$$z_i \sim p_i(z_{i}|\theta, z_{<i})$$ I saw this in a paper and have googled a lot to try make sense of the exact meaning. It seems to be non-standard notation looking at this. Seems to say that the subscript in $$z_{<i}$$ is strictly less that i. Is this the correct interpretation?
The paper reference is here.
In this paper notation $z_{<i}$ is used to denote a vector of $(z_0,z_1,\ldots z_{i-1})$. The term $p(z_i|\theta,z_{<i})$ should be understood as “the probability of state $z_i$ given parameter $\theta$ and all previous states $z_0,\ldots z_{i-1}$”