A "clipping" distribution transformation

I have defined a “clipping” distribution transformation like this:

from pymc3.distributions.transforms import ElemwiseTransform

import aesara.tensor as at
import numpy as np

class MvClippingTransform(ElemwiseTransform):
    name = "MvClippingTransform"
    def __init__(self, lower = None, upper = None):
        if lower is None:
            lower = float("-inf")
        if upper is None:
            upper = float("inf")
        self.lower = lower
        self.upper = upper
    def backward(self, x):
        return x

    def forward(self, x):
        return at.clip(x, self.lower, self.upper)

    def forward_val(self, x, point=None):
        return np.clip(x, self.lower, self.upper)

    def jacobian_det(self, x):
        # The backwards transformation of clipping as I've defined it is the identity function (perhaps that will change)
        # I have an intuition that the jacobian determinant of the identity function is 1, so log(abs(1)) -> 0
        return at.zeros(x.shape)

And I have applied it to a MvNormal with an LKJ Cholesky prior like this:

import importlib, clipping; importlib.reload(clipping)

with pm.Model() as m:
    # Taken from https://docs.pymc.io/pymc-examples/examples/case_studies/LKJ.html
    chol, corr, stds = pm.LKJCholeskyCov(
        # Specifying compute_corr=True also unpacks the cholesky matrix in the returns (otherwise we'd have to unpack ourselves)
        "chol", n=3, eta=2.0, sd_dist=pm.Exponential.dist(1.0), compute_corr=True 
    cov = pm.Deterministic("cov", chol.dot(chol.T))
    μ = pm.Uniform("μ", -10, 10, shape=3, testval=samples.mean(axis=0))
    clipping = clipping.MvClippingTransform(lower = None, upper = upper_truncation)    
    mv = pm.MvNormal("mv", mu = μ, chol=chol, shape = 3, transform = clipping, observed=samples) # , observed = samples
    trace = pm.sample(random_seed=44, init="adapt_diag", return_inferencedata=True, target_accept = 0.9)
    ppc = pm.sample_posterior_predictive(
        trace, var_names=["mv"], random_seed=42

(upper truncation is a numpy array)

Now, I have generated simulated data by defining a covariance matrix for a multivariate normal distribution and applying clipping to it, to get this:

But when I sample from the PPC, there is no clipping. I’d embed a second image but new users are not aloud to.

Even if I define the clipping to be [0,0,0], it still doesn’t work.

Why isn’t the PPC (or the parameter sampling, for that matter) reflecting the clipping transformation?


PPC does not accommodate transforms. They are only used in normal sampling.

You can add a deterministic with theano.clip to save clipped values during PPC if you need it.

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Hi Ricardo. Thank you for your answer! If I understand you correctly, you are saying that the PPC will not reflect any applied transformation. Thank you for that information.

Is it also the case that if a transform is specified on an observed RV, that the transform will be ignored when sampling parameters? Apologies if I am misapplying the terminology.

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You are correct. Transforms are also ignored in observed variables.

Interesting. What is the intended use-case for Distribution Transforms?

They are useful for MCMC. The transforms convert an otherwise bounded distribution to span the real line. This is very helpful for MCMC samplers (and NUTS in particular) which don’t do so well with sharp boundaries in the logp.

In addition, there are some tricks where transforms can be used to force a bounded or sorted distribution, but that only works during MCMC sampling

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