import torch
from ._BaseLoss import BaseLoss
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class Exponential(BaseLoss):
"""
The exponential loss. Used for binary classification.
Args:
reduction (str, optional): The reduction method. Must be one of "mean" or "sum". Defaults to "mean".
"""
def __init__(self, reduction="mean"):
if reduction not in ["mean", "sum"]:
raise ValueError('reduction must be in ["mean", "sum"].')
self.reduction = reduction
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def loss(self, prediction, true_output):
"""
Calculates the exponential loss with the equations:
.. math::
\\begin{align*}
l_i &= y_i\\cdot e^{-f(x_i)} + (1 - y_i)\\cdot e^{f(x_i)},\\\\
L_{sum} &= \\sum_{i=1}^n l_i \\text{ or } L_{mean} = \\frac{1}{n}\\sum_{i=1}^n l_i,
\\end{align*}
where :math:`f(x_i)` is the predicted value and :math:`y_i` is the true value.
Args:
prediction (torch.Tensor): A tensor of predicted values as a probability distribution. Must be the same shape as the true_output.
true_output (torch.Tensor): A one-hot encoded tensor of true values. Must be the same shape as the prediction.
Returns:
torch.Tensor: A tensor containing a single value with the loss.
"""
if not isinstance(prediction, torch.Tensor) or not isinstance(true_output, torch.Tensor):
raise TypeError("prediction and true_output must be torch tensors.")
if prediction.shape != true_output.shape:
raise ValueError("prediction and true_output must have the same shape.")
if set(torch.unique(true_output).numpy()) != {0, 1}:
raise ValueError("The classes must be labelled 0 and 1.")
prediction = 2 * prediction - 1
true_output = 2 * true_output - 1
loss = torch.exp(-prediction * true_output)
if self.reduction == "mean":
return loss.mean()
return loss.sum()
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def gradient(self, prediction, true_output):
"""
Calculates the gradient of the exponential loss.
Args:
prediction (torch.Tensor): A tensor of predicted values in range [0, 1]. Must be the same shape as the true_output.
true_output (torch.Tensor): A tensor of true values labeled with 0 or 1. Must be the same shape as the prediction.
Returns:
torch.Tensor: A tensor of the same shape as the inputs containing the gradients.
"""
if not isinstance(prediction, torch.Tensor) or not isinstance(true_output, torch.Tensor):
raise TypeError("prediction and true_output must be torch tensors.")
if prediction.shape != true_output.shape:
raise ValueError("prediction and true_output must have the same shape.")
if set(torch.unique(true_output).numpy()) != {0, 1}:
raise ValueError("The classes must be labelled 0 and 1.")
prediction = 2 * prediction - 1
true_output = 2 * true_output - 1
grad = -2 * true_output * torch.exp(-prediction * true_output)
if self.reduction == "mean":
return grad / prediction.shape[0]
return grad
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def hessian(self, prediction, true_output):
"""
Calculates the diagonal of the hessian matrix of the exponential loss.
Args:
prediction (torch.Tensor): A tensor of predicted values in range [0, 1]. Must be the same shape as the true_output.
true_output (torch.Tensor): A tensor of true values labeled with 0 or 1. Must be the same shape as the prediction.
Returns:
torch.Tensor: A tensor of the same shape as the inputs containing the diagonal of the hessian matrix.
"""
if not isinstance(prediction, torch.Tensor) or not isinstance(true_output, torch.Tensor):
raise TypeError("prediction and true_output must be torch tensors.")
if prediction.shape != true_output.shape:
raise ValueError("prediction and true_output must have the same shape.")
if set(torch.unique(true_output).numpy()) != {0, 1}:
raise ValueError("The classes must be labelled 0 and 1.")
prediction = 2 * prediction - 1
true_output = 2 * true_output - 1
grad = 4 * true_output ** 2 * torch.exp(-prediction * true_output)
if self.reduction == "mean":
return grad / prediction.shape[0]
return grad