A Gaussian Kernel in Theano

Theano Gaussian Kernel

import theano, theano.tensor as T, numpy as np

def _outer_substract(x, y):
    x = x.dimshuffle(0, 1, 'x')
    x = T.addbroadcast(x, 2)
    return (x - y.T).T
def _gaussian_kernel(x, y, beta = 0.1):
    K = _outer_substract(x,y)
    return T.exp( -beta * K.norm(L=2,axis=1))
x = T.matrix()
z = T.matrix()

gaussian_kernel = theano.function([x, z], _gaussian_kernel(x,z), allow_input_downcast=True)


N = 100
M = 200
DIMS = 10
a = np.random.randn(N, DIMS)
b = np.random.randn(M, DIMS)

%timeit gaussian_kernel(a, b)
# 1000 loops, best of 3: 1.04 ms per loop

def np_outer_substract(x, y):
    return (x[:,:, np.newaxis] - y.T).T

def np_gaussian_kernel(x,y, beta=0.1):
    K = np_outer_substract(x,y)
    return np.exp( -beta * np.linalg.norm(K, axis=1))

%timeit np_gaussian_kernel(a,b)
# 1000 loops, best of 3: 1.14 ms per loop