Defining multiple BART RVs in a pymc-bart model

[cspanbauer]

Is it possible to define two BART RVs with different X and Y inputs in the same pymc-bart model? For example, using BART to estimate the nonlinear relationship for each link of a network? I seem to run into an error when trying a simple independent example for this that suggests this may not be possible so I wanted to be sure.

Assume we have Y1 = f1(X1) + e1 and Y2 = f2(X2) + e2 where e1 and e2 are independent errors for simplicity and X1 and X2 are distinct. I understand you can use 'size=2' when defining a BART RV, as in the heteroskedasticity example, but in this case we have two different inputs for X and Y. I'm guessing Y is needed to set the BART priors and X is used for the splitting rules. Is there a way to specify this model, or is it not currently possible? My use-case will eventually involve correlated errors, but that should be easy enough to incorporate with an LKJ prior and MvNormal as the likelihood specification.

Here's a simple example. Thanks in advance for any help you can provide.

### Simulate Data ###

import numpy as np
import pymc as pm
import pymc_bart as pmb

sigma1, sigma2 = 1, 1
n = 200

# Predictor variable
X11 = np.random.uniform(-2,2,n)
X12 = np.random.uniform(-2,2,n)
X21 = np.random.uniform(-2,2,n)
X22 = np.random.uniform(-2,2,n)

X1=np.c_[X11,X12]
X2=np.c_[X21,X22]

f1 = X1[:,0]

f2 = (X2[:,0]-0.5*X2[:,0]**3)/4

zeta1 = np.random.normal(0,1,n)
zeta2 = np.random.normal(0,1,n)

Y1 = f1 + sigma1*zeta1
Y2 = f2 + sigma2*zeta2

### Specify Model ###

netBART = pm.Model()
with netBART:    

    f1=pmb.BART("f1",X=X1,Y=Y2)
    f2=pmb.BART("f2",X=X2,Y=Y2)
    mu1=pm.Deterministic("mu1",f1)
    mu2=pm.Deterministic("mu2",f2)
    sigma1Sq=pm.InverseGamma("sigma1Sq",1,1)
    sigma2Sq=pm.InverseGamma("sigma2Sq",1,1)
    sigma1=pm.Deterministic("sigma1",sigma1Sq**0.5)
    sigma2=pm.Deterministic("sigma2",sigma2Sq**0.5)

    like1=pm.Normal("like1",mu=mu1,sigma=sigma1,observed=Y1)
    like2=pm.Normal("like2",mu=mu2,sigma=sigma2,observed=Y2)

    idata=pm.sample(draws=100,tune=50,chains=4)

Output:

Only 100 samples in chain.

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In[116], line 16
     13 like1=pm.Normal("like1",mu=mu1,sigma=sigma1,observed=Y1)
     14 like2=pm.Normal("like2",mu=mu2,sigma=sigma2,observed=Y2)
---> 16 idata=pm.sample(draws=100,tune=50,chains=4)

File ~/miniconda3/envs/pymc_env/lib/python3.10/site-packages/pymc/sampling/mcmc.py:452, in sample(draws, step, init, n_init, initvals, trace, chains, cores, tune, progressbar, model, random_seed, discard_tuned_samples, compute_convergence_checks, callback, jitter_max_retries, return_inferencedata, keep_warning_stat, idata_kwargs, mp_ctx, **kwargs)
    449         auto_nuts_init = False
    451 initial_points = None
--> 452 step = assign_step_methods(model, step, methods=pm.STEP_METHODS, step_kwargs=kwargs)
    454 if isinstance(step, list):
    455     step = CompoundStep(step)

File ~/miniconda3/envs/pymc_env/lib/python3.10/site-packages/pymc/sampling/mcmc.py:194, in assign_step_methods(model, step, methods, step_kwargs)
    186         selected = max(
    187             methods,
    188             key=lambda method, var=rv_var, has_gradient=has_gradient: method._competence(
    189                 var, has_gradient
    190             ),
    191         )
    192         selected_steps[selected].append(var)
--> 194 return instantiate_steppers(model, steps, selected_steps, step_kwargs)

File ~/miniconda3/envs/pymc_env/lib/python3.10/site-packages/pymc/sampling/mcmc.py:112, in instantiate_steppers(model, steps, selected_steps, step_kwargs)
    110         args = step_kwargs.get(step_class.name, {})
    111         used_keys.add(step_class.name)
--> 112         step = step_class(vars=vars, model=model, **args)
    113         steps.append(step)
    115 unused_args = set(step_kwargs).difference(used_keys)

File ~/miniconda3/envs/pymc_env/lib/python3.10/site-packages/pymc/step_methods/compound.py:89, in BlockedStep.__new__(cls, *args, **kwargs)
     86 step = super().__new__(cls)
     87 # If we don't return the instance we have to manually
     88 # call __init__
---> 89 step.__init__([var], *args, **kwargs)
     90 # Hack for creating the class correctly when unpickling.
     91 step.__newargs = ([var],) + args, kwargs

TypeError: PGBART.__init__() got an unexpected keyword argument 'blocked'

[aloctavodia]

Unfortunately, you are right. Currently, having more than one BART RV per model is not impossible.

[ggmirandac]

Hi, are there any plans to having multiple BART trees in the same model to work into more complex types of interactions between the covariates. For example, what we see In this example in the PyMC documentation. Where we could replace some of the linear regressions with BART models.

[aloctavodia]

The top priority is speeding up the current implementation and fixing some issues with parallel sampling. But allowing multiple BART RVs is something we should add at some point. Notice that you can have separated trees, under certain circumstances, see https://github.com/pymc-devs/pymc-bart/pull/98