Binocular fusion takes place over a limited region smaller than one degree of visual angle (Panum's fusional area), which is on the order of the range of preferred disparities measured in populations of disparity-tuned neurons in the visual cortex. However, the actual range of binocular disparities encountered in natural scenes ranges over tens of degrees. This discrepancy suggests that there must be a mechanism for detecting whether the stimulus disparity is either inside or outside of the range of the preferred disparities in the population. Here, we present a statistical framework to derive feature in a population of V1 disparity neuron to determine the stimulus disparity within the preferred disparity range of the neural population. When optimized for natural images, it yields a feature that can be explained by the normalization which is a common model in V1 neurons. We further makes use of the feature to estimate the disparity in natural images. Our proposed model generates more correct estimates than coarse-to-fine multiple scales approaches and it can also identify regions with occlusion. The approach suggests another critical role for normalization in robust disparity estimation.

In this paper we formulate a novel AND/OR graph representation capable of describing thedifferent configurations of deformable articulated objects such as horses. The representation makes use of the summarization principle so that lower level nodes in the graph only pass on summary statistics to the higher level nodes. The probability distributions are invariant to position, orientation, and scale. We develop a novel inference algorithm that combined a bottom-up process for proposing configurations for horses together with a top-down process for refining and validating these proposals. The strategy of surround suppression isapplied to ensure that the inference time is polynomial in the size of input data. The algorithm was applied to the tasks of detecting, segmenting and parsing horses. We demonstrate that the algorithm is fast and comparable with the state of the art approaches.

In bioinformatics it is often desirable to combine data from various measurement sources and thus structured feature vectors are to be analyzed that possess different intrinsic blocking characteristics (e.g., different patterns of missing values, observation noiselevels, effective intrinsic dimensionalities). We propose a new machine learning tool, heterogeneous component analysis (HCA), for feature extraction in order to better understand the factors that underlie such complex structured heterogeneous data. HCA is a linear block-wise sparse Bayesian PCA based not only on a probabilistic model with block-wise residual variance terms but also on a Bayesian treatment of a block-wise sparse factor-loading matrix. We study various algorithmsthat implement our HCA concept extracting sparse heterogeneous structure by obtaining common components for the blocks and specific components withineach block. Simulations on toy and bioinformatics data underline the usefulness of the proposed structured matrix factorization concept.

Abstract Missing

Statistical models on full and partial rankings of n items are often of limited practical usefor large n due to computational consideration. We explore the use of nonparametric models for partially ranked data and derive efficient procedures for their use for large n. The derivations are largely possible through combinatorial and algebraic manipulations based on the lattice of partial rankings. In particular, we demonstrate for the first time a nonparametric coherent and consistent model capable of efficiently aggregating partially ranked data of different types.

When we have several related tasks, solving them simultaneously is shown to be more effective than solving them individually. This approach is called multi-task learning (MTL) and has been studied extensively. Existing approaches to MTL often treat all the tasks as \emph{uniformly related to each other and the relatedness of the tasks is controlled globally. For this reason, the existing methods can lead to undesired solutions when some tasks are not highly related to each other, and some pairs of related tasks can have significantly different solutions. In this paper, we propose a novel MTL algorithm that can overcome these problems. Our method makes use of a task network, which describes the relation structure among tasks. This allows us to deal with intricate relation structures in a systematic way. Furthermore, we control the relatedness of the tasks locally, so all pairs of related tasks are guaranteed to have similar solutions. We apply the above idea to support vector machines (SVMs) and show that the optimization problem can be cast as a second order cone program, which is convex and can be solved efficiently. The usefulness of our approach is demonstrated through simulations with protein super-family classification and ordinal regression problems.

It appears that biological systems use a combination of these two mechanisms.

We propose a new measure of conditional dependence of random variables, based on normalized cross-covariance operators on reproducing kernel Hilbert spaces. Unlike previous kernel dependence measures, the proposed criterion does not depend onthe choice of kernel in the limit of infinite data, for a wide class of kernels. Atthe same time, it has a straightforward empirical estimate with good convergence behaviour. We discuss the theoretical properties of the measure, and demonstrate its application in experiments.

Support Vector Machines (SVMs) suffer from a widely recognized scalability problem in both memory use and computational time. To improve scalability, we have developed a parallel SVM algorithm (PSVM), which reduces memory use through performing a row-based, approximate matrix factorization, and which loads only essential data to each machine to perform parallel computation. Let $n$ denote the number of training instances, $p$ the reduced matrix dimension after factorization ($p$ is significantly smaller than $n$), and $m$ the number of machines. PSVM reduces the memory requirement from $\MO$($n^2$) to $\MO$($np/m$), and improves computation time to $\MO$($np^2/m$). Empirical studies on up to $500$ computers shows PSVM to be effective.

The problem of obtaining the maximum a posteriori estimate of a general discrete randomfield (i.e. a random field defined using a finite and discrete set of labels) is known to be