Geometrically based methods for various tasks of machine learning have attracted considerable attention over the last few years. In this paper we show convergence of eigenvectors of the point cloud Laplacian to the eigenfunctions of the Laplace-Beltrami operator on the underlying manifold, thus establishing the first convergence results for a spectral dimensionality reduction algorithm in the manifold setting.

Selective attention is the strategy used by biological sensory systems to solve the problem of limited parallel processing capacity: salient subregions of the input stimuli are serially processed, while non-salient regions are suppressed. We present an mixed mode analog/digital Very Large Scale Integration implementation of a building block for a multi-chip neuromorphic hardware model of selective attention. We describe the chip's architecture and its behavior, when its is part of a multi-chip system with a spiking retina as input, and show how it can be used to implement in real-time flexible models of bottom-up attention.

The risk, or probability of error, of the classifier produced by the AdaBoost algorithm is investigated. In particular, we consider the stopping strategy to be used in AdaBoost to achieve universal consistency.

We consider methods that try to find a good policy for a Markov decision process by choosing one from a given class. The policy is chosen based on its empirical performance in simulations. We are interested in conditions on the complexity of the policy class that ensure the success of such simulation based policy search methods. We show that under bounds on the amount of computation involved in computing policies, transition dynamics and rewards, uniform convergence of empirical estimates to true value functions occurs. Previously, such results were derived by assuming boundedness of pseudodimension and Lipschitz continuity. These assumptions and ours are both stronger than the usual combinatorial complexity measures. We show, via minimax inequalities, that this is essential: boundedness of pseudodimension or fat-shattering dimension alone is not sufficient.

We introduce a method for approximate smoothed inference in a class of switching linear dynamical systems, based on a novel form of Gaussian Sum smoother. This class includes the switching Kalman Filter and the more general case of switch transitions dependent on the continuous latent state. The method improves on the standard Kim smoothing approach by dispensing with one of the key approximations, thus making fuller use of the available future information. Whilst the only central assumption required is projection to a mixture of Gaussians, we show that an additional conditional independence assumption results in a simpler but stable and accurate alternative. Unlike the alternative unstable Expectation Propagation procedure, our method consists only of a single forward and backward pass and is reminiscent of the standard smoothing'correction' recursions in the simpler linear dynamical system. The algorithm performs well on both toy experiments and in a large scale application to noise robust speech recognition.

Linear Gaussian State-Space Models are widely used and a Bayesian treatment of parameters is therefore of considerable interest. The approximate Variational Bayesian method applied to these models is an attractive approach, used successfully in applications ranging from acoustics to bioinformatics. The most challenging aspect of implementing the method is in performing inference on the hidden state sequence of the model. We show how to convert the inference problem so that standard Kalman Filtering/Smoothing recursions from the literature may be applied. This is in contrast to previously published approaches based on Belief Propagation. Our framework both simplifies and unifies the inference problem, so that future applications may be more easily developed. We demonstrate the elegance of the approach on Bayesian temporal ICA, with an application to finding independent dynamical processes underlying noisy EEG signals.

We address the problem of subordinate class recognition, like the distinction between different types of motorcycles. Our approach is motivated by observations from cognitive psychology, which identify parts as the defining component of basic level categories (like motorcycles), while subordinate categories are more often defined by part properties (like'jagged wheels'). Accordingly, we suggest a two-stage algorithm: First, a relational part based object model is learnt using unsegmented object images from the inclusive class (e.g., motorcycles in general). The model is then used to build a class-specific vector representation for images, where each entry corresponds to a model's part. In the second stage we train a standard discriminative classifier to classify subclass instances (e.g., cross motorcycles) based on the class-specific vector representation. We describe extensive experimental results with several subclasses. The proposed algorithm typically gives better results than a competing one-step algorithm, or a two stage algorithm where classification is based on a model of the subordinate class.

Bob offers a face-detection web service where clients can submit their images for analysis. Alice would very much like to use the service, but is reluctant to reveal the content of her images to Bob. Bob, for his part, is reluctant to release his face detector, as he spent a lot of time, energy and money constructing it. Secure Multi-Party computations use cryptographic tools to solve this problem without leaking any information. Unfortunately, these methods are slow to compute and we introduce a couple of machine learning techniques that allow the parties to solve the problem while leaking a controlled amount of information. The first method is an information-bottleneck variant of AdaBoost that lets Bob find a subset of features that are enough for classifying an image patch, but not enough to actually reconstruct it. The second machine learning technique is active learning that allows Alice to construct an online classifier, based on a small number of calls to Bob's face detector. She can then use her online classifier as a fast rejector before using a cryptographically secure classifier on the remaining image patches.

We present a learning algorithm for undiscounted reinforcement learning. Our interest lies in bounds for the algorithm's online performance after some finite number of steps. In the spirit of similar methods already successfully applied for the exploration-exploitation tradeoff in multi-armed bandit problems, we use upper confidence bounds to show that our UCRL algorithm achieves logarithmic online regret in the number of steps taken with respect to an optimal policy.

We present a method for learning a low-dimensional representation which is shared across a set of multiple related tasks. The method builds upon the wellknown 1-norm regularization problem using a new regularizer which controls the number of learned features common for all the tasks. We show that this problem is equivalent to a convex optimization problem and develop an iterative algorithm for solving it. The algorithm has a simple interpretation: it alternately performs a supervised and an unsupervised step, where in the latter step we learn commonacross-tasks representations and in the former step we learn task-specific functions using these representations. We report experiments on a simulated and a real data set which demonstrate that the proposed method dramatically improves the performance relative to learning each task independently. Our algorithm can also be used, as a special case, to simply select - not learn - a few common features across the tasks.