A foundational problem in semi-supervised learning is the construction of a graph underlying the data. We propose to use a method which optimally combinesa number of differently constructed graphs.

Dean P. Foster University of Pennsylvania We present a competitive analysis of some nonparametric Bayesian algorithms ina worst-case online learning setting, where no probabilistic assumptions about the generation of the data are made. We consider models which use a Gaussian process prior (over the space of all functions) andprovide bounds on the regret (under the log loss) for commonly usednon-parametric Bayesian algorithms -- including Gaussian regression and logistic regression -- which show how these algorithms can perform favorably under rather general conditions.

Learning patterns of human behavior from sensor data is extremely important for high-level activity inference. We show how to extract and label a person's activities and significant places from traces of GPS data. In contrast to existing techniques, our approach simultaneously detects and classifies the significant locations of a person and takes the high-level context into account. Our system uses relational Markov networks to represent the hierarchical activity model that encodes the complex relations among GPS readings, activities and significant places. We apply FFT-based message passing to perform efficient summation over large numbers of nodes in the networks.

This paper explores the statistical relationship between natural images and their underlying range (depth) images. We look at how this relationship changesover scale, and how this information can be used to enhance low resolution range data using a full resolution intensity image. Based on our findings, we propose an extension to an existing technique known as shape recipes [3], and the success of the two methods are compared using images and laser scans of real scenes. Our extension is shown to provide a twofold improvement over the current method. Furthermore, wedemonstrate that ideal linear shape-from-shading filters, when learned from natural scenes, may derive even more strength from shadow cues than from the traditional linear-Lambertian shading cues.

We consider the task of depth estimation from a single monocular image. Wetake a supervised learning approach to this problem, in which we begin by collecting a training set of monocular images (of unstructured outdoorenvironments which include forests, trees, buildings, etc.) and their corresponding ground-truth depthmaps. Then, we apply supervised learningto predict the depthmap as a function of the image. Depth estimation is a challenging problem, since local features alone are insufficient to estimate depth at a point, and one needs to consider the global context of the image. Our model uses a discriminatively-trained Markov Random Field (MRF) that incorporates multiscale local-and global-image features, and models both depths at individual points as well as the relation between depths at different points. We show that, even on unstructured scenes, our algorithm is frequently able to recover fairly accurate depthmaps.

We extend a previously developed Bayesian framework for perception to account for sensory adaptation. We first note that the perceptual effects ofadaptation seems inconsistent with an adjustment of the internally represented prior distribution. Instead, we postulate that adaptation increases the signal-to-noise ratio of the measurements by adapting the operational range of the measurement stage to the input range. We show that this changes the likelihood function in such a way that the Bayesian estimator model can account for reported perceptual behavior. In particular, wecompare the model's predictions to human motion discrimination data and demonstrate that the model accounts for the commonly observed perceptual adaptation effects of repulsion and enhanced discriminability.

In this paper we propose a new basis selection criterion for building sparse GP regression models that provides promising gains in accuracy as well as efficiency over previous methods. Our algorithm is much faster than that of Smola and Bartlett, while, in generalization it greatly outperforms theinformation gain approach proposed by Seeger et al, especially on the quality of predictive distributions.

The instantaneous input frequency can affect the response amplitude and phase delay.

This paper presents representation and logic for labeling contrast edges and ridges in visual scenes in terms of both surface occlusion (border ownership) and thinline objects. In natural scenes, thinline objects include sticksand wires, while in human graphical communication thinlines include connectors, dividers, and other abstract devices. Our analysis is directed at both natural and graphical domains. The basic problem is to formulate the logic of the interactions among local image events, specifically contrast edges, ridges, junctions, and alignment relations, such as to encode the natural constraints among these events in visual scenes. In a sparse heterogeneous Markov Random Field framework, we define a set of interpretation nodes and energy/potential functions among them. The minimum energy configuration found by Loopy Belief Propagation isshown to correspond to preferred human interpretation across a wide range of prototypical examples including important illusory contour figuressuch as the Kanizsa Triangle, as well as more difficult examples. Inpractical terms, the approach delivers correct interpretations of inherently ambiguous hand-drawn box-and-connector diagrams at low computational cost.

This paper presents a diffusion based probabilistic interpretation of spectral clustering and dimensionality reduction algorithms that use the eigenvectors of the normalized graph Laplacian. Given the pairwise adjacency matrixof all points, we define a diffusion distance between any two data points and show that the low dimensional representation of the data by the first few eigenvectors of the corresponding Markov matrix is optimal undera certain mean squared error criterion.