters w.
Finds (approximately) armin_y np.dot(w, joint_feature(x, y)) using self.inference_method.
Parameters:x : tuple
Instance of a graph with unary evidence. x=(unaries, edges) unaries are an nd-array of shape (n_nodes, n_states), edges are an nd-array of shape (n_edges, 2)
w : ndarray, shape=(size_joint_feature,)
Parameters for the CRF energy function.
relaxed : bool, default=False
Whether relaxed inference should be performed. Only meaningful if inference method is ‘lp’ or ‘ad3’. By default fractional solutions are rounded. If relaxed=True, fractional solutions are returned directly.
return_energy : bool, default=False
Returns:Whether to return the energy of the solution (x, y) that was found.
y_pred : ndarray or tuple
By default an inter ndarray of shape=(width, height) of variable assignments for x is returned. If
relaxed=Trueand inference_method islporad3, a tuple (unary_marginals, pairwise_marginals) containing the relaxed inference result is returned. unary marginals is an array of shape (width, height, n_states), pairwise_marginals is an array of shape (n_states, n_states) of accumulated pairwise marginals.
joint_feature(x, y)[source]¶
Feature vector associated with instance (x, y).
Feature representation joint_feature, such that the energy of the configuration (x, y) and a weight vector w is given by np.dot(w, joint_feature(x, y)).
Parameters:x : tuple
Unary evidence.
y : ndarray or tuple
Returns:Either y is an integral ndarray, giving a complete labeling for x. Or it is the result of a linear programming relaxation. In this case,
y=(unary_marginals, pariwise_marginals).
p : ndarray, shape (size_joint_feature,)
Feature vector associated with state (x, y).
loss_augmented_inference(x, y, w, relaxed=False, return_energy=False)¶
Loss-augmented Inference for x relative to y using parameters w.
Finds (approximately) armin_y_hat np.dot(w, joint_feature(x, y_hat)) + loss(y, y_hat) using self.inference_method.
Parameters:x : tuple
Instance of a graph with unary evidence. x=(unaries, edges) unaries are an nd-array of shape (n_nodes, n_features), edges are an nd-array of shape (n_edges, 2)
y : ndarray, shape (n_nodes,)
Ground truth labeling relative to which the loss will be measured.
w : ndarray, shape=(size_joint_feature,)
Parameters for the CRF energy function.
relaxed : bool, default=False
Whether relaxed inference should be performed. Only meaningful if inference method is ‘lp’ or ‘ad3’. By default fractional solutions are rounded. If relaxed=True, fractional solutions are returned directly.
return_energy : bool, default=False
Returns:Whether to return the energy of the solution (x, y) that was found.
y_pred : ndarray or tuple
By default an inter ndarray of shape=(n_nodes) of variable assignments for x is returned. If
relaxed=Trueand inference_method islporad3, a tuple (unary_marginals, pairwise_marginals) containing the relaxed inference result is returned. unary marginals is an array of shape (n_nodes, n_states), pairwise_marginals is an array of shape (n_states, n_states) of accumulated pairwise marginals.
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