http://hdl.handle.net/1721.1/29807 http://hdl.handle.net/1721.1/41940 A Note on Perturbation Results for Learning Empirical Operators Rosasco, Lorenzo Belkin, Mikhail De Vito, Ernesto A large number of learning algorithms, for example, spectralclustering, kernel Principal Components Analysis and many manifoldmethods are based on estimating eigenvalues and eigenfunctions ofoperators defined by a similarity function or a kernel, given empiricaldata. Thus for the analysis of algorithms, it is an important problem tobe able to assess the quality of such approximations. The contributionof our paper is two-fold:1. We use a technique based on a concentration inequality for Hilbertspaces to provide new much simplified proofs for a number of results inspectral approximation.2. Using these methods we provide several new results for estimatingspectral properties of the graph Laplacian operator extending andstrengthening results from [26]. Mon, 18 Aug 2008 22:58:59 GMT http://hdl.handle.net/1721.1/41938 Transductive Ranking on Graphs Agarwal, Shivani In ranking, one is given examples of order relationships amongobjects, and the goal is to learn from these examples a real-valuedranking function that induces a ranking or ordering over the objectspace. We consider the problem of learning such a ranking function ina transductive, graph-based setting, where the object space is finiteand is represented as a graph in which vertices correspond to objectsand edges encode similarities between objects. Building on recentdevelopments in regularization theory for graphs and correspondingLaplacian-based learning methods, we develop an algorithmic frameworkfor learning ranking functions on graphs. We derive generalizationbounds for our algorithms in transductive models similar to those usedto study other transductive learning problems, and give experimentalevidence of the potential benefits of our framework. Wed, 06 Aug 2008 22:58:59 GMT http://hdl.handle.net/1721.1/41920 Adaptive Envelope MDPs for Relational Equivalence-based Planning Gardiol, Natalia H. Kaelbling, Leslie Pack We describe a method to use structured representations of the environment’s dynamics to constrain and speed up the planning process. Given a problem domain described in a probabilistic logical description language, we develop an anytime technique that incrementally improves on an initial, partial policy. This partial solution is found by first reducing the number of predicates needed to represent a relaxed version of the problem to a minimum, and then dynamically partitioning the action space into a set of equivalence classes with respect to this minimal representation. Our approach uses the envelope MDP framework, which creates a Markov decision process out of a subset of the full state space as de- termined by the initial partial solution. This strategy permits an agent to begin acting within a restricted part of the full state space and to expand its envelope judiciously as resources permit. Mon, 28 Jul 2008 22:58:59 GMT http://hdl.handle.net/1721.1/41892 Understanding camera trade-offs through a Bayesian analysis of light field projections - A revision Levin, Anat Freeman, William Durand, Fredo Computer vision has traditionally focused on extracting structure,such as depth, from images acquired using thin-lens or pinholeoptics. The development of computational imaging is broadening thisscope; a variety of unconventional cameras do not directly capture atraditional image anymore, but instead require the jointreconstruction of structure and image information. For example, recentcoded aperture designs have been optimized to facilitate the jointreconstruction of depth and intensity. The breadth of imaging designs requires new tools to understand the tradeoffs implied bydifferent strategies. This paper introduces a unified framework for analyzing computational imaging approaches.Each sensor element is modeled as an inner product over the 4D light field.The imaging task is then posed as Bayesian inference: giventhe observed noisy light field projections and a new prior on light field signals, estimate the original light field. Under common imaging conditions, we compare theperformance of various camera designs using 2D light field simulations. Thisframework allows us to better understand the tradeoffs of each camera type and analyze their limitations. Sun, 27 Jul 2008 22:58:59 GMT