code: def hsic(kx, ky, device):
      """
      Perform independent test with Hilbert-Schmidt Independence Criterion (HSIC) between two sets of variables x and y.
  
      Args:
          kx (2-D tensor): kernel matrix of x, shape (n_samples, n_samples)
          ky (2-D tensor): kernel matrix of y, shape (n_samples, n_samples)
          device (torch.device): the desired device of returned tensor
  
      Returns:
          [tensor]: Independent test score >= 0
  
      Reference:
          [1] Gretton, Arthur, Bousquet, Olivier, Smola, Alex, and Schölkopf, Bernhard. Measuring Statistical Dependence
              with Hilbert-Schmidt Norms. In Algorithmic Learning Theory (ALT), pp. 63–77. 2005.
          [2] Gretton, Arthur, Fukumizu, Kenji, Teo, Choon H., Song, Le, Schölkopf, Bernhard, and Smola, Alex J. A Kernel
              Statistical Test of Independence. In Advances in Neural Information Processing Systems, pp. 585–592. 2008.
      """
  
      n = kx.shape[0]
      if ky.shape[0] != n:
          raise ValueError(
              "kx and ky are expected to have the same sample sizes."
          )
      ctr_mat = (
          torch.eye(n, device=device)
          - torch.ones((n, n), device=device) / n
      )
      return torch.trace(
          torch.mm(torch.mm(torch.mm(kx, ctr_mat), ky), ctr_mat)
      ) / (n**2)
  
file_path: pykale/kale/predict/losses.py
imports: import torch
  import torch.nn
  from torch.autograd import grad
  from torch.nn import functional
label_desc: Use image node_id 9 for calling a global function with example usage: hsic(kx, ky, device) and returns: unknown