median is not implemented

autograd.numpy.median() is not implemented.

[duvenaud]

The gradient will be zero for all elements except for the median element (or the two elements averaged to get the median). Here’s pseudocode:

def median_vjp(a, g):
  N = len(a)
  index_of_median = ((N - 1) / 2) + 0.5
  grad_out = np.zeros_like(a)
  s = numpy.argsort(a)
  if is_odd(N):
    grad_out[s[int(index_of_median)]] = g
  else:
    grad_out[s[int(index_of_median + 0.5)]] = g / 2
    grad_out[s[int(index_of_median - 0.5)]] = g / 2
  return grad_out

If you want to be fancy, you can make it divide the gradient evenly in the case where there’s more than one identical element of a that affects the median.

[dcasasor-purdue]

@dcasasor-purdue that’s hard to fact check,

>>> x = np.random.randn(100, 100)
>>> l, r = x.sum(axis=0) - x.max(axis=0) - x.min(axis=0), np.median(x,axis=0)
>>> np.mean((l-r)**2)                                                       
100.7067891474971

btw, I saw that TFP implements a percentile function so I guess it’s a matter of spelunking in their source to see how the gradient is defined.

sorry @duvenaud the relu comment didn’t lead to enlightenment for me.

@maedoc you are absolutely right. My particular case is actually an implementation of the discontinuous mid function, which takes only three arguments and selects the middle value. This is intended for piecewise continuous process modeling, rather than for a general implementation of the median function. Thanks for the clarification.