I am using PyMC3 for parameter estimation using a particular likelihood function which has to be defined. I googled it and found out that I should use the densitydist method for implementing the user defined likelihood functions but it is not working. How to incorporate a user defined likelihood function in PyMC3 and to find out the maximum a posteriori (MAP) estimate for my model? My code is given below. Here L is the analytic form of my Likelihood function. I have some observational data for the radial velocity(vr) and postion (r) for some objects, which is imported from excel file.
data_ = np.array(pandas.read_excel('aaa.xlsx',header=None))
gamma=3.77;
G = 4.302*10**-6;
rmin = 3.0;
R = 95.7;
vr=data_[:,1];
r= data_[:,0];
h= np.pi;
class integrateOut(theano.Op):
def __init__(self,f,t,t0,tf,*args,**kwargs):
super(integrateOut,self).__init__()
self.f = f
self.t = t
self.t0 = t0
self.tf = tf
def make_node(self,*inputs):
self.fvars=list(inputs)
try:
self.gradF = tt.grad(self.f,self.fvars)
except:
self.gradF = None
return theano.Apply(self,self.fvars,[tt.dscalar().type()])
def perform(self,node, inputs, output_storage):
args = tuple(inputs)
f = theano.function([self.t]+self.fvars,self.f)
output_storage[0][0] = quad(f,self.t0,self.tf,args=args)[0]
def grad(self,inputs,grads):
return [integrateOut(g,self.t,self.t0,self.tf)(*inputs)*grads[0] \
for g in self.gradF]
basic_model = pm.Model()
with basic_model:
M=[]
beta=[]
interval=0.01*10**12
M=pm.Uniform('M',
lower=0.5*10**12,upper=3.50*10**12,transform='interval')
beta=pm.Uniform('beta',lower=2.001,upper=2.999,transform='interval')
gamma=3.77
logp=[]
arr=[]
vnew=[]
rnew=[]
theta = tt.scalar('theta')
beta = tt.scalar('beta')
z = tt.cos(theta)**(2*( (gamma/(beta - 2)) - 3/2) + 3)
intZ = integrateOut(z,theta,-(np.pi)/2,(np.pi)/2)(beta)
gradIntZ = tt.grad(intZ,[beta])
funcIntZ = theano.function([beta],intZ)
funcGradIntZ = theano.function([beta],gradIntZ)
for j in np.arange(0,59,1):
vnew.append(vr[j]+(0.05*vr[j]*float(dm.Decimal(rm.randrange(1,
20))/10)));
rnew.append(r[j]+(0.05*r[j]*float(dm.Decimal(rm.randrange(1,
20))/10)));
vn=np.array(vnew)
rn=np.array(rnew)
for beta in np.arange (2.01,2.99,0.01):
for M in np.arange (0.5,2.50,0.01):
i=np.arange(0,59,1)
q =( gamma/(beta - 2)) - 3/2
B = (G*M*10**12)/((beta -2 )*( R**(3 - beta)))
K = (gamma - 3)/((rmin**(3 - gamma))*funcIntZ(beta)*m.sqrt(2*B))
logp= -np.log(K*((1 -(( 1/(2*B) )*((vn[i]**2)*rn[i]**(beta -
2))))**(q+1))*(rn[i]**(1-gamma +(beta/2))))
arr.append(logp.sum())
def logp_func(rn,vn):
return min(np.array(arr))
logpvar = pm.DensityDist("logpvar", logp_func, observed={"rn": rn,"vn":vn})
start = pm.find_MAP(model=basic_model)
step = pm.Metropolis()
basicmodeltrace = pm.sample(10000, step=step,
start=start,random_seed=1,progressbar=True)
print(pm.summary(basicmodeltrace))
map_estimate = pm.find_MAP(model=basic_model)
print(map_estimate)
I am getting the following error message:
ValueError: Cannot compute test value: input 0 (theta) of Op
Elemwise{cos,no_inplace}(theta) missing default value.
Backtrace when that variable is created:
I am unable to get the output since the numerical integration is not working. I have used custom theano op for numerical integration code which i got from Custom Theano Op to do numerical integration . The integration works if I run it seperately inputting a particular value of beta, but not within the model.
I made a few changes to your code, this still does not work, but I hope it is closer to a solution. Please check this thread, as someone is trying so solve essentially the same problem.
class integrateOut(theano.Op):
def __init__(self, f, t, t0, tf,*args, **kwargs):
super(integrateOut,self).__init__()
self.f = f
self.t = t
self.t0 = t0
self.tf = tf
def make_node(self, *inputs):
self.fvars=list(inputs)
try:
self.gradF = tt.grad(self.f, self.fvars)
except:
self.gradF = None
return theano.Apply(self, self.fvars, [tt.dscalar().type()])
def perform(self,node, inputs, output_storage):
args = tuple(inputs)
f = theano.function([self.t] + self.fvars,self.f)
output_storage[0][0] = quad(f, self.t0, self.tf, args=args)[0]
def grad(self,inputs,grads):
return [integrateOut(g, self.t, self.t0, self.tf)(*inputs)*grads[0] \
for g in self.gradF]
gamma = 3.77
G = 4.302E-6
rmin = 3.0
R = 95.7
vr = data[:,1]
r = data[:,0]
h = np.pi
interval = 1E10
vnew = []
rnew = []
for j in np.arange(0,59,1):
vnew.append(vr[j]+(0.05*vr[j] * float(dm.Decimal(rm.randrange(1, 20))/10)))
rnew.append(r[j]+(0.05*r[j] * float(dm.Decimal(rm.randrange(1, 20))/10)))
vn = np.array(vnew)
rn = np.array(rnew)
def integ(gamma, beta, theta):
z = tt.cos(theta)**(2*((gamma/(beta - 2)) - 3/2) + 3)
return integrateOut(z, theta, -(np.pi)/2, (np.pi)/2)(beta)
with pm.Model() as basic_model:
M = pm.Uniform('M', lower=0.5*10**12, upper=3.50*10**12)
beta = pm.Uniform('beta', lower=2.001, upper=2.999)
theta = pm.Normal('theta', 0, 10**2)
def logp_func(rn,vn):
q = (gamma/(beta - 2)) - 3/2
B = (G*M*1E12) / ((beta -2 )*(R**(3 - beta)))
K = (gamma - 3) / ((rmin**(3 - gamma)) * integ(gamma, beta, theta) * (2*B)**0.5)
logp = - np.log(K*((1 -((1/(2*B))*((vn**2)*rn**(beta -
2))))**(q+1))*(rn**(1-gamma +(beta/2))))
return logp.sum()
logpvar = pm.DensityDist("logpvar", logp_func, observed={"rn": rn,"vn":vn})
start = pm.find_MAP()
#basicmodeltrace = pm.sample()
print(start)
Related
I get this error from the following Pytorch code:
RuntimeError: one of the variables needed for gradient computation has been modified by an inplace operation: [torch.DoubleTensor [3]] is at version 10; expected version 9 instead.
As it is seen the code does not have inplace operations.
import torch
device = torch.device('cpu')
class MesNet(torch.nn.Module):
def __init__(self):
super(MesNet, self).__init__()
self.cov_lin = torch.nn.Sequential(torch.nn.Linear(6, 5)).double()
def forward(self, u):
z_cov = self.cov_lin(u.transpose(0, 2).squeeze(-1))
return z_cov
class UpdateModel(torch.nn.Module):
def __init__(self):
torch.nn.Module.__init__(self)
self.P_dim = 18
self.Id3 = torch.eye(3).double()
def run_KF(self):
N = 10
u = torch.randn(N, 6).double()
v = torch.zeros(N, 3).double()
model = MesNet()
measurements_covs_l = model(u.t().unsqueeze(0))
# remember to remove this afterwards
torch.autograd.set_detect_anomaly(True)
for i in range(1, N):
v[i] = self.update_pos(v[i].detach(), measurements_covs_l[i-1])
criterion = torch.nn.MSELoss(reduction="sum")
targ = torch.rand(10, 3).double()
loss = criterion(v, targ)
loss = torch.mean(loss)
loss.backward()
return v, p
def update_pos(self, v, measurement_cov):
Omega = torch.eye(3).double()
H = torch.ones((5, self.P_dim)).double()
R = torch.diag(measurement_cov)
Kt = H.t().mm(torch.inverse(R))
# it is indicating inplace error even with this:
# Kt = H.t().mm(R)
dx = Kt.mv(torch.ones(5).double())
dR = self.trans(dx[:9].clone())
v_up = dR.mv(v)
return v_up
def trans(self, xi):
phi = xi[:3].clone()
angle = torch.norm(phi.clone())
if angle.abs().lt(1e-10):
skew_phi = torch.eye(3).double()
J = self.Id3 + 0.5 * skew_phi
Rot = self.Id3 + skew_phi
else:
axis = phi / angle
skew_axis = torch.eye(3).double()
s = torch.sin(angle)
c = torch.cos(angle)
Rot = c * self.Id3
return Rot
net = UpdateModel()
net.run_KF()
I think the issue is that you are overwriting v[i] elements.
You could instead construct an auxiliary list v_ from the loop, then convert it tensor:
v_ = [v[0]]
for i in range(1, N):
v_.append(self.update_pos(v[i].detach(), measurements_covs_l[i-1]))
v = torch.stack(v_)
there is a code written with tensorflow1 on this link.
https://github.com/carlthome/tensorflow-convlstm-cell/blob/master/cell.py
I want to use this class as a layer in TensorFlow.Keras. So it should be written with TensorFlow version 2.
How can do it?
this is this code:
import tensorflow as tf
class ConvLSTMCell(tf.nn.rnn_cell.RNNCell):
"""A LSTM cell with convolutions instead of multiplications.
Reference:
Xingjian, S. H. I., et al. "Convolutional LSTM network: A machine learning approach for precipitation nowcasting." Advances in Neural Information Processing Systems. 2015.
"""
def __init__(self, shape, filters, kernel, forget_bias=1.0, activation=tf.tanh, normalize=True, peephole=True, data_format='channels_last', reuse=None):
super(ConvLSTMCell, self).__init__(_reuse=reuse)
self._kernel = kernel
self._filters = filters
self._forget_bias = forget_bias
self._activation = activation
self._normalize = normalize
self._peephole = peephole
if data_format == 'channels_last':
self._size = tf.TensorShape(shape + [self._filters])
self._feature_axis = self._size.ndims
self._data_format = None
elif data_format == 'channels_first':
self._size = tf.TensorShape([self._filters] + shape)
self._feature_axis = 0
self._data_format = 'NC'
else:
raise ValueError('Unknown data_format')
#property
def state_size(self):
return tf.nn.rnn_cell.LSTMStateTuple(self._size, self._size)
#property
def output_size(self):
return self._size
def call(self, x, state):
c, h = state
x = tf.concat([x, h], axis=self._feature_axis)
n = x.shape[-1].value
m = 4 * self._filters if self._filters > 1 else 4
W = tf.get_variable('kernel', self._kernel + [n, m])
y = tf.nn.convolution(x, W, 'SAME', data_format=self._data_format)
if not self._normalize:
y += tf.get_variable('bias', [m], initializer=tf.zeros_initializer())
j, i, f, o = tf.split(y, 4, axis=self._feature_axis)
if self._peephole:
i += tf.get_variable('W_ci', c.shape[1:]) * c
f += tf.get_variable('W_cf', c.shape[1:]) * c
if self._normalize:
j = tf.contrib.layers.layer_norm(j)
i = tf.contrib.layers.layer_norm(i)
f = tf.contrib.layers.layer_norm(f)
f = tf.sigmoid(f + self._forget_bias)
i = tf.sigmoid(i)
c = c * f + i * self._activation(j)
if self._peephole:
o += tf.get_variable('W_co', c.shape[1:]) * c
if self._normalize:
o = tf.contrib.layers.layer_norm(o)
c = tf.contrib.layers.layer_norm(c)
o = tf.sigmoid(o)
h = o * self._activation(c)
state = tf.nn.rnn_cell.LSTMStateTuple(c, h)
return h, state
I am trying to implement parts of Facebook's prophet with some help from this example.
https://github.com/luke14free/pm-prophet/blob/master/pmprophet/model.py
This goes well :), but I am having some problems with the dot product I don't understand. Note that I am implementing the linear trends.
ds = pd.to_datetime(df['dagindex'], format='%d-%m-%y')
m = pm.Model()
changepoint_prior_scale = 0.05
n_changepoints = 25
changepoints = pd.date_range(
start=pd.to_datetime(ds.min()),
end=pd.to_datetime(ds.max()),
periods=n_changepoints + 2
)[1: -1]
with m:
# priors
sigma = pm.HalfCauchy('sigma', 10, testval=1)
#trend
growth = pm.Normal('growth', 0, 10)
prior_changepoints = pm.Laplace('changepoints', 0, changepoint_prior_scale, shape=len(changepoints))
y = np.zeros(len(df))
# indexes x_i for the changepoints.
s = [np.abs((ds - i).values).argmin() for i in changepoints]
g = growth
x = np.arange(len(ds))
# delta
d = prior_changepoints
regression = x * g
base_piecewise_regression = []
for i in s:
local_x = x.copy()[:-i]
local_x = np.concatenate([np.zeros(i), local_x])
base_piecewise_regression.append(local_x)
piecewise_regression = np.array(base_piecewise_regression)
# this dot product doesn't work?
piecewise_regression = pm.math.dot(theano.shared(piecewise_regression).T, d)
# If I comment out this line and use that one as dot product. It works fine
# piecewise_regression = (piecewise_regression.T * d[None, :]).sum(axis=-1)
regression += piecewise_regression
y += regression
obs = pm.Normal('y',
mu=(y - df.gebruikers.mean()) / df.gebruikers.std(),
sd=sigma,
observed=(df.gebruikers - df.gebruikers.mean()) / df.gebruikers.std())
start = pm.find_MAP(maxeval=10000)
trace = pm.sample(500, step=pm.NUTS(), start=start)
If I run the snippet above with
piecewise_regression = (piecewise_regression.T * d[None, :]).sum(axis=-1)
the model works as expected. However I cannot get it to work with a dot product. The NUTS sampler doesn't sample at all.
piecewise_regression = pm.math.dot(theano.shared(piecewise_regression).T, d)
EDIT
Ive got a minimal working example
The problem still occurs with theano.shared. I’ve got a minimal working example:
np.random.seed(5)
n_changepoints = 10
t = np.arange(1000)
s = np.sort(np.random.choice(t, size=n_changepoints, replace=False))
a = (t[:, None] > s) * 1
real_delta = np.random.normal(size=n_changepoints)
y = np.dot(a, real_delta) * t
with pm.Model():
sigma = pm.HalfCauchy('sigma', 10, testval=1)
delta = pm.Laplace('delta', 0, 0.05, shape=n_changepoints)
g = tt.dot(a, delta) * t
obs = pm.Normal('obs',
mu=(g - y.mean()) / y.std(),
sd=sigma,
observed=(y - y.mean()) / y.std())
trace = pm.sample(500)
It seems to have something to do with the size of matrix a. NUTS doesnt’t sample if I start with
t = np.arange(1000)
however the example above does sample when I reduce the size of t to:
t = np.arange(100)
I am trying to extract the decisions of an RNN for all tokens in a sequence but receive the error mentioned at the end of the post.
Any help will be appreciated!
Code:
# gated recurrent unit
def gru_step(x, h_prev, W_xm, W_hm, W_xh, W_hh):
m = theano.tensor.nnet.sigmoid(theano.tensor.dot(x, W_xm) + theano.tensor.dot(h_prev, W_hm))
r = _slice(m, 0, 2)
z = _slice(m, 1, 2)
_h = theano.tensor.tanh(theano.tensor.dot(x, W_xh) + theano.tensor.dot(r * h_prev, W_hh))
h = z * h_prev + (1.0 - z) * _h
return h
# return h, theano.scan_module.until(previous_power*2 > max_value)
W_xm = self.create_parameter_matrix('W_xm', (word_embedding_size, recurrent_size*2))
W_hm = self.create_parameter_matrix('W_hm', (recurrent_size, recurrent_size*2))
W_xh = self.create_parameter_matrix('W_xh', (word_embedding_size, recurrent_size))
W_hh = self.create_parameter_matrix('W_hh', (recurrent_size, recurrent_size))
initial_hidden_vector = theano.tensor.alloc(numpy.array(0, dtype=floatX), recurrent_size)
initial_process_vector = theano.tensor.alloc(recurrent_size, n_classes)
hidden_vector, _ = theano.scan(
gru_step,
sequences = input_vectors,
outputs_info = initial_hidden_vector,
non_sequences = [W_xm, W_hm, W_xh, W_hh]
)
W_output = self.create_parameter_matrix('W_output', (n_classes,recurrent_size))
rnn_output = theano.tensor.nnet.softmax([theano.tensor.dot(W_output, hidden_vector[-1])])[0]
rnn+predicted_class = theano.tensor.argmax(output)
# Process hidden_vector to decision vectors
def process_hidden_vector(x, W_dot):
return theano.tensor.dot(W_dot, x)
all_tokens_output_vector = theano.scan(process_hidden_vector, sequences=hidden_vector, non_sequences=W_output)
The results should be the "all_tokens_output_vector", but I get the following error when trying to output it:
TypeError: Outputs must be theano Variable or Out instances. Received (for{cpu,scan_fn}.0, OrderedUpdates()) of type <type 'tuple'>
What are you doing with "all_tokens_output_vector" after that? Your print it directly?
There should be a theano.function to compile the graph
I need to optimize a non-convex problem (max likelihood), and when I try quadratic optmiziation algorithms such as bfgs, Nelder-Mead, it fails to find the extremum, I frequently get saddle point, instead.
You can download data from here.
import numpy as np
import csv
from scipy.stats import norm
f=open('data.csv','r')
reader = csv.reader(f)
headers = next(reader)
column={}
for h in headers:
column[h] = []
for row in reader:
for h,v in zip(headers, row):
column[h].append(float(v))
ini=[-0.0002,-0.01,.002,-0.09,-0.04,0.01,-0.02,-.0004]
for i in range(0,len(x[0])):
ini.append(float(x[0][i]))
x_header = list(Coef_headers)
N = 19 # no of observations
I = 4
P =7
Yobs=np.zeros(N)
Yobs[:] = column['size']
X=np.zeros((N,P))
X[:,0] = column['costTon']
X[:,1] = column['com1']
X[:,2] = column['com3']
X[:,3] = column['com4']
X[:,4] = column['com5']
X[:,5] = column['night']
X[:,6] = 1 #constant
def myfunction(B):
beta = B[0.299,18.495,2.181,2.754,3.59,2.866,-12.846]
theta = 30
U=np.zeros((N,I))
mm=np.zeros(I)
u = np.zeros((N,I))
F = np.zeros((N,I))
G = np.zeros(N)
l = 0
s1 = np.expm1(-theta)
for n in range (0,N):
m = 0
U[n,0] = B[0]*column['cost_van'][n]+ B[4]*column['cap_van'][n]
U[n,1] = B[1]+ B[5]*column['ex'][n]+ B[8]*column['dist'][n]+ B[0]*column['cost_t'][n]+ B[4]*column['cap_t'][n]
U[n,2] = B[2]+ B[6]*column['ex'][n]+ B[9]*column['dist'][n] + B[0]*column['cost_Ht'][n]+ B[4]*column['cap_Ht'][n]
U[n,3] = B[3]+ B[7]*column['ex'][n]+ B[10]*column['dist'][n]+ B[0]*column['cost_tr'][n]+ B[4]*column['cap_tr'][n]
for i in range(0,I):
mm[i]=np.exp(U[n,i])
m= sum(mm)
for i in range(0,I):
u[n,i]=1/(1+ np.exp(U[n,i]- np.log(m-np.exp(U[n,i]))))
F[n,i] = np.expm1(-u[n,i]*theta)
CDF = np.zeros(N)
Y = X.dot(beta)
resid = 0
for n in range (0,N):
resid = resid + (np.square(Yobs[n]-Y[n]))
SSR = resid / N
dof = N - P - 1
s2 = resid/dof # MSE, or variance: the mean squarred error of residuals
for n in range(0,N):
CDF[n] = norm.cdf((Yobs[n]+1),SSR,s2) - norm.cdf((Yobs[n]-1),SSR,s2)
G[n] = np.expm1(-CDF[n]*theta)
k = column['Choice_Veh'][n]-1
l = l + (np.log10(1+(F[n,k]*G[n]/s1))/(-theta))
loglikelihood = np.log10(l)
return -loglikelihood
rranges = np.repeat(slice(-10, 10, 1),11, axis = 0)
a = rranges
from scipy import optimize
resbrute = optimize.brute(myfunction, rranges, full_output=True,finish=optimize.fmin)
print("# global minimum:", resbrute[0])
print("function value at global minimum :", resbrute[1])
Now, I decided to go for grid search and tried scipy.optimize.brute, but I get this error. In fact, my real variables are 47, I decreased it to 31 to work, but still doesn't. please help.
File "C:\...\site-packages\numpy\core\numeric.py", line 1906, in indices
res = empty((N,)+dimensions, dtype=dtype)
ValueError: array is too big.