I'm a total neophyte when it comes to Autograd, so I feel like I may be doing something very obviously wrong. However, I've spent a full day struggling on this.
I am trying to calculate the derivative of a function that includes a normal cdf. I had no success with Autograd, so I broke it up into smaller and smaller parts until I isolated the source of error as the Normal CDF. Here is a minimal working example:
import autograd.numpy as np
from autograd.misc.optimizers import adam, rmsprop, sgd
from autograd import grad
from autograd.scipy.stats import norm
def test_func(x,t):
return norm.cdf(x)
grad_test = grad(test_func)
def callback(params, t, g):
print(params, " Gradient: ", g, " Derivative: ", norm.pdf(params))
print(adam(grad_test, 0.0 ,num_iters = 10, step_size= 0.1, callback = callback))
I know it doesn't make sense to optimize a CDF, I just did this to get the output from the callback, which is below:
0.0 Gradient: 0.24197072451914337 Derivative: 0.398942280401
-0.09999999586726883 Gradient: 0.26608524890906193 Derivative: 0.396952547641
-0.20013469787000787 Gradient: 0.2897227684832687 Derivative: 0.391032156046
-0.30048876968878535 Gradient: 0.31236074851454854 Derivative: 0.38133185077
-0.40113882898768705 Gradient: 0.33345215596996947 Derivative: 0.368102181121
-0.5021500752550674 Gradient: 0.35244319911051986 Derivative: 0.351686233767
-0.6035729426432459 Gradient: 0.3687944858147128 Derivative: 0.332508890217
-0.7054397817605528 Gradient: 0.38200507149861374 Derivative: 0.311062576619
-0.8077615706004915 Gradient: 0.391638389745137 Derivative: 0.287889684926
-0.910524672771251 Gradient: 0.3973485394632615 Derivative: 0.263562137446
The gradients calculated by Autograd dont match the theoretical derivative, represented by the normal PDF.
Am I implementing this incorrectly? I feel it's unlikely that such a widely used package would have a hole like this. How can I use Autograd (or other packages in Python) in order to get efficient numerical derivatives of a function that outputs a scalar.
