Source code for monai.metrics.mmd

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from __future__ import annotations

from import Callable

import torch

from monai.metrics.metric import Metric

[docs] class MMDMetric(Metric): """ Unbiased Maximum Mean Discrepancy (MMD) is a kernel-based method for measuring the similarity between two distributions. It is a non-negative metric where a smaller value indicates a closer match between the two distributions. Gretton, A., et al,, 2012. A kernel two-sample test. The Journal of Machine Learning Research, 13(1), pp.723-773. Args: y_mapping: Callable to transform the y tensors before computing the metric. It is usually a Gaussian or Laplace filter, but it can be any function that takes a tensor as input and returns a tensor as output such as a feature extractor or an Identity function., e.g. `y_mapping = lambda x: x.square()`. """ def __init__(self, y_mapping: Callable | None = None) -> None: super().__init__() self.y_mapping = y_mapping def __call__(self, y: torch.Tensor, y_pred: torch.Tensor) -> torch.Tensor: return compute_mmd(y, y_pred, self.y_mapping)
[docs] def compute_mmd(y: torch.Tensor, y_pred: torch.Tensor, y_mapping: Callable | None) -> torch.Tensor: """ Args: y: first sample (e.g., the reference image). Its shape is (B,C,W,H) for 2D data and (B,C,W,H,D) for 3D. y_pred: second sample (e.g., the reconstructed image). It has similar shape as y. y_mapping: Callable to transform the y tensors before computing the metric. """ if y_pred.shape[0] == 1 or y.shape[0] == 1: raise ValueError("MMD metric requires at least two samples in y and y_pred.") if y_mapping is not None: y = y_mapping(y) y_pred = y_mapping(y_pred) if y_pred.shape != y.shape: raise ValueError( "y_pred and y shapes dont match after being processed " f"by their transforms, received y_pred: {y_pred.shape} and y: {y.shape}" ) for d in range(len(y.shape) - 1, 1, -1): y = y.squeeze(dim=d) y_pred = y_pred.squeeze(dim=d) y = y.view(y.shape[0], -1) y_pred = y_pred.view(y_pred.shape[0], -1) y_y =, y.t()) y_pred_y_pred =, y_pred.t()) y_pred_y =, y.t()) m = y.shape[0] n = y_pred.shape[0] # Ref. 1 Eq. 3 (found under Lemma 6) # term 1 c1 = 1 / (m * (m - 1)) a = torch.sum(y_y - torch.diag(torch.diagonal(y_y))) # term 2 c2 = 1 / (n * (n - 1)) b = torch.sum(y_pred_y_pred - torch.diag(torch.diagonal(y_pred_y_pred))) # term 3 c3 = 2 / (m * n) c = torch.sum(y_pred_y) mmd = c1 * a + c2 * b - c3 * c return mmd