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.

Ex 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.

Ex Output:
Model Reduction Techniques for Computing Approximately Optimal Solutions for Markov Decision Processes

Ex Input:
Recommender systems play an increasingly important role in online applications to help users find what they need or prefer. Collaborative filtering algorithms that generate predictions by analyzing the user-item rating matrix perform poorly when the matrix is sparse. To alleviate this problem, this paper proposes a simple recommendation algorithm that fully exploits the similarity information among users and items and intrinsic structural information of the user-item matrix. The proposed method constructs a new representation which preserves affinity and structure information in the user-item rating matrix and then performs recommendation task. To capture proximity information about users and items, two graphs are constructed. Manifold learning idea is used to constrain the new representation to be smooth on these graphs, so as to enforce users and item proximities. Our model is formulated as a convex optimization problem, for which we need to solve the well known Sylvester equation only. We carry out extensive empirical evaluations on six benchmark datasets to show the effectiveness of this approach.

Ex Output:
Top-N Recommendation on Graphs

Ex Input:
This paper summarizes the recent progress we have made for the computer vision technologies in physical therapy with the accessible and affordable devices. We first introduce the remote health coaching system we build with Microsoft Kinect. Since the motion data captured by Kinect is noisy, we investigate the data accuracy of Kinect with respect to the high accuracy motion capture system. We also propose an outlier data removal algorithm based on the data distribution. In order to generate the kinematic parameter from the noisy data captured by Kinect, we propose a kinematic filtering algorithm based on Unscented Kalman Filter and the kinematic model of human skeleton. The proposed algorithm can obtain smooth kinematic parameter with reduced noise compared to the kinematic parameter generated from the raw motion data from Kinect.

Ex Output:
Remote Health Coaching System and Human Motion Data Analysis for Physical Therapy with Microsoft Kinect