Getting Mass matrix contains zeros on the diagonal

Questions
1

Sorry, still very green learning how to use PYMC3. I know this has been asked before but after reading through quite a few posts, I still cannot figure out why I am getting the following error:

Traceback (most recent call last):
  File "/usr/local/lib/python3.7/dist-packages/pymc3/parallel_sampling.py", line 137, in run
    self._start_loop()
  File "/usr/local/lib/python3.7/dist-packages/pymc3/parallel_sampling.py", line 191, in _start_loop
    point, stats = self._compute_point()
  File "/usr/local/lib/python3.7/dist-packages/pymc3/parallel_sampling.py", line 216, in _compute_point
    point, stats = self._step_method.step(self._point)
  File "/usr/local/lib/python3.7/dist-packages/pymc3/step_methods/arraystep.py", line 276, in step
    apoint, stats = self.astep(array)
  File "/usr/local/lib/python3.7/dist-packages/pymc3/step_methods/hmc/base_hmc.py", line 147, in astep
    self.potential.raise_ok(self._logp_dlogp_func._ordering.vmap)
  File "/usr/local/lib/python3.7/dist-packages/pymc3/step_methods/hmc/quadpotential.py", line 272, in raise_ok
    raise ValueError("\n".join(errmsg))
ValueError: Mass matrix contains zeros on the diagonal. 
The derivative of RV `a_bin`.ravel()[5] is zero.
The derivative of RV `a_bin`.ravel()[6] is zero.
The derivative of RV `a_bin`.ravel()[7] is zero.
The derivative of RV `sd_bin_log__`.ravel()[0] is zero.
The derivative of RV `b_up_log__`.ravel()[0] is zero.

This the model I am trying to run is:

with pm.Model() as _model:
    a = pm.Normal('a', mu=3, sd=.75)
    b_up = pm.Exponential('b_up', 1) 
    b_down = pm.Exponential('b_down', 1/0.5)
    swp = pm.Normal('swp', 1, sigma=7)
    sd_bin = pm.Exponential('sd_bin', 3) 
    a_bin = pm.Normal('a_bin', 0, sd_bin, shape=num_bins) 
    sigma  = pm.Exponential('sigma', 1) 

    def get_mu(price):
        price_sc = price / 100

        _b = tt.switch(
            tt.lt(price_sc, swp),
            b_up, # rise
            -b_down # fall
        )

        return a + _b * (price_sc - swp) # scaled for: log(value) / price ratio  

    mu_i = get_mu(prices) + a_bin[bin_index] 
    lk = pm.Lognormal.dist(mu_i, sigma)

    pm.Potential('obs', freq*lk.logp(values))
    post = pm.sample(tune=5000, draws=1000, chains=2)

To debug, I’ve tried:

  • Setting the priors to static numbers and then adding in priors as distributions one at a time. I end up just getting the above error message with different RVs
  • Smoothing the piecewise function
  • Doing prior predictive sampling to make sure the mu_i values are reasonable
  • Adjusting the init setting in the sample method
  • Removing the hierarchical component

Not sure what to try next. Again, not sure exactly if what I am doing is even reasonable for the model definition. Any help would be greatly appreciated. Thank you!!

2

This might not be the main issue but you need to make sure swp (prior) is between the min and max of price_sc. If it goes outside the range, the piecewise will be wasted.

3

Thanks Dirk. I did try to set the values of swp to be tighter so that it doesn’t fall outside the range of price_sc but still no luck. But I will verify again.