Spline regression via PyMC3

Question

I've looked through PyMC3 documentation and haven't seen any tutorials/resources on learning to use Splines w/ PyMC3. Could anyone recommend a resource? I see that Stan tutorials are available. I figure if one isn't available in the official PyMC3 documentation, someone here might have written one.

Answer 1

Here is a minimal example, which works for a DataFrame df with columns X and Y. It uses patsy, which is (still) my go-to package for splines in Python

df = pd.DataFrame({'X':np.arange(-5, 5, .1),
                   'Y':Y  # add your data here
                  })
B = patsy.dmatrix('bs(X, knots=np.arange(-5,5,1), degree=3)', df, 
                  return_type='dataframe')

with pm.Model() as model:
    a_raw = pm.Normal('a_raw', mu=0, sd=1, shape=num_basis)
    tau = pm.Cauchy('tau', alpha=1, beta=1)
    sigma = pm.Cauchy('sigma', alpha=1, beta=1)
    y_hat = pm.Deterministic('y_hat', tt.dot(B, a_raw*tau))
    y = pm.Normal('y', mu=y_hat, sd=sigma, observed=df.Y)
    trace = pm.sample(500, cores=2)

It seems to work:

Here is a notebook that puts the whole thing in context: https://gist.github.com/aflaxman/d34ceddec6663c15930abff7257d84f9