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mdn.py
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"""A module for a mixture density network layer."""
importtorch
importtorch.nnasnn
fromtorch.distributionsimportCategorical
fromspirl.modules.variational_inferenceimportMultivariateGaussian
fromspirl.utils.pytorch_utilsimportten2ar
classMDN(nn.Module):
"""A mixture density network layer"""
def__init__(self,input_size,output_size,num_gaussians):
super(MDN,self).__init__()
self.input_size=input_size
self.output_size=output_size
self.num_gaussians=num_gaussians
self.pi=nn.Sequential(
nn.Linear(input_size,num_gaussians),
nn.Softmax(dim=1)
)
self.log_sigma=nn.Linear(input_size,output_size*num_gaussians)
self.mu=nn.Linear(input_size,output_size*num_gaussians)
defforward(self,inputs):
returntorch.clamp(self.pi(inputs),min=1e-6), \
self.mu(inputs).reshape(-1,self.num_gaussians,self.output_size), \
torch.clamp(self.log_sigma(inputs).reshape(-1,self.num_gaussians,self.output_size),-10,2)
classGMM:
"""Gaussian Mixture Model class."""
def__init__(self,pi,mu=None,log_sigma=None):
ifmuisNoneandlog_sigmaisNone:
ifisinstance(pi,tuple):
pi,mu,log_sigma=pi# in case inputs are passed in as tuple
else:
pi,mu,log_sigma=self.tensor2gmm(pi)
self.pi=pi
self.mu=mu
self.log_sigma=log_sigma
self._components= [MultivariateGaussian(mu[...,idx, :],log_sigma[...,idx, :])foridxinrange(mu.shape[-2])]
defnll(self,x):
return-1*self.log_prob(x)
deflog_prob(self,x):
returntorch.logsumexp(torch.log(self.pi)+
MultivariateGaussian(self.mu,self.log_sigma).log_prob(x[:,None]),dim=1)
defsample(self):
"""Differentiable sampling function."""
return (MultivariateGaussian(self.mu,self.log_sigma).sample()*
torch.nn.functional.one_hot(Categorical(self.pi).sample(),
num_classes=self.pi.shape[-1])[...,None].float()).sum(dim=1)
defrsample(self):
returnself.sample()
defentropy(self):
"""!!! This is not the true entropy of the GMM (there is no closed form) but only an indicator. !!!"""
returntorch.stack([c.entropy()forcinself._components],dim=1)
defdetach(self):
returnGMM(self.pi.detach(),self.mu.detach(),self.log_sigma.detach())
deftensor(self):
"""Returns flat tensor representation of GMM."""
returntorch.cat((self.pi,self.mu.flatten(start_dim=1),self.log_sigma.flatten(start_dim=1),
self.pi.shape[1]*torch.ones((self.pi.shape[0],1),device=self.pi.device)),dim=-1)
@staticmethod
deftensor2gmm(tensor):
"""Unwraps flattened tensor representation generated by tensor() function."""
num_gaussians=tensor[0,-1].long()
nz= (tensor.shape[1]-1-num_gaussians)/num_gaussians/2
pi=tensor[:, :num_gaussians]
mu=tensor[:,num_gaussians :num_gaussians+ (num_gaussians*nz)].reshape(-1,num_gaussians,nz)
log_sigma=tensor[:,-(num_gaussians*nz+1) :-1].reshape(-1,num_gaussians,nz)
returnpi,mu,log_sigma
defto_numpy(self):
"""Convert internal variables to numpy arrays."""
returnGMM(ten2ar(self.pi),ten2ar(self.mu),ten2ar(self.log_sigma))
@staticmethod
defstack(*argv,dim):
returnGMM._combine(torch.stack,*argv,dim=dim)
@staticmethod
defcat(*argv,dim):
returnGMM._combine(torch.cat,*argv,dim=dim)
@staticmethod
def_combine(fcn,*argv,dim):
pi,mu,log_sigma= [], [], []
forginargv:
pi.append(g.pi);mu.append(g.mu);log_sigma.append(g.log_sigma)
pi,mu,log_sigma=fcn(pi,dim),fcn(mu,dim),fcn(log_sigma,dim)
returnGMM(pi,mu,log_sigma)
def__getitem__(self,item):
returnGMM(self.pi[item],self.mu[item],self.log_sigma[item])
def__iter__(self):
forpi,cinzip(self.pi,self._components):
yieldpi,c
if__name__=="__main__":
### VISUALIZE
# from spirl.utils.pytorch_utils import ten2ar
fromspirl.utils.general_utilsimportsplit_along_axis
# import numpy as np
frommatplotlibimportpyplotasplt
frommatplotlib.patchesimportEllipse
# gmm = GMM(torch.rand((1, 5)), torch.tensor([[[0., 0], [1, 1], [1, -1], [-1, 1], [-1, -1]]]),
# torch.tensor([[[-1, -0.3], [-2, -1], [-2, -0.4], [-3, -1], [-0.5, -2]]]))
#
def_draw_gaussian(ax,gauss_tensor,color,weight=None):
px,py,p_logsig_x,p_logsig_y=split_along_axis(ten2ar(gauss_tensor),axis=0)
deflogsig2std(logsig):
returnnp.exp(logsig)
ell=Ellipse(xy=(px,py),
width=2*logsig2std(p_logsig_x),height=2*logsig2std(p_logsig_y),
angle=0,color=color)# this assumes diagonal gaussian
ifweightisnotNone:
ell.set_alpha(weight)
else:
ell.set_facecolor('none')
ax.add_artist(ell)
#
#
# fig = plt.figure()
# ax = plt.subplot(111)
# plt.xlim(-2, 2); plt.ylim(-2, 2)
# [_draw_gaussian(ax, component.tensor(), 'green', ten2ar(weight)) for weight, component in gmm[0]]
#
# samples = np.concatenate([gmm.sample() for _ in range(1000)])
# plt.scatter(samples[:, 0], samples[:, 1])
# plt.savefig("test.png")
### TRAIN
importnumpyasnp
importmatplotlib.pyplotasplt
fromspirl.utils.general_utilsimportAttrDict
fromspirl.modules.layersimportLayerBuilderParams
fromspirl.modules.subnetworksimportPredictor
# generate data
pi=torch.tensor([0.7,0.1,0.1,0.1])[None].repeat(256,1)
mu=torch.tensor([[1.0,-1.0,0.0,0.0], [0.0,0.0,1.0,-1.0]])[None].repeat(256,1,1).transpose(-1,-2)
log_sigma=torch.zeros_like(mu)+torch.tensor(np.log(0.1))
data_dist=GMM(pi=pi,mu=mu,log_sigma=log_sigma)
data=data_dist.sample().data.numpy()
# set up flow model
trainable_input=torch.zeros((256,2),requires_grad=True)
hp=AttrDict({
'nz_mid':32,
'n_processing_layers':3,
})
hp.builder=LayerBuilderParams(False,'batch')
model=torch.nn.Sequential(
Predictor(hp,input_size=2,output_size=hp.nz_mid),
MDN(input_size=hp.nz_mid,output_size=2,num_gaussians=4)
)
pydata=torch.tensor(data,dtype=torch.float32)
optimizer=torch.optim.Adam(model.parameters(),lr=0.005)
# train flow model
foriinrange(6000):
optimizer.zero_grad()
gmm_dist=GMM(model(trainable_input))
loss_samples= []
for_inrange(10):
data_sample=data_dist.sample()
gmm_sample=gmm_dist.rsample()
# loss = gmm_dist.nll(pydata).mean()
# loss = (gmm_dist.log_prob(gmm_sample) - data_dist.log_prob(gmm_sample))
loss= (data_dist.log_prob(data_sample)-gmm_dist.log_prob(data_sample))
# loss = (gmm_dist.log_prob(gmm_sample) - data_dist.log_prob(gmm_sample)) + \
# (data_dist.log_prob(data_sample) - gmm_dist.log_prob(data_sample))
loss_samples.append(loss)
loss=torch.cat(loss_samples).mean()
loss.backward()
optimizer.step()
ifi%100==0:
print(f"Iter:{i}\t"+
f"NLL:{loss.mean().data:.2f}\t")
# visualize samples
samples=gmm_dist.sample().data.numpy()
fig=plt.figure()
ax=plt.subplot(111)
plt.xlim(-2,2);plt.ylim(-2,2)
# plt.scatter(data[:, 0], data[:, 1], c='black', alpha=0.1)
# plt.scatter(samples[:, 0], samples[:, 1], c='green', alpha=0.5)
[_draw_gaussian(ax,component.tensor(),'green',ten2ar(weight))forweight,componentingmm_dist[0]]
plt.axis("equal")
plt.savefig("gmm_fit.png")
# plt.show()