def np_ortho(shape, random_state, scale=1.):
"""
Builds a numpy variable filled with orthonormal random values
Parameters
----------
shape, tuple of ints or tuple of tuples
shape of values to initialize
tuple of ints should be single shape
tuple of tuples is primarily for convnets and should be of form
((n_in_kernels, kernel_width, kernel_height),
(n_out_kernels, kernel_width, kernel_height))
random_state, numpy.random.RandomState() object
scale, float (default 1.)
default of 1. results in orthonormal random values sacled by 1.
Returns
-------
initialized_ortho, array-like
Array-like of random values the same size as shape parameter
References
----------
Exact solutions to the nonlinear dynamics of learning in deep linear
neural networks
A. Saxe, J. McClelland, S. Ganguli
"""
if type(shape[0]) is tuple:
shp = (shape[1][0], shape[0][0]) + shape[1][1:]
flat_shp = (shp[0], np.prd(shp[1:]))
else:
shp = shape
flat_shp = shape
g = random_state.randn(*flat_shp)
U, S, VT = linalg.svd(g, full_matrices=False)
res = U if U.shape == flat_shp else VT # pick one with the correct shape
res = res.reshape(shp)
return (scale * res).astype("float32")
def np_ortho(shp, random_state, scale=1.):
"""Builds a numpy variable filled with orthonormal random values.
Args:
shp: tuple of ints or tuple of tuples
shape of values to initialize
tuple of ints should be single shape
tuple of tuples is primarily for convnets and should be of form
((n_in_kernels, kernel_width, kernel_height),
(n_out_kernels, kernel_width, kernel_height))
random_state: numpy.random.RandomState() object
scale: float (default 1.)
default of 1. results in orthonormal random values sacled by 1.
Returns:
initialized_ortho, array-like
Array-like of random values the same size as shape parameter
References
----------
Exact solutions to the nonlinear dynamics of learning in deep linear
neural networks
A. Saxe, J. McClelland, S. Ganguli
"""
if isinstance(shp[0], tuple):
shp = (shp[1][0], shp[0][0]) + shp[1][1:]
flat_shp = (shp[0], np.prd(shp[1:]))
else:
flat_shp = shp
g = random_state.randn(*flat_shp)
u, _, vt = linalg.svd(g, full_matrices=False)
res = u if u.shape == flat_shp else vt # pick one with the correct shape
res = res.reshape(shp)
return (scale * res).astype('float32')
def np_ortho(shape, random_state, scale=1.):
if type(shape[0]) is tuple:
shp = (shape[1][0], shape[0][0]) + shape[1][1:]
flat_shp = (shp[0], np.prd(shp[1:]))
else:
shp = shape
flat_shp = shape
g = random_state.randn(*flat_shp)
U, S, VT = linalg.svd(g, full_matrices=False)
res = U if U.shape == flat_shp else VT # pick one with the correct shape
res = res.reshape(shp)
return (scale * res).astype(theano.config.floatX)
def Wishart_eval(n, V, W, dV=None, dW=None, piV=None):
"""
Evaluation of the probability of W under Wishart(n,V)
Parameters
----------
n: float,
the number of degrees of freedom (dofs)
V: array of shape (n,n)
the scale matrix of the Wishart density
W: array of shape (n,n)
the sample to be evaluated
dV: float, optional,
determinant of V
dW: float, optional,
determinant of W
piV: array of shape (n,n), optional
psuedo-inverse of V
Returns
-------
(float) the density
"""
# check that shape(V)==shape(W)
p = V.shape[0]
if dV == None:
dV = np.prd(eigvalsh(V))
if dW == None:
dW = np.prod(eigvalsh(W))
if piV==None:
piV = inv(V)
ldW = np.log(dW)*(n-p-1)/2
ltr = - np.trace(np.dot(piV, W))/2
la = ( n*p*np.log(2) + np.log(dV)*n )/2
lg = np.log(np.pi)*p*(p-1)/4
#for j in range(p):
# lg += gammaln((n-j)/2)
lg += gammaln(np.arange(n-p+1, n+1).astype(np.float)/2).sum()
lt = ldW + ltr -la -lg
return np.exp(lt)
