def _build_prior(self, name, Xs, jitter, **kwargs):
self.N = int(np.prod([len(X) for X in Xs]))
mu = self.mean_func(cartesian(*Xs))
chols = [cholesky(stabilize(cov(X), jitter)) for cov, X in zip(self.cov_funcs, Xs)]
v = pm.Normal(name + "_rotated_", mu=0.0, sigma=1.0, size=self.N, **kwargs)
f = pm.Deterministic(name, mu + at.flatten(kron_dot(chols, v)))
return f
def max_pool(images, imgshp, maxpoolshp):
"""Implements a max pooling layer
Takes as input a 2D tensor of shape batch_size x img_size and
performs max pooling. Max pooling downsamples by taking the max
value in a given area, here defined by maxpoolshp. Outputs a 2D
tensor of shape batch_size x output_size.
:param images: 2D tensor containing images on which to apply convolution.
Assumed to be of shape batch_size x img_size
:param imgshp: tuple containing image dimensions
:param maxpoolshp: tuple containing shape of area to max pool over
:return: out1, symbolic result (2D tensor)
:return: out2, logical shape of the output
"""
poolsize = np.int64(np.prod(maxpoolshp))
# imgshp contains either 2 entries (height,width) or 3 (nfeatures,h,w)
# in the first case, default nfeatures to 1
if np.size(imgshp) == 2:
imgshp = (1, ) + imgshp
# construct indices and index pointers for sparse matrix, which,
# when multiplied with input images will generate a stack of image
# patches
indices, indptr, spmat_shape, sptype, outshp = convolution_indices.conv_eval(
imgshp, maxpoolshp, maxpoolshp, mode="valid")
# print 'XXXXXXXXXXXXXXXX MAX POOLING LAYER XXXXXXXXXXXXXXXXXXXX'
# print 'imgshp = ', imgshp
# print 'maxpoolshp = ', maxpoolshp
# print 'outshp = ', outshp
# build sparse matrix, then generate stack of image patches
csc = aesara.sparse.CSM(sptype)(np.ones(indices.size), indices, indptr,
spmat_shape)
patches = sparse.structured_dot(csc, images.T).T
pshape = aet.stack([
images.shape[0] * aet.as_tensor(np.prod(outshp)),
aet.as_tensor(imgshp[0]),
aet.as_tensor(poolsize),
])
patch_stack = reshape(patches, pshape, ndim=3)
out1 = tt_max(patch_stack, axis=2)
pshape = aet.stack([
images.shape[0],
aet.as_tensor(np.prod(outshp)),
aet.as_tensor(imgshp[0]),
])
out2 = reshape(out1, pshape, ndim=3)
out3 = DimShuffle(out2.broadcastable, (0, 2, 1))(out2)
return aet.flatten(out3, 2), outshp
def jacobian1(f, v):
"""jacobian of f wrt v"""
f = at.flatten(f)
idx = at.arange(f.shape[0], dtype="int32")
def grad_i(i):
return gradient1(f[i], v)
return aesara.map(grad_i, idx)[0]
def _build_prior(self, name, Xs, **kwargs):
self.N = np.prod([len(X) for X in Xs])
mu = self.mean_func(cartesian(*Xs))
chols = [
cholesky(stabilize(cov(X))) for cov, X in zip(self.cov_funcs, Xs)
]
# remove reparameterization option
v = pm.Normal(name + "_rotated_",
mu=0.0,
sigma=1.0,
shape=self.N,
**kwargs)
f = pm.Deterministic(name, mu + at.flatten(kron_dot(chols, v)))
return f
def test_log1msigm_to_softplus(self):
x = matrix()
out = log(1 - sigmoid(x))
f = aesara.function([x], out, mode=self.m)
topo = f.maker.fgraph.toposort()
assert len(topo) == 2
assert isinstance(topo[0].op.scalar_op, ScalarSoftplus)
assert isinstance(topo[1].op.scalar_op, aesara.scalar.Neg)
# assert check_stack_trace(f, ops_to_check='all')
f(np.random.rand(54, 11).astype(config.floatX))
# Same test with a flatten
out = log(1 - aet.flatten(sigmoid(x)))
f = aesara.function([x], out, mode=self.m)
# assert check_stack_trace(f, ops_to_check='all')
topo = f.maker.fgraph.toposort()
assert len(topo) == 3
assert aet.is_flat(topo[0].outputs[0])
assert isinstance(topo[1].op.scalar_op, ScalarSoftplus)
assert isinstance(topo[2].op.scalar_op, aesara.scalar.Neg)
f(np.random.rand(54, 11).astype(config.floatX))
# Same test with a reshape
out = log(1 - sigmoid(x).reshape([x.size]))
f = aesara.function([x], out, mode=self.m)
topo = f.maker.fgraph.toposort()
# assert len(topo) == 3
assert any(isinstance(node.op, Reshape) for node in topo)
assert any(
isinstance(
getattr(node.op, "scalar_op", None),
ScalarSoftplus,
) for node in topo)
f(np.random.rand(54, 11).astype(config.floatX))
def gradient1(f, v):
"""flat gradient of f wrt v"""
return at.flatten(grad(f, v, disconnected_inputs="warn"))
def conv2d(
input,
filters,
image_shape=None,
filter_shape=None,
border_mode="valid",
subsample=(1, 1),
**kargs,
):
"""
signal.conv.conv2d performs a basic 2D convolution of the input with the
given filters. The input parameter can be a single 2D image or a 3D tensor,
containing a set of images. Similarly, filters can be a single 2D filter or
a 3D tensor, corresponding to a set of 2D filters.
Shape parameters are optional and will result in faster execution.
Parameters
----------
input : Symbolic aesara tensor for images to be filtered.
Dimensions: ([num_images], image height, image width)
filters : Symbolic aesara tensor for convolution filter(s).
Dimensions: ([num_filters], filter height, filter width)
border_mode: {'valid', 'full'}
See scipy.signal.convolve2d.
subsample
Factor by which to subsample output.
image_shape : tuple of length 2 or 3
([num_images,] image height, image width).
filter_shape : tuple of length 2 or 3
([num_filters,] filter height, filter width).
kwargs
See aesara.tensor.nnet.conv.conv2d.
Returns
-------
symbolic 2D,3D or 4D tensor
Tensor of filtered images, with shape
([number images,] [number filters,] image height, image width).
"""
assert input.ndim in (2, 3)
assert filters.ndim in (2, 3)
# use shape information if it is given to us ###
if filter_shape and image_shape:
if input.ndim == 3:
bsize = image_shape[0]
else:
bsize = 1
imshp = (1, ) + tuple(image_shape[-2:])
if filters.ndim == 3:
nkern = filter_shape[0]
else:
nkern = 1
kshp = filter_shape[-2:]
else:
nkern, kshp = None, None
bsize, imshp = None, None
# reshape tensors to 4D, for compatibility with ConvOp ###
if input.ndim == 3:
sym_bsize = input.shape[0]
else:
sym_bsize = 1
if filters.ndim == 3:
sym_nkern = filters.shape[0]
else:
sym_nkern = 1
new_input_shape = aet.join(0, aet.stack([sym_bsize, 1]), input.shape[-2:])
input4D = reshape(input, new_input_shape, ndim=4)
new_filter_shape = aet.join(0, aet.stack([sym_nkern, 1]),
filters.shape[-2:])
filters4D = reshape(filters, new_filter_shape, ndim=4)
# perform actual convolution ###
op = conv.ConvOp(
output_mode=border_mode,
dx=subsample[0],
dy=subsample[1],
imshp=imshp,
kshp=kshp,
nkern=nkern,
bsize=bsize,
**kargs,
)
output = op(input4D, filters4D)
# flatten to 3D tensor if convolving with single filter or single image
if input.ndim == 2 and filters.ndim == 2:
if config.warn__signal_conv2d_interface:
warnings.warn(
"aesara.tensor.signal.conv2d() now outputs a 2d tensor when both"
" inputs are 2d. To disable this warning, set the Aesara flag"
" warn__signal_conv2d_interface to False",
stacklevel=3,
)
output = aet.flatten(output.T, ndim=2).T
elif input.ndim == 2 or filters.ndim == 2:
output = aet.flatten(output.T, ndim=3).T
return output
def convolve(
kerns,
kshp,
nkern,
images,
imgshp,
step=(1, 1),
bias=None,
mode="valid",
flatten=True,
):
"""Convolution implementation by sparse matrix multiplication.
:note: For best speed, put the matrix which you expect to be
smaller as the 'kernel' argument
"images" is assumed to be a matrix of shape batch_size x img_size,
where the second dimension represents each image in raster order
If flatten is "False", the output feature map will have shape:
.. code-block:: python
batch_size x number of kernels x output_size
If flatten is "True", the output feature map will have shape:
.. code-block:: python
batch_size x number of kernels * output_size
.. note::
IMPORTANT: note that this means that each feature map (image
generate by each kernel) is contiguous in memory. The memory
layout will therefore be: [ <feature_map_0> <feature_map_1>
... <feature_map_n>], where <feature_map> represents a
"feature map" in raster order
kerns is a 2D tensor of shape nkern x N.prod(kshp)
:param kerns: 2D tensor containing kernels which are applied at every pixel
:param kshp: tuple containing actual dimensions of kernel (not symbolic)
:param nkern: number of kernels/filters to apply.
nkern=1 will apply one common filter to all input pixels
:param images: tensor containing images on which to apply convolution
:param imgshp: tuple containing image dimensions
:param step: determines number of pixels between adjacent receptive fields
(tuple containing dx,dy values)
:param mode: 'full', 'valid' see CSM.evaluate function for details
:param sumdims: dimensions over which to sum for the tensordot operation.
By default ((2,),(1,)) assumes kerns is a nkern x kernsize
matrix and images is a batchsize x imgsize matrix
containing flattened images in raster order
:param flatten: flatten the last 2 dimensions of the output. By default,
instead of generating a batchsize x outsize x nkern tensor,
will flatten to batchsize x outsize*nkern
:return: out1, symbolic result
:return: out2, logical shape of the output img (nkern,heigt,width)
:TODO: test for 1D and think of how to do n-d convolutions
"""
# start by computing output dimensions, size, etc
kern_size = np.int64(np.prod(kshp))
# inshp contains either 2 entries (height,width) or 3 (nfeatures,h,w)
# in the first case, default nfeatures to 1
if np.size(imgshp) == 2:
imgshp = (1, ) + imgshp
# construct indices and index pointers for sparse matrix, which,
# when multiplied with input images will generate a stack of image
# patches
indices, indptr, spmat_shape, sptype, outshp = convolution_indices.conv_eval(
imgshp, kshp, step, mode)
# build sparse matrix, then generate stack of image patches
csc = aesara.sparse.CSM(sptype)(np.ones(indices.size), indices, indptr,
spmat_shape)
patches = (sparse.structured_dot(csc, images.T)).T
# compute output of linear classifier
pshape = aet.stack([
images.shape[0] * aet.as_tensor(np.prod(outshp)),
aet.as_tensor(imgshp[0] * kern_size),
])
patch_stack = reshape(patches, pshape, ndim=2)
# kern is of shape: nkern x ksize*number_of_input_features
# output is thus of shape: bsize*outshp x nkern
output = dot(patch_stack, kerns.T)
# add bias across each feature map (more efficient to do it now)
if bias is not None:
output += bias
# now to have feature maps in raster order ...
# go from bsize*outshp x nkern to bsize x nkern*outshp
newshp = aet.stack([
images.shape[0],
aet.as_tensor(np.prod(outshp)),
aet.as_tensor(nkern)
])
tensout = reshape(output, newshp, ndim=3)
output = DimShuffle((False, ) * tensout.ndim, (0, 2, 1))(tensout)
if flatten:
output = aet.flatten(output, 2)
return output, np.hstack((nkern, outshp))
def diag(self, X):
X, _ = self._slice(X, None)
cov_diag = self.cov_func(X, diag=True)
scf_diag = at.square(at.flatten(self.scaling_func(X, self.args)))
return cov_diag * scf_diag
