def _compute_phi_from_parents(*u_parents): # Compute weighted average of the parameters # Cluster parameters Phi = distribution._compute_phi_from_parents(*(u_parents[1:])) # Contributions/weights/probabilities P = u_parents[0][0] phi = list() for ind in range(len(Phi)): # Compute element-wise product and then sum over K clusters. # Note that the dimensions aren't perfectly aligned because # the cluster dimension (K) may be arbitrary for phi, and phi # also has dimensions (Dd,..,D0) of the parameters. # Shape(phi) = [Nn,..,K,..,N0,Dd,..,D0] # Shape(p) = [Nn,..,N0,K] # Shape(result) = [Nn,..,N0,Dd,..,D0] # General broadcasting rules apply for Nn,..,N0, that is, # preceding dimensions may be missing or dimension may be # equal to one. Probably, shape(phi) has lots of missing # dimensions and/or dimensions that are one. if cluster_plate < 0: cluster_axis = cluster_plate - distribution.ndims[ind] #else: # cluster_axis = cluster_plate # Move cluster axis to the last: # Shape(phi) = [Nn,..,N0,Dd,..,D0,K] phi.append(utils.moveaxis(Phi[ind], cluster_axis, -1)) # Add axes to p: # Shape(p) = [Nn,..,N0,K,1,..,1] p = utils.add_trailing_axes(P, distribution.ndims[ind]) # Move cluster axis to the last: # Shape(p) = [Nn,..,N0,1,..,1,K] p = utils.moveaxis(p, -(distribution.ndims[ind]+1), -1) #print('Mixture.compute_phi, p:', np.sum(p, axis=-1)) #print('mixture.compute_phi shapes:') #print(np.shape(p)) #print(np.shape(phi[ind])) # Now the shapes broadcast perfectly and we can sum # p*phi over the last axis: # Shape(result) = [Nn,..,N0,Dd,..,D0] phi[ind] = utils.sum_product(p, phi[ind], axes_to_sum=-1) return phi
def _compute_phi_from_parents(*u_parents): # Compute weighted average of the parameters # Cluster parameters Phi = distribution._compute_phi_from_parents(*(u_parents[1:])) # Contributions/weights/probabilities P = u_parents[0][0] phi = list() for ind in range(len(Phi)): # Compute element-wise product and then sum over K clusters. # Note that the dimensions aren't perfectly aligned because # the cluster dimension (K) may be arbitrary for phi, and phi # also has dimensions (Dd,..,D0) of the parameters. # Shape(phi) = [Nn,..,K,..,N0,Dd,..,D0] # Shape(p) = [Nn,..,N0,K] # Shape(result) = [Nn,..,N0,Dd,..,D0] # General broadcasting rules apply for Nn,..,N0, that is, # preceding dimensions may be missing or dimension may be # equal to one. Probably, shape(phi) has lots of missing # dimensions and/or dimensions that are one. if cluster_plate < 0: cluster_axis = cluster_plate - distribution.ndims[ind] #else: # cluster_axis = cluster_plate # Move cluster axis to the last: # Shape(phi) = [Nn,..,N0,Dd,..,D0,K] phi.append(utils.moveaxis(Phi[ind], cluster_axis, -1)) # Add axes to p: # Shape(p) = [Nn,..,N0,K,1,..,1] p = utils.add_trailing_axes(P, distribution.ndims[ind]) # Move cluster axis to the last: # Shape(p) = [Nn,..,N0,1,..,1,K] p = utils.moveaxis(p, -(distribution.ndims[ind] + 1), -1) #print('Mixture.compute_phi, p:', np.sum(p, axis=-1)) #print('mixture.compute_phi shapes:') #print(np.shape(p)) #print(np.shape(phi[ind])) # Now the shapes broadcast perfectly and we can sum # p*phi over the last axis: # Shape(result) = [Nn,..,N0,Dd,..,D0] phi[ind] = utils.sum_product(p, phi[ind], axes_to_sum=-1) return phi
def compute_phi_from_parents(self, *u_parents, mask=True): # Compute weighted average of the parameters # Cluster parameters Phi = self.distribution.compute_phi_from_parents(*(u_parents[1:])) # Contributions/weights/probabilities P = u_parents[0][0] phi = list() for ind in range(len(Phi)): # Compute element-wise product and then sum over K clusters. # Note that the dimensions aren't perfectly aligned because # the cluster dimension (K) may be arbitrary for phi, and phi # also has dimensions (Dd,..,D0) of the parameters. # Shape(phi) = [Nn,..,K,..,N0,Dd,..,D0] # Shape(p) = [Nn,..,N0,K] # Shape(result) = [Nn,..,N0,Dd,..,D0] # General broadcasting rules apply for Nn,..,N0, that is, # preceding dimensions may be missing or dimension may be # equal to one. Probably, shape(phi) has lots of missing # dimensions and/or dimensions that are one. if self.cluster_plate < 0: cluster_axis = self.cluster_plate - self.distribution.ndims[ind] else: raise RuntimeError("Cluster plate should be negative") # Move cluster axis to the last: # Shape(phi) = [Nn,..,N0,Dd,..,D0,K] if np.ndim(Phi[ind]) >= abs(cluster_axis): phi.append(utils.moveaxis(Phi[ind], cluster_axis, -1)) else: phi.append(Phi[ind][...,None]) # Add axes to p: # Shape(p) = [Nn,..,N0,K,1,..,1] p = utils.add_trailing_axes(P, self.distribution.ndims[ind]) # Move cluster axis to the last: # Shape(p) = [Nn,..,N0,1,..,1,K] p = utils.moveaxis(p, -(self.distribution.ndims[ind]+1), -1) # Now the shapes broadcast perfectly and we can sum # p*phi over the last axis: # Shape(result) = [Nn,..,N0,Dd,..,D0] phi[ind] = utils.sum_product(p, phi[ind], axes_to_sum=-1) return phi
def _compute_cgf_from_parents(*u_parents): # Compute weighted average of g over the clusters. # Shape(g) = [Nn,..,K,..,N0] # Shape(p) = [Nn,..,N0,K] # Shape(result) = [Nn,..,N0] # Compute g for clusters: # Shape(g) = [Nn,..,K,..,N0] g = distribution._compute_cgf_from_parents(*(u_parents[1:])) # Move cluster axis to last: # Shape(g) = [Nn,..,N0,K] g = utils.moveaxis(g, cluster_plate, -1) # Cluster assignments/contributions/probabilities/weights: # Shape(p) = [Nn,..,N0,K] p = u_parents[0][0] # Weighted average of g over the clusters. As p and g are # properly aligned, you can just sum p*g over the last # axis and utilize broadcasting: # Shape(result) = [Nn,..,N0] #print('mixture.compute_g_from_parents p and g:', np.shape(p), np.shape(g)) g = utils.sum_product(p, g, axes_to_sum=-1) #print('mixture.compute_g_from_parents g:', np.sum(g), np.shape(g)) return g
def compute_cgf_from_parents(self, *u_parents): # Compute weighted average of g over the clusters. # Shape(g) = [Nn,..,K,..,N0] # Shape(p) = [Nn,..,N0,K] # Shape(result) = [Nn,..,N0] # Compute g for clusters: # Shape(g) = [Nn,..,K,..,N0] g = self.distribution.compute_cgf_from_parents(*(u_parents[1:])) # Move cluster axis to last: # Shape(g) = [Nn,..,N0,K] g = utils.moveaxis(g, self.cluster_plate, -1) # Cluster assignments/contributions/probabilities/weights: # Shape(p) = [Nn,..,N0,K] p = u_parents[0][0] # Weighted average of g over the clusters. As p and g are # properly aligned, you can just sum p*g over the last # axis and utilize broadcasting: # Shape(result) = [Nn,..,N0] g = utils.sum_product(p, g, axes_to_sum=-1) return g
def integrated_logpdf_from_parents(self, x, index): """ Approximates the posterior predictive pdf \int p(x|parents) q(parents) dparents in log-scale as \int q(parents_i) exp( \int q(parents_\i) \log p(x|parents) dparents_\i ) dparents_i.""" if index == 0: # Integrate out the cluster assignments # First, integrate the cluster parameters in log-scale # compute_logpdf(cls, u, phi, g, f): # Shape(x) = [M1,..,Mm,N1,..,Nn,D1,..,Dd] # Add the cluster axis to x: # Shape(x) = [M1,..,Mm,N1,..,1,..,Nn,D1,..,Dd] cluster_axis = self.cluster_plate - \ self._moments.ndim_observations x = np.expand_dims(x, axis=cluster_axis) u_parents = self._message_from_parents() # Shape(u) = [M1,..,Mm,N1,..,1,..,Nn,D1,..,Dd] # Shape(f) = [M1,..,Mm,N1,..,1,..,Nn] (u, f) = self._distribution.distribution.compute_fixed_moments_and_f(x) # Shape(phi) = [N1,..,K,..,Nn,D1,..,Dd] phi = self._distribution.distribution.compute_phi_from_parents(*(u_parents[1:])) # Shape(g) = [N1,..,K,..,Nn] g = self._distribution.distribution.compute_cgf_from_parents(*(u_parents[1:])) # Shape(lpdf) = [M1,..,Mm,N1,..,K,..,Nn] lpdf = self._distribution.distribution.compute_logpdf(u, phi, g, f) # From logpdf to pdf, but avoid over/underflow lpdf_max = np.max(lpdf, axis=self.cluster_plate, keepdims=True) pdf = np.exp(lpdf-lpdf_max) # Move cluster axis to be the last: # Shape(pdf) = [M1,..,Mm,N1,..,Nn,K] pdf = utils.moveaxis(pdf, self.cluster_plate, -1) # Cluster assignments/probabilities/weights # Shape(p) = [N1,..,Nn,K] p = u_parents[0][0] # Weighted average. TODO/FIXME: Use einsum! # Shape(pdf) = [M1,..,Mm,N1,..,Nn] pdf = np.sum(pdf * p, axis=self.cluster_plate) # Back to log-scale (add the overflow fix!) lpdf_max = np.squeeze(lpdf_max, axis=self.cluster_plate) lpdf = np.log(pdf) + lpdf_max return lpdf raise NotImplementedError()
def _compute_message_to_parent(parent, index, u, *u_parents): """ . """ #print('Mixture.compute_message:') if index == 0: # Shape(phi) = [Nn,..,K,..,N0,Dd,..,D0] # Shape(L) = [Nn,..,K,..,N0] # Shape(u) = [Nn,..,N0,Dd,..,D0] # Shape(result) = [Nn,..,N0,K] # Compute g: # Shape(g) = [Nn,..,K,..,N0] g = distribution._compute_cgf_from_parents(*(u_parents[1:])) # Reshape(g): # Shape(g) = [Nn,..,N0,K] g = utils.moveaxis(g, cluster_plate, -1) # Compute phi: # Shape(phi) = [Nn,..,K,..,N0,Dd,..,D0] phi = distribution._compute_phi_from_parents(*(u_parents[1:])) # Reshape phi: # Shape(phi) = [Nn,..,N0,K,Dd,..,D0] for ind in range(len(phi)): phi[ind] = utils.moveaxis( phi[ind], cluster_plate - distribution.ndims[ind], -1 - distribution.ndims[ind]) # Reshape u: # Shape(u) = [Nn,..,N0,1,Dd,..,D0] u_self = list() for ind in range(len(u)): u_self.append( np.expand_dims(u[ind], axis=(-1 - distribution.ndims[ind]))) # Compute logpdf: # Shape(L) = [Nn,..,N0,K] L = distribution._compute_logpdf(u_self, phi, g, 0) # Sum over other than the cluster dimensions? No! # Hmm.. I think the message passing method will do # that automatically ## print(np.shape(phi[0])) ## print(np.shape(u_self[0])) ## print(np.shape(g)) ## print(np.shape(L)) return [L] elif index >= 1: # Parent index for the distribution used for the # mixture. index = index - 1 # Reshape u: # Shape(u) = [Nn,..1,..,N0,Dd,..,D0] u_self = list() for ind in range(len(u)): if cluster_plate < 0: cluster_axis = cluster_plate - distribution.ndims[ind] else: cluster_axis = cluster_plate u_self.append(np.expand_dims(u[ind], axis=cluster_axis)) # Message from the mixed distribution m = distribution._compute_message_to_parent( index, u_self, *(u_parents[1:])) # Weigh the messages with the responsibilities for i in range(len(m)): # Shape(m) = [Nn,..,K,..,N0,Dd,..,D0] # Shape(p) = [Nn,..,N0,K] # Shape(result) = [Nn,..,K,..,N0,Dd,..,D0] # Number of axes for the variable dimensions for # the parent message. D = distribution.ndims_parents[index][i] # Responsibilities for clusters are the first # parent's first moment: # Shape(p) = [Nn,..,N0,K] p = u_parents[0][0] # Move the cluster axis to the proper place: # Shape(p) = [Nn,..,K,..,N0] p = utils.moveaxis(p, -1, cluster_plate) # Add axes for variable dimensions to the contributions # Shape(p) = [Nn,..,K,..,N0,1,..,1] p = utils.add_trailing_axes(p, D) if cluster_plate < 0: # Add the variable dimensions cluster_axis = cluster_plate - D # Add axis for clusters: # Shape(m) = [Nn,..,1,..,N0,Dd,..,D0] #m[i] = np.expand_dims(m[i], axis=cluster_axis) # # TODO: You could do summing here already so that # you wouldn't compute huge matrices as # intermediate result. Use einsum. ## print(np.shape(m[i])) ## print(np.shape(p)) # Compute the message contributions for each # cluster: # Shape(result) = [Nn,..,K,..,N0,Dd,..,D0] m[i] = m[i] * p #print(np.shape(m[i])) return m
def compute_message_to_parent(self, parent, index, u, *u_parents): if index == 0: # Shape(phi) = [Nn,..,K,..,N0,Dd,..,D0] # Shape(L) = [Nn,..,K,..,N0] # Shape(u) = [Nn,..,N0,Dd,..,D0] # Shape(result) = [Nn,..,N0,K] # Compute g: # Shape(g) = [Nn,..,K,..,N0] g = self.distribution.compute_cgf_from_parents(*(u_parents[1:])) # Reshape(g): # Shape(g) = [Nn,..,N0,K] g = utils.moveaxis(g, self.cluster_plate, -1) # Compute phi: # Shape(phi) = [Nn,..,K,..,N0,Dd,..,D0] phi = self.distribution.compute_phi_from_parents(*(u_parents[1:])) # Move phi axis: # Shape(phi) = [Nn,..,N0,K,Dd,..,D0] for ind in range(len(phi)): if self.cluster_plate < 0: axis_from = self.cluster_plate - self.ndims[ind] else: raise RuntimeError("Cluster plate axis must be negative") axis_to = -1 - self.ndims[ind] if np.ndim(phi[ind]) >= abs(axis_from): # Cluster plate axis exists, move it to the correct position phi[ind] = utils.moveaxis(phi[ind], axis_from, axis_to) else: # No cluster plate axis, just add a new axis to the correct # position, if phi has something on that axis if np.ndim(phi[ind]) >= abs(axis_to): phi[ind] = np.expand_dims(phi[ind], axis=axis_to) # Reshape u: # Shape(u) = [Nn,..,N0,1,Dd,..,D0] u_self = list() for ind in range(len(u)): u_self.append(np.expand_dims(u[ind], axis=(-1 - self.ndims[ind]))) # Compute logpdf: # Shape(L) = [Nn,..,N0,K] L = self.distribution.compute_logpdf(u_self, phi, g, 0, self.ndims) # Sum over other than the cluster dimensions? No! # Hmm.. I think the message passing method will do # that automatically m = [L] return m elif index >= 1: # Parent index for the distribution used for the # mixture. index = index - 1 # Reshape u: # Shape(u) = [Nn,..1,..,N0,Dd,..,D0] u_self = list() for ind in range(len(u)): if self.cluster_plate < 0: cluster_axis = self.cluster_plate - self.ndims[ind] else: cluster_axis = self.cluster_plate u_self.append(np.expand_dims(u[ind], axis=cluster_axis)) # Message from the mixed distribution m = self.distribution.compute_message_to_parent(parent, index, u_self, *(u_parents[1:])) # Weigh the messages with the responsibilities for i in range(len(m)): # Shape(m) = [Nn,..,K,..,N0,Dd,..,D0] # Shape(p) = [Nn,..,N0,K] # Shape(result) = [Nn,..,K,..,N0,Dd,..,D0] # Number of axes for the variable dimensions for # the parent message. D = self.ndims_parents[index][i] # Responsibilities for clusters are the first # parent's first moment: # Shape(p) = [Nn,..,N0,K] p = u_parents[0][0] # Move the cluster axis to the proper place: # Shape(p) = [Nn,..,K,..,N0] p = utils.atleast_nd(p, abs(self.cluster_plate)) p = utils.moveaxis(p, -1, self.cluster_plate) # Add axes for variable dimensions to the contributions # Shape(p) = [Nn,..,K,..,N0,1,..,1] p = utils.add_trailing_axes(p, D) if self.cluster_plate < 0: # Add the variable dimensions cluster_axis = self.cluster_plate - D # Add axis for clusters: # Shape(m) = [Nn,..,1,..,N0,Dd,..,D0] # m[i] = np.expand_dims(m[i], axis=cluster_axis) # # TODO: You could do summing here already so that # you wouldn't compute huge matrices as # intermediate result. Use einsum. # Compute the message contributions for each # cluster: # Shape(result) = [Nn,..,K,..,N0,Dd,..,D0] m[i] = m[i] * p return m
def compute_phi_from_parents(self, *u_parents, mask=True): # Compute weighted average of the parameters # Cluster parameters Phi = self.distribution.compute_phi_from_parents(*(u_parents[1:])) # Contributions/weights/probabilities P = u_parents[0][0] phi = list() nans = False for ind in range(len(Phi)): # Compute element-wise product and then sum over K clusters. # Note that the dimensions aren't perfectly aligned because # the cluster dimension (K) may be arbitrary for phi, and phi # also has dimensions (Dd,..,D0) of the parameters. # Shape(phi) = [Nn,..,K,..,N0,Dd,..,D0] # Shape(p) = [Nn,..,N0,K] # Shape(result) = [Nn,..,N0,Dd,..,D0] # General broadcasting rules apply for Nn,..,N0, that is, # preceding dimensions may be missing or dimension may be # equal to one. Probably, shape(phi) has lots of missing # dimensions and/or dimensions that are one. if self.cluster_plate < 0: cluster_axis = self.cluster_plate - self.ndims[ind] else: raise RuntimeError("Cluster plate should be negative") # Move cluster axis to the last: # Shape(phi) = [Nn,..,N0,Dd,..,D0,K] if np.ndim(Phi[ind]) >= abs(cluster_axis): phi.append(utils.moveaxis(Phi[ind], cluster_axis, -1)) else: phi.append(Phi[ind][..., None]) # Add axes to p: # Shape(p) = [Nn,..,N0,K,1,..,1] p = utils.add_trailing_axes(P, self.ndims[ind]) # Move cluster axis to the last: # Shape(p) = [Nn,..,N0,1,..,1,K] p = utils.moveaxis(p, -(self.ndims[ind] + 1), -1) # Now the shapes broadcast perfectly and we can sum # p*phi over the last axis: # Shape(result) = [Nn,..,N0,Dd,..,D0] phi[ind] = utils.sum_product(p, phi[ind], axes_to_sum=-1) if np.any(np.isnan(phi[ind])): nans = True if nans: warnings.warn( "The natural parameters of mixture distribution " "contain nans. This may happen if you use fixed " "parameters in your model. Technically, one possible " "reason is that the cluster assignment probability " "for some element is zero (p=0) and the natural " "parameter of that cluster is -inf, thus " "0*(-inf)=nan. Solution: Use parameters that assign " "non-zero probabilities for the whole domain." ) return phi
def compute_message_to_parent(self, parent, index, u, *u_parents): if index == 0: # Shape(phi) = [Nn,..,K,..,N0,Dd,..,D0] # Shape(L) = [Nn,..,K,..,N0] # Shape(u) = [Nn,..,N0,Dd,..,D0] # Shape(result) = [Nn,..,N0,K] # Compute g: # Shape(g) = [Nn,..,K,..,N0] g = self.distribution.compute_cgf_from_parents(*(u_parents[1:])) # Reshape(g): # Shape(g) = [Nn,..,N0,K] g = utils.moveaxis(g, self.cluster_plate, -1) # Compute phi: # Shape(phi) = [Nn,..,K,..,N0,Dd,..,D0] phi = self.distribution.compute_phi_from_parents(*(u_parents[1:])) # Move phi axis: # Shape(phi) = [Nn,..,N0,K,Dd,..,D0] for ind in range(len(phi)): if self.cluster_plate < 0: axis_from = self.cluster_plate-self.distribution.ndims[ind] else: raise RuntimeError("Cluster plate axis must be negative") axis_to = -1-self.distribution.ndims[ind] if np.ndim(phi[ind]) >= abs(axis_from): # Cluster plate axis exists, move it to the correct position phi[ind] = utils.moveaxis(phi[ind], axis_from, axis_to) else: # No cluster plate axis, just add a new axis to the correct # position, if phi has something on that axis if np.ndim(phi[ind]) >= abs(axis_to): phi[ind] = np.expand_dims(phi[ind], axis=axis_to) # Reshape u: # Shape(u) = [Nn,..,N0,1,Dd,..,D0] u_self = list() for ind in range(len(u)): u_self.append(np.expand_dims(u[ind], axis=(-1-self.distribution.ndims[ind]))) # Compute logpdf: # Shape(L) = [Nn,..,N0,K] L = self.distribution.compute_logpdf(u_self, phi, g, 0) # Sum over other than the cluster dimensions? No! # Hmm.. I think the message passing method will do # that automatically m = [L] return m elif index >= 1: # Parent index for the distribution used for the # mixture. index = index - 1 # Reshape u: # Shape(u) = [Nn,..1,..,N0,Dd,..,D0] u_self = list() for ind in range(len(u)): if self.cluster_plate < 0: cluster_axis = self.cluster_plate - self.distribution.ndims[ind] else: cluster_axis = self.cluster_plate u_self.append(np.expand_dims(u[ind], axis=cluster_axis)) # Message from the mixed distribution m = self.distribution.compute_message_to_parent(parent, index, u_self, *(u_parents[1:])) # Weigh the messages with the responsibilities for i in range(len(m)): # Shape(m) = [Nn,..,K,..,N0,Dd,..,D0] # Shape(p) = [Nn,..,N0,K] # Shape(result) = [Nn,..,K,..,N0,Dd,..,D0] # Number of axes for the variable dimensions for # the parent message. D = self.distribution.ndims_parents[index][i] # Responsibilities for clusters are the first # parent's first moment: # Shape(p) = [Nn,..,N0,K] p = u_parents[0][0] # Move the cluster axis to the proper place: # Shape(p) = [Nn,..,K,..,N0] p = utils.atleast_nd(p, abs(self.cluster_plate)) p = utils.moveaxis(p, -1, self.cluster_plate) # Add axes for variable dimensions to the contributions # Shape(p) = [Nn,..,K,..,N0,1,..,1] p = utils.add_trailing_axes(p, D) if self.cluster_plate < 0: # Add the variable dimensions cluster_axis = self.cluster_plate - D # Add axis for clusters: # Shape(m) = [Nn,..,1,..,N0,Dd,..,D0] #m[i] = np.expand_dims(m[i], axis=cluster_axis) # # TODO: You could do summing here already so that # you wouldn't compute huge matrices as # intermediate result. Use einsum. # Compute the message contributions for each # cluster: # Shape(result) = [Nn,..,K,..,N0,Dd,..,D0] m[i] = m[i] * p return m
def _compute_message_to_parent(parent, index, u, *u_parents): """ . """ #print('Mixture.compute_message:') if index == 0: # Shape(phi) = [Nn,..,K,..,N0,Dd,..,D0] # Shape(L) = [Nn,..,K,..,N0] # Shape(u) = [Nn,..,N0,Dd,..,D0] # Shape(result) = [Nn,..,N0,K] # Compute g: # Shape(g) = [Nn,..,K,..,N0] g = distribution._compute_cgf_from_parents(*(u_parents[1:])) # Reshape(g): # Shape(g) = [Nn,..,N0,K] g = utils.moveaxis(g, cluster_plate, -1) # Compute phi: # Shape(phi) = [Nn,..,K,..,N0,Dd,..,D0] phi = distribution._compute_phi_from_parents(*(u_parents[1:])) # Reshape phi: # Shape(phi) = [Nn,..,N0,K,Dd,..,D0] for ind in range(len(phi)): phi[ind] = utils.moveaxis(phi[ind], cluster_plate-distribution.ndims[ind], -1-distribution.ndims[ind]) # Reshape u: # Shape(u) = [Nn,..,N0,1,Dd,..,D0] u_self = list() for ind in range(len(u)): u_self.append(np.expand_dims(u[ind], axis=(-1-distribution.ndims[ind]))) # Compute logpdf: # Shape(L) = [Nn,..,N0,K] L = distribution._compute_logpdf(u_self, phi, g, 0) # Sum over other than the cluster dimensions? No! # Hmm.. I think the message passing method will do # that automatically ## print(np.shape(phi[0])) ## print(np.shape(u_self[0])) ## print(np.shape(g)) ## print(np.shape(L)) return [L] elif index >= 1: # Parent index for the distribution used for the # mixture. index = index - 1 # Reshape u: # Shape(u) = [Nn,..1,..,N0,Dd,..,D0] u_self = list() for ind in range(len(u)): if cluster_plate < 0: cluster_axis = cluster_plate - distribution.ndims[ind] else: cluster_axis = cluster_plate u_self.append(np.expand_dims(u[ind], axis=cluster_axis)) # Message from the mixed distribution m = distribution._compute_message_to_parent(index, u_self, *(u_parents[1:])) # Weigh the messages with the responsibilities for i in range(len(m)): # Shape(m) = [Nn,..,K,..,N0,Dd,..,D0] # Shape(p) = [Nn,..,N0,K] # Shape(result) = [Nn,..,K,..,N0,Dd,..,D0] # Number of axes for the variable dimensions for # the parent message. D = distribution.ndims_parents[index][i] # Responsibilities for clusters are the first # parent's first moment: # Shape(p) = [Nn,..,N0,K] p = u_parents[0][0] # Move the cluster axis to the proper place: # Shape(p) = [Nn,..,K,..,N0] p = utils.moveaxis(p, -1, cluster_plate) # Add axes for variable dimensions to the contributions # Shape(p) = [Nn,..,K,..,N0,1,..,1] p = utils.add_trailing_axes(p, D) if cluster_plate < 0: # Add the variable dimensions cluster_axis = cluster_plate - D # Add axis for clusters: # Shape(m) = [Nn,..,1,..,N0,Dd,..,D0] #m[i] = np.expand_dims(m[i], axis=cluster_axis) # # TODO: You could do summing here already so that # you wouldn't compute huge matrices as # intermediate result. Use einsum. ## print(np.shape(m[i])) ## print(np.shape(p)) # Compute the message contributions for each # cluster: # Shape(result) = [Nn,..,K,..,N0,Dd,..,D0] m[i] = m[i] * p #print(np.shape(m[i])) return m