!pip install bayeux-ml

import arviz as az
import bayeux as bx
import jax
import matplotlib.pyplot as plt
import numpy as np
import pymc as pm

Using bayeux with pymc

bayeux has a built-in function bx.Model.from_pymc that makes it easy to work with pymc models. More on PyMC here.

We implement a common hierarchical model of the eight schools dataset (Rubin 1981¹), whose details can be seen on the Stan documentation, PyMC documentation, TFP documentation, numpyro documentation, among others.

¹ Rubin, Donald B. 1981. “Estimation in Parallel Randomized Experiments.” Journal of Educational and Behavioral Statistics 6 (4): 377–401.

treatment_effects = np.array([28, 8, -3, 7, -1, 1, 18, 12], dtype=np.float32)
treatment_stddevs = np.array(
    [15, 10, 16, 11, 9, 11, 10, 18], dtype=np.float32)

with pm.Model() as model:
  avg_effect = pm.Normal('avg_effect', 0., 10.)
  avg_stddev = pm.HalfNormal('avg_stddev', 10.)
  school_effects = pm.Normal('school_effects', shape=8)
  pm.Normal('observed',
            avg_effect + avg_stddev * school_effects,
            treatment_stddevs,
            observed=treatment_effects)

bx_model = bx.Model.from_pymc(model)

idata = bx_model.mcmc.blackjax_nuts(seed=jax.random.key(0))

az.summary(idata)

	mean	sd	hdi_3%	hdi_97%	mcse_mean	mcse_sd	ess_bulk	ess_tail	r_hat
avg_effect	6.392	4.207	-1.522	13.967	0.069	0.049	3717.0	2153.0	1.00
avg_stddev	4.681	3.728	0.001	11.391	0.075	0.053	1835.0	1255.0	1.00
school_effects[0]	0.344	0.973	-1.571	2.073	0.016	0.015	3784.0	2729.0	1.01
school_effects[1]	0.051	0.901	-1.784	1.671	0.014	0.014	4265.0	2982.0	1.00
school_effects[2]	-0.126	0.943	-1.917	1.594	0.015	0.015	4037.0	2689.0	1.00
school_effects[3]	0.020	0.911	-1.710	1.733	0.014	0.015	4367.0	3061.0	1.00
school_effects[4]	-0.245	0.899	-1.942	1.423	0.014	0.013	4306.0	2970.0	1.00
school_effects[5]	-0.131	0.921	-1.916	1.554	0.015	0.014	4039.0	2874.0	1.00
school_effects[6]	0.362	0.907	-1.350	2.034	0.013	0.013	4549.0	3204.0	1.00
school_effects[7]	0.066	0.972	-1.678	1.942	0.015	0.016	4481.0	3004.0	1.00

opt_results = bx_model.optimize.optax_adam(seed=jax.random.PRNGKey(0))


fig, ax = plt.subplots(figsize=(12, 2))
ax.plot(opt_results.loss.T)
opt_results.params

{'avg_effect': Array([6.17051501, 6.17051501, 6.17051501, 6.17051501, 6.17051501,
        6.17051501, 6.1705141 , 6.17051501], dtype=float64),
 'avg_stddev': Array([10.6251654 , 10.6251654 , 10.6251654 , 10.6251654 , 10.6251654 ,
        10.6251654 , 10.62516158, 10.6251654 ], dtype=float64),
 'school_effects': Array([[ 0.68643359,  0.09130632, -0.26413604,  0.03768121, -0.39293559,
         -0.23488223,  0.59038842,  0.14177174],
        [ 0.68643359,  0.09130632, -0.26413604,  0.03768121, -0.39293559,
         -0.23488223,  0.59038842,  0.14177174],
        [ 0.68643359,  0.09130632, -0.26413604,  0.03768121, -0.39293559,
         -0.23488223,  0.59038842,  0.14177174],
        [ 0.68643359,  0.09130632, -0.26413604,  0.03768121, -0.39293559,
         -0.23488223,  0.59038842,  0.14177174],
        [ 0.68643359,  0.09130632, -0.26413604,  0.03768121, -0.39293559,
         -0.23488223,  0.59038842,  0.14177174],
        [ 0.68643359,  0.09130632, -0.26413604,  0.03768121, -0.39293559,
         -0.23488223,  0.59038842,  0.14177174],
        [ 0.68643307,  0.09130638, -0.26413599,  0.03768124, -0.39293562,
         -0.23494317,  0.59038848,  0.14177166],
        [ 0.68643359,  0.09130632, -0.26413604,  0.03768121, -0.39293559,
         -0.23488223,  0.59038842,  0.14177174]], dtype=float64)}

surrogate_posterior, losses = bx_model.vi.tfp_factored_surrogate_posterior(
    seed=jax.random.PRNGKey(0))


fig, ax = plt.subplots(figsize=(12, 2))
ax.plot(losses.T)

draws = surrogate_posterior.sample(100, seed=jax.random.PRNGKey(1))
jax.tree.map(lambda x: np.mean(x, axis=(0, 1)), draws)

{'avg_effect': Array(6.462984, dtype=float32),
 'avg_stddev': Array(3.947107, dtype=float32),
 'school_effects': Array([ 0.36255622,  0.05804485, -0.17273399, -0.01884761, -0.2191218 ,
        -0.16507229,  0.3044642 ,  0.06365623], dtype=float32)}