I'm trying to plot the difference between two variables. I'm following the example set here (search for true_p_A and it will be in the right section)
Here is my code
def cool(test):
n_data_points = len(test)
alpha = 1.0/np.mean(test)
lambda_1 = pm.Exponential("lambda_1", alpha) # prior on first behaviour
lambda_2 = pm.Exponential("lambda_2", alpha) # prior on second behaviour
tau = pm.DiscreteUniform("tau", lower=0, upper=len(test)) # prior on behaviour change
"""
The below deterministic functions map an assignment, in this case 0 or 1,
to a set of parameters, located in the (1,2) arrays `taus` and `centers`.
"""
#pm.deterministic
def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2):
out = np.zeros(n_data_points)
out[:tau] = lambda_1 # lambda before tau is lambda1
out[tau:] = lambda_2 # lambda after tau is lambda2
return out
def delta(p_A=lambda_1, p_B=lambda_2):
return p_A - p_B
obs = pm.Poisson("obs", lambda_, value=test, observed=True)
model = pm.Model([obs, lambda_, lambda_1, lambda_2, tau,delta])
mcmc = pm.MCMC(model)
mcmc.sample(5000, 1000, 1)
return mcmc,5000,1
def main_plotter(stats,test):
mcmc,N,bin = stats
n_count_data = len(test)
lambda_1_samples = mcmc.trace('lambda_1')[:]
lambda_2_samples = mcmc.trace('lambda_2')[:]
tau_samples = mcmc.trace('tau')[:]
delta_samples = mcmc.trace('delta')
print(delta_samples)
data = [1,2,1,2.2,5,5.5,6,5.4]
main_plotter( cool(data),data)
In the example no variable is created for delta so no key value is inserted. Whenever I run this code is tells me it can't find the key. My question is what do I need to do to access the delta posterior data?
You are missing the deterministic decorator before the delta function definition. It works if you change starting at line 21:
#pm.deterministic
def delta(p_A=lambda_1, p_B=lambda_2):
return p_A - p_B
Related
I am new to tensorflow and trying to translate a STAN model into TFP. Here is my TFP model using JointDistributionCoroutineAutoBatched.
def make_joint_distribution_coroutine(Depth,N_RNA):
def model():
## c1 prior
c1 = yield tfd.Gamma(concentration = 1.1, rate = 0.005)
## c2 prior
c2 = yield tfd.Gamma(concentration = 1.1, rate = 0.005)
## s prior
s = yield GammaModeSD(1,1)
## theta prior
theta = yield tfd.LogNormal(0,s)
## p prior
p = yield BetaModeConc(0.1,c1)
## tfp bug, need to cast tensor to float32
#theta = tf.cast(theta, tf.float32)
#p = tf.cast(p, tf.float32)
## q formula
q = (theta*p)/(1-p+theta*p)
## qi prior
qi = yield BetaModeConc(tf.repeat(q,N_RNA), c2)
## qi likelihood
k = yield tfd.Binomial(tf.cast(Depth,tf.float32),qi)
# p likelihood
a = yield tfd.Binomial(tf.cast(Depth,tf.float32),p)
return tfd.JointDistributionCoroutineAutoBatched(model)
My model generates two different sets of data which are a and k. If it only has a or k, then I could specify my log_prob function by
def joint_log_prob(*args):
return joint.log_prob(*args, likelihood = data)
or
joint_log_prob = lambda *x: model.log_prob(x + (data,))
But my question is how to incorporate two different sets of data into one log_prob function? Thank you!
The simplest solution would just be specifying both. Assuming data is a tuple:
def joint_log_prob(*args):
return joint.log_prob(*args, a=data[0], k=data[1])
or
joint_log_prob = lambda *x: model.log_prob(x + data)
You might also like to write:
joint_log_prob = joint.experimental_pin(a=.., k=..).unnormalized_log_prob
(See JointDistributionPinned)
I would like to implement the following custom loss function, with argument x as the output of the last layer. Until now I implemented function this as Lambda layer, coupled with the keras mae loss, but I do not want that anymore
def GMM_UNC2(self, x):
tmp = self.create_mr(x) # get mr series
mr = k.sum(tmp, axis=1) # sum over time
tmp = k.square((1/self.T_i) * mr)
tmp = k.dot(tmp, k.transpose(self.T_i))
tmp = (1/(self.T * self.N)) * tmp
f = self.create_factor(x) # get factor
std = k.std(f)
mu = k.mean(f)
tmp = tmp + std/mu
def loss(y_true, y_pred=tmp):
return k.abs(y_true-y_pred)
return loss
self.y_true = np.zeros((1,1))
self.sdf_net = Model(inputs=[self.in_ma, self.in_mi, self.in_re, self.in_si], outputs=w)
self.sdf_net.compile(optimizer=self.optimizer, loss=self.GMM_UNC2(w))
self.sdf_net.fit([self.macro, self.micro, self.R, self.R_sign], self.y_true, epochs=epochs, verbose=1)
The code actually runs but it doesn't actually use tmp as input to loss (I multiplied it with some number, but the loss stays the same)
What am I doing wrong?
It is not completely clear from your question if you want to apply GMM_UNC2 function to the predictions, or it is applied only once to build the loss. If it is the first option, then all that code should be inside the loss and apply it over y_pred, like
def GMM_UNC2(self):
def loss(y_true, y_pred):
tmp = self.create_mr(y_pred) # get mr series
mr = k.sum(tmp, axis=1) # sum over time
tmp = k.square((1/self.T_i) * mr)
tmp = k.dot(tmp, k.transpose(self.T_i))
tmp = (1/(self.T * self.N)) * tmp
f = self.create_factor(x) # get factor
std = k.std(f)
mu = k.mean(f)
tmp = tmp + std/mu
return k.abs(y_true-y_pred)
return loss
If it is the second option, in general, passing objects as default values in a Python function definition is not a good idea, because it can be changed in the function definition. Also, you are assuming that the second argument to the loss has a name y_pred, but when called, it is done without a name, as a positional argument. In summary, you could try using a explicit comparison inside the loss, like
def loss(y_true, y_pred):
if y_pred is None:
y_pred = tmp
return k.abs(y_true - y_pred)
If what you like is ignoring the predictions, and forcibly using tmp, then you can ignore the y_pred argument of the loss and only use tmp, like
def loss(y_true, _):
return k.abs(y_true - tmp)
I have the following optimization problem:
Where X and q are endogenous while the other variables are known.
I use scipy minimize function to solve it. I have no problems with the bounds and constraints:
# objective function
def objective(q,s):
return -sumprod(q,s)
def sumprod(l1,l2):
return sum([x*y for x,y in zip(*[l1,l2])])
# constraints
def cons_periodicflow_min(q):
return q.sum()-qpmin
con1 = {'type':'ineq','fun':cons_periodicflow_min}
def cons_periodicflow_max(q):
return qpmax - q.sum()
con2 = {'type':'ineq','fun':cons_periodicflow_max}
def cons_daily_reservoir(q):#xmin,q,X,a,delta):
return X+a-q-delta-xmin
con3 = {'type':'ineq','fun':cons_daily_reservoir}
def cons_end_reservoir(q):#xend,q,X,a,delta):
return X[-1]+a[-1]-q[-1]-delta[-1]-xend
con4 = {'type':'ineq','fun':cons_end_reservoir}
cons=[con1,con2,con3,con4]
# definition of the parameters
T=3
q0 = np.zeros(T)
s0 = np.array([10,10,10])
qmin = [0,0,0]
qmax = [10,10,10]
delta = [1,1,1]
a = [2,2,2]
X = [10,0,0]
qpmax = 50
qpmin=10
b = [(qmin[t],qmax[t]) for t in range(T)]
sol = sco.minimize(objective,q0,bounds=b,constraints=cons)
My only problem is that X depends on q so I need to update X at each time step, can I add it to the minimize function? Else how to do it?
EDIT:
I can express X in the following way (please don't mind the t / t+1 issues):
Therefore the constraint with Xmin can rewrites:
Does it help to express the optimisation problem?
I want to transfer Matlab code to Jython version, and find that the fminsearch in Matlab might be replaced by Apache-Common-Math-Optimization.
I'm coding on the Mango Medical Image script manager, which uses Jython 2.5.3 as coding language. And the Math version is 3.6.1.
Here is my code:
def f(x,y):
return x^2+y^2
sys.path.append('/home/shujian/APPs/Mango/lib/commons-math3-3.6.1.jar')
sys.add_package('org.apache.commons.math3.analysis')
from org.apache.commons.math3.analysis import MultivariateFunction
sys.add_package('org.apache.commons.math3.optim.nonlinear.scalar.noderiv')
from org.apache.commons.math3.optim.nonlinear.scalar.noderiv import NelderMeadSimplex,SimplexOptimizer
sys.add_package('org.apache.commons.math3.optim.nonlinear.scalar')
from org.apache.commons.math3.optim.nonlinear.scalar import ObjectiveFunction
sys.add_package('org.apache.commons.math3.optim')
from org.apache.commons.math3.optim import MaxEval,InitialGuess
sys.add_package('org.apache.commons.math3.optimization')
from org.apache.commons.math3.optimization import GoalType
initialSolution=[2.0,2.0]
simplex=NelderMeadSimplex([2.0,2.0])
opt=SimplexOptimizer(2**(-6), 2**(-10))
solution=opt.optimize(MaxEval(300),ObjectiveFunction(f),simplex,GoalType.MINIMIZE,InitialGuess([2.0,2.0]))
skewParameters2 = solution.getPointRef()
print skewParameters2;
And I got the error below：
TypeError: optimize(): 1st arg can't be coerced to
I'm quite confused about how to use the optimization in Jython and the examples are all Java version.
I've given up this plan and find another method to perform the fminsearch in Jython. Below is the Jython version code:
import sys
sys.path.append('.../jnumeric-2.5.1_ra0.1.jar') #add the jnumeric path
import Numeric as np
def nelder_mead(f, x_start,
step=0.1, no_improve_thr=10e-6,
no_improv_break=10, max_iter=0,
alpha=1., gamma=2., rho=-0.5, sigma=0.5):
'''
#param f (function): function to optimize, must return a scalar score
and operate over a numpy array of the same dimensions as x_start
#param x_start (float list): initial position
#param step (float): look-around radius in initial step
#no_improv_thr, no_improv_break (float, int): break after no_improv_break iterations with
an improvement lower than no_improv_thr
#max_iter (int): always break after this number of iterations.
Set it to 0 to loop indefinitely.
#alpha, gamma, rho, sigma (floats): parameters of the algorithm
(see Wikipedia page for reference)
return: tuple (best parameter array, best score)
'''
# init
dim = len(x_start)
prev_best = f(x_start)
no_improv = 0
res = [[np.array(x_start), prev_best]]
for i in range(dim):
x=np.array(x_start)
x[i]=x[i]+step
score = f(x)
res.append([x, score])
# simplex iter
iters = 0
while 1:
# order
res.sort(key=lambda x: x[1])
best = res[0][1]
# break after max_iter
if max_iter and iters >= max_iter:
return res[0]
iters += 1
# break after no_improv_break iterations with no improvement
print '...best so far:', best
if best < prev_best - no_improve_thr:
no_improv = 0
prev_best = best
else:
no_improv += 1
if no_improv >= no_improv_break:
return res[0]
# centroid
x0 = [0.] * dim
for tup in res[:-1]:
for i, c in enumerate(tup[0]):
x0[i] += c / (len(res)-1)
# reflection
xr = x0 + alpha*(x0 - res[-1][0])
rscore = f(xr)
if res[0][1] <= rscore < res[-2][1]:
del res[-1]
res.append([xr, rscore])
continue
# expansion
if rscore < res[0][1]:
xe = x0 + gamma*(x0 - res[-1][0])
escore = f(xe)
if escore < rscore:
del res[-1]
res.append([xe, escore])
continue
else:
del res[-1]
res.append([xr, rscore])
continue
# contraction
xc = x0 + rho*(x0 - res[-1][0])
cscore = f(xc)
if cscore < res[-1][1]:
del res[-1]
res.append([xc, cscore])
continue
# reduction
x1 = res[0][0]
nres = []
for tup in res:
redx = x1 + sigma*(tup[0] - x1)
score = f(redx)
nres.append([redx, score])
res = nres
And the test example is as below:
def f(x):
return x[0]**2+x[1]**2+x[2]**2
print nelder_mead(f,[3.4,2.3,2.2])
Actually, the original version is for python, and the link below is the source:
https://github.com/fchollet/nelder-mead
I am trying to model an ordinal predicted variable using PyMC3 based on the approach in chapter 23 of Doing Bayesian Data Analysis. I would like to determine a good starting value using find_MAP, but am receiving an optimization error.
The model:
import pymc3 as pm
import numpy as np
import theano
import theano.tensor as tt
# Some helper functions
def cdf(x, location=0, scale=1):
epsilon = np.array(1e-32, dtype=theano.config.floatX)
location = tt.cast(location, theano.config.floatX)
scale = tt.cast(scale, theano.config.floatX)
div = tt.sqrt(2 * scale ** 2 + epsilon)
div = tt.cast(div, theano.config.floatX)
erf_arg = (x - location) / div
return .5 * (1 + tt.erf(erf_arg + epsilon))
def percent_to_thresh(idx, vect):
return 5 * tt.sum(vect[:idx + 1]) + 1.5
def full_thresh(thresh):
idxs = tt.arange(thresh.shape[0] - 1)
thresh_mod, updates = theano.scan(fn=percent_to_thresh,
sequences=[idxs],
non_sequences=[thresh])
return tt.concatenate([[-1 * np.inf, 1.5], thresh_mod, [6.5, np.inf]])
def compute_ps(thresh, location, scale):
f_thresh = full_thresh(thresh)
return cdf(f_thresh[1:], location, scale) - cdf(f_thresh[:-1], location, scale)
# Generate data
real_ps = [0.05, 0.05, 0.1, 0.1, 0.2, 0.3, 0.2]
data = np.random.choice(7, size=1000, p=real_ps)
# Run model
with pm.Model() as model:
mu = pm.Normal('mu', mu=4, sd=3)
sigma = pm.Uniform('sigma', lower=0.1, upper=70)
thresh = pm.Dirichlet('thresh', a=np.ones(5))
cat_p = compute_ps(thresh, mu, sigma)
results = pm.Categorical('results', p=cat_p, observed=data)
with model:
start = pm.find_MAP()
trace = pm.sample(2000, start=start)
When running this, I receive the following error:
Applied interval-transform to sigma and added transformed sigma_interval_ to model.
Applied stickbreaking-transform to thresh and added transformed thresh_stickbreaking_ to model.
Traceback (most recent call last):
File "cm_net_log.v1-for_so.py", line 53, in <module>
start = pm.find_MAP()
File "/usr/local/lib/python3.5/site-packages/pymc3/tuning/starting.py", line 133, in find_MAP
specific_errors)
ValueError: Optimization error: max, logp or dlogp at max have non-finite values. Some values may be outside of distribution support. max: {'thresh_stickbreaking_': array([-1.04298465, -0.48661088, -0.84326554, -0.44833646]), 'sigma_interval_': array(-2.220446049250313e-16), 'mu': array(7.68422528308479)} logp: array(-3506.530143064723) dlogp: array([ 1.61013190e-06, nan, -6.73994118e-06,
-6.93873894e-06, 6.03358122e-06, 3.18954680e-06])Check that 1) you don't have hierarchical parameters, these will lead to points with infinite density. 2) your distribution logp's are properly specified. Specific issues:
My questions:
How can I determine why dlogp is nan at certain points?
Is there a different way that I can express this model to avoid dlogp being nan?
Also worth noting:
This model runs fine if I don't find_MAP and use a Metropolis sampler. However, I'd like to have the flexibility of using other samplers as this model becomes more complex.
I have a suspicion that the issue is due to the relationship between the thresholds and the normal distribution, but I don't know how to disentangle them for the optimization.
Regarding question 2: I expressed the model for the ordinal predicted variable (single group) differently; I used the Theano #as_op decorator for a function that calculates probabilities for the outcomes. That also explains why I cannot use find_MAP() or gradient based samplers: Theano cannot calculate a gradient for the custom function. (http://pymc-devs.github.io/pymc3/notebooks/getting_started.html#Arbitrary-deterministics)
# Number of outcomes
nYlevels = df.Y.cat.categories.size
thresh = [k + .5 for k in range(1, nYlevels)]
thresh_obs = np.ma.asarray(thresh)
thresh_obs[1:-1] = np.ma.masked
#as_op(itypes=[tt.dvector, tt.dscalar, tt.dscalar], otypes=[tt.dvector])
def outcome_probabilities(theta, mu, sigma):
out = np.empty(nYlevels)
n = norm(loc=mu, scale=sigma)
out[0] = n.cdf(theta[0])
out[1] = np.max([0, n.cdf(theta[1]) - n.cdf(theta[0])])
out[2] = np.max([0, n.cdf(theta[2]) - n.cdf(theta[1])])
out[3] = np.max([0, n.cdf(theta[3]) - n.cdf(theta[2])])
out[4] = np.max([0, n.cdf(theta[4]) - n.cdf(theta[3])])
out[5] = np.max([0, n.cdf(theta[5]) - n.cdf(theta[4])])
out[6] = 1 - n.cdf(theta[5])
return out
with pm.Model() as ordinal_model_single:
theta = pm.Normal('theta', mu=thresh, tau=np.repeat(.5**2, len(thresh)),
shape=len(thresh), observed=thresh_obs, testval=thresh[1:-1])
mu = pm.Normal('mu', mu=nYlevels/2.0, tau=1.0/(nYlevels**2))
sigma = pm.Uniform('sigma', nYlevels/1000.0, nYlevels*10.0)
pr = outcome_probabilities(theta, mu, sigma)
y = pm.Categorical('y', pr, observed=df.Y.cat.codes.as_matrix())
http://nbviewer.jupyter.org/github/JWarmenhoven/DBDA-python/blob/master/Notebooks/Chapter%2023.ipynb