 
Summary: Supplementary Material for "Learning the Structure of Deep Sparse
Graphical Models"
Ryan Prescott Adams Hanna M. Wallach Zoubin Ghahramani
1 Proof of General CIBP Termination
In the main paper, we discussed that the cascading Indian buffet process (CIBP) for fixed and finite and
eventually reaches a restaurant in which the customers choose no dishes. Every deeper restaurant also has
no dishes. Here, we show a more general result, for IBP parameters that vary with depth: (m)
and (m)
.
Let there be an inhomogeneous Markov chain M with state space N. Let m index time and let the state
at time m be denoted K(m)
. The initial state K(0)
is finite. The probability mass function describing the
transition distribution for M at time m is given by the following equation:
p(K(m+1)
= k  K(m)
, (m)
, (m)
) =
1
