I am using PyMC3 to calculate something which I won't get into here but you can get the idea from this link if interested.
The '2-lambdas' case is basically a switch function, which needs to be compiled to a Theano function to avoid dtype errors and looks like this:
import theano
from theano.tensor import lscalar, dscalar, lvector, dvector, argsort
@theano.compile.ops.as_op(itypes=[lscalar, dscalar, dscalar], otypes=[dvector])
def lambda_2_distributions(tau, lambda_1, lambda_2):
"""
Return values of `lambda_` for each observation based on the
transition value `tau`.
"""
out = zeros(num_observations)
out[: tau] = lambda_1 # lambda before tau is lambda1
out[tau:] = lambda_2 # lambda after (and including) tau is lambda2
return out
I am trying to generalize this to apply to 'n-lambdas', where taus.shape[0] = lambdas.shape[0] - 1, but I can only come up with this horribly slow numpy implementation.
@theano.compile.ops.as_op(itypes=[lvector, dvector], otypes=[dvector])
def lambda_n_distributions(taus, lambdas):
out = zeros(num_observations)
np_tau_indices = argsort(taus).eval()
num_taus = taus.shape[0]
for t in range(num_taus):
if t == 0:
out[: taus[np_tau_indices[t]]] = lambdas[t]
elif t == num_taus - 1:
out[taus[np_tau_indices[t]]:] = lambdas[t + 1]
else:
out[taus[np_tau_indices[t]]: taus[np_tau_indices[t + 1]]] = lambdas[t]
return out
Any ideas on how to speed this up using pure Theano (avoiding the call to .eval())? It's been a few years since I've used it and so don't know the right approach.
