Extracting the interaction rules of biological agents from movement sequences pose challenges in various domains.

For the convenience of the reader, we summarize a list of notations blow. 1. null G In Appendix B.1, we present a general statement of Theorem 3.1 (a) along with its proof. Theorem 3.1 (a) states the order recovery guarantee for a specified parameter We summarize the bounds for (I) and (II) in Lemma B.1 and Lemma B.2, which can be found in Collecting the results in Lemma B.1 and Lemma B.2 and reorganizing the terms in the inequalities, we have the following conclusion. We now state the proof of this Lemma. Then we bound the first term using the concentration bound on Chi-squared random variables. For the non-identifiable models, we can use Lemma H.1 in a similar way to obtain that with probability We now state the proof of this Lemma.

Lastly, our analysis also shows the consistency of union support recovery of the structures.

Distributed learning has attracted significant attention recently with the increasing popularity of distributed systems and distributed data.

In contrast to MCMC approaches like Hamiltonian Monte Carlo, no stochastic step is required. Instead, the proposed deterministic dynamics in an extended state space exactly sample the target distribution, specified by an energy function, under an assumption of ergodicity. Alternatively, the dynamics can be interpreted as a normalizing flow that samples a specified energy model without training.

X, Y are compact sets. Assumption 1.1, C is a contraction mapping w.r .t. to the sup norm k . By combining Theorem 2.3 and the Banach fixed point theorem [57], we First note that by Assumption 1.1, we have that Suppose that Assumption 1.1 holds, and that 1. for all Suppose that Assumption 1.1 holds, and that 1. for all By Theorem 2.1 and Theorem 2.3 we know that The proof follows exactly the same, albeit the optimality conditions on the inner player's policy By Theorem 3.1, the necessary optimality conditions for the stochastic Stackelberg game are that for all states This reduced the market to a deterministic repeated market setting in which the amount of budget saved by the buyers differentiates different states of the market. As a result, we had to use fitted variant of value iteration. This time, we implemented a stochastic transitions.

We take advantage of NF preconditioning and NF based Metropolis-Hastings updates for a faster convergence.