sampled 0.1.2

sampled

Decorator for reusable models in PyMC3

Provides syntactic sugar for reusable models with PyMC3. This lets you separate creating a generative model from using the model.

Here is an example of creating a model:

import numpy as np
import pymc3 as pm
from sampled import sampled

@sampled
def linear_model(X, y):
    shape = X.shape
    X = pm.Normal('X', mu=np.mean(X, axis=0), sd=np.std(X, axis=0), shape=shape)
    coefs = pm.Normal('coefs', mu=np.zeros(shape[1]), sd=np.ones(shape[1]), shape=shape[1])
    pm.Normal('y', mu=np.dot(X, coefs), sd=np.ones(shape[0]), shape=shape[0])

Now here is how to use the model:

X = np.random.normal(size=(1000, 10))
w = np.random.normal(size=10)
y = X.dot(w) + np.random.normal(scale=0.1, size=1000)

with linear_model(X=X, y=y):
    sampled_coefs = pm.sample(draws=1000, tune=500)

np.allclose(sampled_coefs.get_values('coefs').mean(axis=0), w, atol=0.1) # True

You can also use this to build graphical networks – here is a continuous version of the STUDENT example from Koller and Friedman’s “Probabilistic Graphical Models”, chapter 3:

@sampled
def student():
    difficulty = pm.Beta('difficulty', alpha=5, beta=5)
    intelligence = pm.Beta('intelligence', alpha=5, beta=5)
    SAT = pm.Beta('SAT', alpha=20 * intelligence, beta=20 * (1 - intelligence))
    grade_avg = 0.5 + 0.5 * tt.sqrt((1 - difficulty) * intelligence)
    grade = pm.Beta('grade', alpha=20 * grade_avg, beta=20 * (1 - grade_avg))
    recommendation = pm.Binomial('recommendation', n=1, p=0.7 * grade)

Observations may be passed into any node, and we can observe how that changes posterior expectations:

# no prior knowledge
with student():
    prior = pm.sample(draws=1000, tune=500)

prior.get_values('recommendation').mean()  # 0.502

# 99th percentile SAT score --> higher chance of a recommendation
with student(SAT=0.99):
    good_sats = pm.sample(draws=1000, tune=500)

good_sats.get_values('recommendation').mean()  # 0.543

# A good grade in a hard class --> very high chance of recommendation
with student(difficulty=0.99, grade=0.99):
    hard_class_good_grade = pm.sample(draws=1000, tune=500)

hard_class_good_grade.get_values('recommendation').mean()  # 0.705

References

• Koller, Daphne, and Nir Friedman. Probabilistic graphical models: principles and techniques. MIT press, 2009.