  We study grammar induction with mildly context-sensitive grammars for
unsupervised discontinuous parsing. Using the probabilistic linear context-free
rewriting system (LCFRS) formalism, our approach fixes the rule structure in
advance and focuses on parameter learning with maximum likelihood. To reduce
the computational complexity of both parsing and parameter estimation, we
restrict the grammar formalism to LCFRS-2 (i.e., binary LCFRS with fan-out two)
and further discard rules that require O(n^6) time to parse, reducing inference
to O(n^5). We find that using a large number of nonterminals is beneficial and
thus make use of tensor decomposition-based rank-space dynamic programming with
an embedding-based parameterization of rule probabilities to scale up the
number of nonterminals. Experiments on German and Dutch show that our approach
is able to induce linguistically meaningful trees with continuous and
discontinuous structures
