The category of visual stimuli has been reliably decoded from patterns of neural activity in extrastriate visual cortex [1]. It has yet to be seen whether object identity can be inferred from this activity. We present fMRI data measuring responses in human extrastriate cortex to a set of 12 distinct object images. We use a simple winner-take-all classifier, using half the data from each recording session as a training set, to evaluate encoding of object identity across fMRI voxels. Since this approach is sensitive to the inclusion of noisy voxels, we describe two methods for identifying subsets of voxels in the data which optimally distinguish object identity. One method characterizes the reliability of each voxel within subsets of the data, while another estimates the mutual information of each voxel with the stimulus set. We find that both metrics can identify subsets of the data which reliably encode object identity, even when noisy measurements are artificially added to the data. The mutual information metric is less efficient at this task, likely due to constraints in fMRI data.

We present a novel approach to the characterization of complex sensory neurons. One of the main goals of characterizing sensory neurons is to characterize dimensions in stimulus space to which the neurons are highly sensitive (causing large gradients in the neural responses) or alternatively dimensions in stimulus space to which the neuronal response are invariant (defining iso-response manifolds). We formulate this problem as that of learning a geometry on stimulus space that is compatible with the neural responses: the distance between stimuli should be large when the responses they evoke are very different, and small when the responses they evoke are similar. Here we show how to successfully train such distance functions using rather limited amount of information. The data consisted of the responses of neurons in primary auditory cortex (A1) of anesthetized cats to 32 stimuli derived from natural sounds. For each neuron, a subset of all pairs of stimuli was selected such that the responses of the two stimuli in a pair were either very similar or very dissimilar. The distance function was trained to fit these constraints. The resulting distance functions generalized to predict the distances between the responses of a test stimulus and the trained stimuli.

We present a new connectionist model for constructive, intuitionistic modal reasoning. We use ensembles of neural networks to represent intuitionistic modal theories, and show that for each intuitionistic modal program there exists a corresponding neural network ensemble that computes the program. This provides a massively parallel model for intuitionistic modal reasoning, and sets the scene for integrated reasoning, knowledge representation, and learning of intuitionistic theories in neural networks, since the networks in the ensemble can be trained by examples using standard neural learning algorithms.

Given a probability measure P and a reference measure µ, one is often interested in the minimum µ-measure set with P-measure at least α. Minimum volume sets of this type summarize the regions of greatest probability mass of P, and are useful for detecting anomalies and constructing confidence regions. This paper addresses the problem of estimating minimum volume sets based on independent samples distributed according to P. Other than these samples, no other information is available regarding P, but the reference measure µ is assumed to be known. We introduce rules for estimating minimum volume sets that parallel the empirical risk minimization and structural risk minimization principles in classification. As in classification, we show that the performances of our estimators are controlled by the rate of uniform convergence of empirical to true probabilities over the class from which the estimator is drawn. Thus we obtain finite sample size performance bounds in terms of VC dimension and related quantities. We also demonstrate strong universal consistency and an oracle inequality. Estimators based on histograms and dyadic partitions illustrate the proposed rules.

This paper presents a non-asymptotic statistical analysis of Kernel-PCA with a focus different from the one proposed in previous work on this topic. Here instead of considering the reconstruction error of KPCA we are interested in approximation error bounds for the eigenspaces themselves. We prove an upper bound depending on the spacing between eigenvalues but not on the dimensionality of the eigenspace. As a consequence this allows to infer stability results for these estimated spaces.

This paper explores the statistical relationship between natural images and their underlying range (depth) images. We look at how this relationship changes over 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, we demonstrate 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 propose a fast manifold learning algorithm based on the methodology of domain decomposition. Starting with the set of sample points partitioned into two subdomains, we develop the solution of the interface problem that can glue the embeddings on the two subdomains into an embedding on the whole domain. We provide a detailed analysis to assess the errors produced by the gluing process using matrix perturbation theory. Numerical examples are given to illustrate the efficiency and effectiveness of the proposed methods.

When trying to understand the brain, it is of fundamental importance to analyse (e.g. from EEG/MEG measurements) what parts of the cortex interact with each other in order to infer more accurate models of brain activity. Common techniques like Blind Source Separation (BSS) can estimate brain sources and single out artifacts by using the underlying assumption of source signal independence. However, physiologically interesting brain sources typically interact, so BSS will--by construction-- fail to characterize them properly. Noting that there are truly interacting sources and signals that only seemingly interact due to effects of volume conduction, this work aims to contribute by distinguishing these effects. For this a new BSS technique is proposed that uses anti-symmetrized cross-correlation matrices and subsequent diagonalization. The resulting decomposition consists of the truly interacting brain sources and suppresses any spurious interaction stemming from volume conduction. Our new concept of interacting source analysis (ISA) is successfully demonstrated on MEG data.

We present a generalization of temporal-difference networks to include temporally abstract options on the links of the question network. Temporal-difference (TD) networks have been proposed as a way of representing and learning a wide variety of predictions about the interaction between an agent and its environment. These predictions are compositional in that their targets are defined in terms of other predictions, and subjunctive in that that they are about what would happen if an action or sequence of actions were taken. In conventional TD networks, the interrelated predictions are at successive time steps and contingent on a single action; here we generalize them to accommodate extended time intervals and contingency on whole ways of behaving. Our generalization is based on the options framework for temporal abstraction. The primary contribution of this paper is to introduce a new algorithm for intra-option learning in TD networks with function approximation and eligibility traces.

We consider the task of depth estimation from a single monocular image. We take a supervised learning approach to this problem, in which we begin by collecting a training set of monocular images (of unstructured outdoor environments which include forests, trees, buildings, etc.) and their corresponding ground-truth depthmaps. Then, we apply supervised learning to 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.