import numpy as np
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def accuracy(preds, labels):
"""
Compute accuracy of the model.
Parameters
----------
preds : numpy array
Predictions for all data points and each classes from a softmax function. preds[i, j] correspond
to the prediction of data point i to belong to class j.
labels : numpy array
The labels of the original dataset, as int.
Returns
-------
Accuracy: float
The computed accuracy, as a float.
"""
return np.mean(np.argmax(preds, axis=1) == labels)
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def cross_entropy(preds, labels):
"""
Compute negative cross entropy for given predictions and data.
Parameters
----------
preds: numpy array
Predictions for all data points and each classes from a softmax function. preds[i, j] correspond
to the prediction of data point i to belong to class j.
labels: numpy array
The labels of the original dataset, as int.
Returns
-------
Cross entropy : float
The negative cross-entropy, as float.
"""
num_data = len(labels)
data_idx = np.arange(num_data)
return -np.mean(np.log(preds[data_idx, labels]))
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def binary_cross_entropy(preds, labels):
"""
Compute binary cross entropy for given predictions and data.
Parameters
----------
preds: numpy array
Predictions for all data points and each classes from a sigmoid function. preds[i, j] correspond
to the prediction of data point i to belong to class j.
labels: numpy array
The labels of the original dataset, as int.
Returns
-------
Cross entropy : float
The negative cross-entropy, as float.
"""
preds = preds.reshape(-1)
return -np.mean(labels * np.log(preds) + (1 - labels) * np.log(1 - preds))
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def mse(preds, target):
"""
Compute mean squared error for given predictions and data.
Parameters
----------
preds: numpy array
Predictions for all data points and each classes from a regression model. preds[i, j] correspond
to the prediction of data point i for class j.
target: numpy array
The target values of the original dataset.
Returns
-------
Mean squared error : float
The mean squared error, as float.
"""
return np.mean((preds.reshape(-1) - target) ** 2)
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def weighted_binary_cross_entropy(logits, labels):
"""
Compute weighted binary cross entropy for given logits and data.
The weights are all ones. This function is used in the ordinal
regression model with coral estimation.
Parameters
----------
logits: numpy array
Logits for all data points and each classes. logits[i, j] correspond
to the logits of data point i to class j.
labels: numpy array
The labels of the original dataset, as int.
Returns
-------
Cross entropy : float
The negative cross-entropy, as float.
"""
binary_labels = labels.reshape(-1, 1) > np.arange(logits.shape[1])
logits_exp = np.log(1 + np.exp(logits))
loss = (1 - binary_labels) * logits -logits_exp
return -np.mean(loss)
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def safe_softplus(x, beta = 1, threshold = 20):
"""
Compute the softplus function in a safe way to avoid numerical issues.
Parameters
----------
x: numpy array
The input of the softplus function.
beta: float
The beta parameter for the softplus function.
threshold: float
The threshold for the input of the exponential function.
Returns
-------
Softplus : numpy array
The softplus function applied to x.
"""
return np.where(beta * x > threshold, x, (1 / beta) * np.logaddexp(0, beta * x))
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def coral_eval(preds, labels):
"""
Evaluate the Coral model using the multilabel binary cross-entropy loss function.
Parameters
----------
preds : np.array
The predictions of the model.
labels : np.array
The labels of the dataset.
Returns
-------
loss : float
The cross-entropy loss.
"""
sigmoids = - np.cumsum(preds, axis=1)[:, :-1] + 1
classes = np.arange(preds.shape[1] - 1)
levels = labels[:, None] > classes[None, :]
return - np.mean(np.log(sigmoids) * levels + np.log(1 - sigmoids) * (1 - levels), axis=1).mean()