Sometimes, it is very useful to update a set of parameters together. For example, variables that are highly correlated are often good to update together. In PyMC 3 block updating is simple, as example will demonstrate.
Here we have a LASSO regression model where the two coefficients are strongly correlated. Normally, we would define the coefficient parameters as a single random variable, but here we define them separately to show how to do block updates.
First we generate some fake data.
%matplotlib inline
from matplotlib.pylab import *
from pymc3 import *
import numpy as np
d = np.random.normal(size=(3, 30))
d1 = d[0] + 4
d2 = d[1] + 4
yd = .2*d1 +.3*d2 + d[2]
Then define the random variables.
lam = 3
with Model() as model:
s = Exponential('s', 1)
tau = Uniform('tau', 0, 1000)
b = lam * tau
m1 = Laplace('m1', 0, b)
m2 = Laplace('m2', 0, b)
p = d1*m1 + d2*m2
y = Normal('y', mu=p, sigma=s, observed=yd)
For most samplers, including Metropolis and HamiltonianMC, simply pass a list of variables to sample as a block. This works with both scalar and array parameters.
with model:
start = find_MAP()
step1 = Metropolis([m1, m2])
step2 = Slice([s, tau])
trace = sample(10000, [step1, step2], start=start)
Multiprocess sampling (4 chains in 4 jobs) CompoundStep >CompoundStep >>Metropolis: [m2] >>Metropolis: [m1] >CompoundStep >>Slice: [tau] >>Slice: [s]
Sampling 4 chains for 1_000 tune and 10_000 draw iterations (4_000 + 40_000 draws total) took 53 seconds. The number of effective samples is smaller than 10% for some parameters.
traceplot(trace);
/dependencies/arviz/arviz/data/io_pymc3.py:89: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context. FutureWarning,
hexbin(trace[m1],trace[m2], gridsize = 50)
axis('off');
%load_ext watermark
%watermark -n -u -v -iv -w
platform 1.0.8 matplotlib 3.2.1 re 2.2.1 numpy 1.18.5 logging 0.5.1.2 last updated: Fri Jun 12 2020 CPython 3.7.7 IPython 7.15.0 watermark 2.0.2