We describe a novel noisy-logical distribution for representing the distribution of a binary output variable conditioned on multiple binary input variables. The distribution is represented in terms of noisy-or's and noisy-and-not's of causal features which are conjunctions of the binary inputs. The standard noisy-or and noisy-and-not models, used in causal reasoning and artificial intelligence, are special cases of the noisy-logical distribution. We prove that the noisy-logical distribution is complete in the sense that it can represent all conditional distributions provided a sufficient number of causal factors are used. We illustrate the noisy-logical distribution by showing that it can account for new experimental findings on how humans perform causal reasoning in more complex contexts. Finally, we speculate on the use of the noisy-logical distribution for causal reasoning and artificial intelligence.

Reward-modulated spike-timing-dependent plasticity (STDP) has recently emerged as a candidate for a learning rule that could explain how local learning rules at single synapses support behaviorally relevant adaptive changes in complex networksof spiking neurons. However the potential and limitations of this learning rule could so far only be tested through computer simulations. This article providestools for an analytic treatment of reward-modulated STDP, which allow us to predict under which conditions reward-modulated STDP will be able to achieve a desired learning effect. In particular, we can produce in this way a theoretical explanation and a computer model for a fundamental experimental finding on biofeedback in monkeys (reported in [1]).

We propose a Gaussian process (GP) framework for robust inference in which a GP prior on the mixing weights of a two-component noise model augments the standard process over latent function values. This approach is a generalization of the mixture likelihood used in traditional robust GP regression, and a specialization of the GP mixture models suggested by Tresp (2000) and Rasmussen and Ghahramani (2002). The value of this restriction is in its tractable expectation propagation updates, which allow for faster inference and model selection, and better convergence than the standard mixture. An additional benefit over the latter method lies in our ability to incorporate knowledge of the noise domain to influence predictions, and to recover with the predictive distribution information about the outlier distribution via the gating process. The model has asymptotic complexity equal to that of conventional robust methods, but yields more confident predictions on benchmark problems than classical heavy-tailed models and exhibits improved stability for data with clustered corruptions, for which they fail altogether. We show further how our approach can be used without adjustment for more smoothly heteroscedastic data, and suggest how it could be extended to more general noise models. We also address similarities with the work of Goldberg et al. (1998), and the more recent contributions of Tresp, and Rasmussen and Ghahramani.

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.

Sound localization by barn owls is commonly modeled as a matching procedure where localization cues derived from auditory inputs are compared to stored templates. While the matching models can explain properties of neural responses, no model explains how the owl resolves spatial ambiguity in the localization cues to produce accurate localization near the center of gaze. Here, we examine two models for the barn owl's sound localization behavior. First, we consider a maximum likelihood estimator in order to further evaluate the cue matching model. Second, we consider a maximum a posteriori estimator to test if a Bayesian model with a prior that emphasizes directions near the center of gaze can reproduce the owl's localization behavior. We show that the maximum likelihood estimator can not reproduce the owl's behavior, while the maximum a posteriori estimator is able to match the behavior. This result suggests that the standard cue matching model will not be sufficient to explain sound localization behavior in the barn owl. The Bayesian model provides a new framework for analyzing sound localization in the barn owl and leads to predictions about the owl's localization behavior.

We describe an analog-VLSI neural network for face recognition based on subspace methods. The system uses a dimensionality-reduction network whose coefficients can be either programmed or learned on-chip to perform PCA, or programmed to perform LDA. A second network with user-programmed coefficients performs classification with Manhattan distances. The system uses on-chip compensation techniques to reduce the effects of device mismatch. Using the ORL database with 12x12-pixel images, our circuit achieves up to 85% classification performance (98% of an equivalent software implementation).

This paper considers kernels invariant to translation, rotation and dilation. We show that no nontrivial positive definite (p.d.) kernels exist which are radial and dilation invariant, only conditionally positive definite (c.p.d.) ones. Accordingly, we discuss the c.p.d.

We describe a neurobiologically plausible model to implement dynamic routing using the concept of neuronal communication through neuronal coherence. The model has a three-tier architecture: a raw input tier, a routing control tier, and an invariant output tier. The correct mapping between input and output tiers is realized byan appropriate alignment of the phases of their respective background oscillations by the routing control units. We present an example architecture, implemented ona neuromorphic chip, that is able to achieve circular-shift invariance.

Maximum variance unfolding (MVU) is an effective heuristic for dimensionality reduction. It produces a low-dimensional representation of the data by maximizing thevariance of their embeddings while preserving the local distances of the original data. We show that MVU also optimizes a statistical dependence measure which aims to retain the identity of individual observations under the distancepreserving constraints.This general view allows us to design "colored" variants of MVU, which produce low-dimensional representations for a given task, e.g.

Many formal models of cognition implicitly use subjective probability distributions to capture the assumptions of human learners.