NaNs in gradients when fitting RSLDS

[bantin]

I sometimes get errors (seems to be random based on the initialization) when trying to fit an RSLDS. The following lines reproduce the error:

import ssm
import autograd.numpy as np
np.random.seed(seed=123457)
true_lds = ssm.SLDS(15, 3, 10, transitions="rbf_recurrent", dynamics="gaussian", emissions="gaussian")
z, x, y = true_lds.sample(100)

new_lds = ssm.SLDS(15, 3, 10, transitions="rbf_recurrent", dynamics="gaussian", emissions="gaussian")
new_lds.fit(y, method="svi", variational_posterior="mf")

The traceback looks like this:

Traceback (most recent call last):
  File "/Users/bantin/Documents/Linderman-Shenoy/ssm/ssm/quick_test.py", line 8, in <module>
    new_lds.fit(y, method="svi", variational_posterior="mf")
  File "/Users/bantin/Documents/Linderman-Shenoy/ssm/ssm/util.py", line 108, in wrapper
    return f(self, datas, inputs=inputs, masks=masks, tags=tags, **kwargs)
  File "/Users/bantin/Documents/Linderman-Shenoy/ssm/ssm/lds.py", line 862, in fit
    elbos = _fitting_methods[method](posterior, datas, inputs, masks, tags, learning=True, **kwargs)
  File "/Users/bantin/Documents/Linderman-Shenoy/ssm/ssm/lds.py", line 430, in _fit_svi
    params, val, g, state = step(value_and_grad(_objective), params, itr, state)
  File "/Users/bantin/Documents/Linderman-Shenoy/ssm/ssm/optimizers.py", line 44, in _step
    step(_value_and_grad, _x, itr, state=state, *args, **kwargs)
  File "/Users/bantin/Documents/Linderman-Shenoy/ssm/ssm/optimizers.py", line 75, in adam_step
    val, g = value_and_grad(x, itr)
  File "/Users/bantin/Documents/Linderman-Shenoy/ssm/ssm/optimizers.py", line 41, in _value_and_grad
    v, g = value_and_grad(unflatten(x), i)
  File "/Users/Bantin/anaconda3/lib/python3.7/site-packages/autograd/wrap_util.py", line 20, in nary_f
    return unary_operator(unary_f, x, *nary_op_args, **nary_op_kwargs)
  File "/Users/Bantin/anaconda3/lib/python3.7/site-packages/autograd/differential_operators.py", line 140, in value_and_grad
    return ans, vjp(vspace(ans).ones())
  File "/Users/Bantin/anaconda3/lib/python3.7/site-packages/autograd/core.py", line 14, in vjp
    def vjp(g): return backward_pass(g, end_node)
  File "/Users/Bantin/anaconda3/lib/python3.7/site-packages/autograd/core.py", line 21, in backward_pass
    ingrads = node.vjp(outgrad[0])
  File "/Users/Bantin/anaconda3/lib/python3.7/site-packages/autograd/core.py", line 78, in <lambda>
    return lambda g: (vjp_0(g), vjp_1(g))
  File "/Users/Bantin/anaconda3/lib/python3.7/site-packages/autograd/scipy/linalg.py", line 29, in vjp
    v = al2d(solve_triangular(a, g, trans=_flip(a, trans), lower=lower))
  File "/Users/Bantin/anaconda3/lib/python3.7/site-packages/autograd/tracer.py", line 48, in f_wrapped
    return f_raw(*args, **kwargs)
  File "/Users/Bantin/anaconda3/lib/python3.7/site-packages/scipy/linalg/basic.py", line 336, in solve_triangular
    b1 = _asarray_validated(b, check_finite=check_finite)
  File "/Users/Bantin/anaconda3/lib/python3.7/site-packages/scipy/_lib/_util.py", line 239, in _asarray_validated
    a = toarray(a)
  File "/Users/Bantin/anaconda3/lib/python3.7/site-packages/numpy/lib/function_base.py", line 496, in asarray_chkfinite
    "array must not contain infs or NaNs")
ValueError: array must not contain infs or NaNs

I also get a message that LBFGS-B ran out of iteration before converging, during the initialization ARHMM fitting, which might be related.

[bantin]

Looks like this was caused by taking log of zero in messages.py:

alphas[0] = np.log(pi0) + log_likes[0]

This is addressed in 1927f6f