In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Example Input: We present a method for solving implicit (factored) Markov decision processes (MDPs) with very large state spaces. We intro­ duce a property of state space partitions which we call f-homogeneity. Intuitively, an f-homogeneous partition groups together states that behave approximately the same under all or some subset of policies. Borrow­ ing from recent work on model minimization in computer-aided software verification, we present an algorithm that takes a factored representation of an MDP and an 0 � f � I and computes a factored f-homogeneous par­ tition of the state space. This partition defines a family of related MOPs-those MOP's with state space equal to the blocks of the partition, and transition probabilities "appro:X:imately" like those of any (original MDP) state in the source block. To formally study such families of MDPs, we introduce the new notion of a "bounded parameter MDP" (BMDP), which is a fam­ ily of (traditional) MOPs defined by speci­ fying upper and lower bounds on the transi­ tion probabilities and rewards. We describe algorithms that operate on BMDPs to find policies that are approximately optimal with respect to the original MDP. In combination, our method for reducing a large implicit MDP to a possibly much smaller BMDP using an f-homogeneous par­ tition, and our methods for selecting actions in BMDP's constitute a new approach for an­ alyzing large implicit MOP's. Among its ad­ vantages, this new approach provides insight into existing algorithms to solving implicit MDPs, provides useful connections to work in automata theory and model minimization, and suggests methods, which involve vary­ ing f, to trade time and space (specifically in terms of the size of the corresponding state space) for solution quality.
Example Output: Model Reduction Techniques for Computing Approximately Optimal Solutions for Markov Decision Processes

Example Input: We introduce the nonparametric metadata dependent relational (NMDR) model, a Bayesian nonparametric stochastic block model for network data. The NMDR allows the entities associated with each node to have mixed membership in an unbounded collection of latent communities. Learned regression models allow these memberships to depend on, and be predicted from, arbitrary node metadata. We develop efficient MCMC algorithms for learning NMDR models from partially observed node relationships. Retrospective MCMC methods allow our sampler to work directly with the infinite stickbreaking representation of the NMDR, avoiding the need for finite truncations. Our results demonstrate recovery of useful latent communities from real-world social and ecological networks, and the usefulness of metadata in link prediction tasks.
Example Output: The Nonparametric Metadata Dependent Relational Model

Example Input: This paper presents complexity analysis and variational methods for inference in probabilistic description logics featuring Boolean operators, quantification, qualified number restrictions, nominals, inverse roles and role hierarchies. Inference is shown to be PEXP-complete, and variational methods are designed so as to exploit logical inference whenever possible.
Example Output:
Complexity Analysis and Variational Inference for Interpretation-based Probabilistic Description Logics