Clustering and prediction of sets of curves is an important problem in many areas of science and engineering. It is often the case that curves tend to be misaligned from each other in a continuous manner, either in space (across the measurements) or in time. We develop a probabilistic framework that allows for joint clustering and continuous alignment of sets of curves in curve space (as opposed to a fixed-dimensional featurevector space).The proposed methodology integrates new probabilistic alignment models with model-based curve clustering algorithms. The probabilistic approach allows for the derivation of consistent EM learning algorithmsfor the joint clustering-alignment problem. Experimental results are shown for alignment of human growth data, and joint clustering andalignment of gene expression time-course data.

We propose an alternative approach in which multiplicative pixel interactions are described by a series of Wiener functionals.

We describe a framework for learning an object classifier from a single example. This goal is achieved by emphasizing the relevant dimensions for classification using available examples of related classes. Learning to accurately classify objects from a single training example is often unfeasible dueto overfitting effects. However, if the instance representation provides that the distance between each two instances of the same class is smaller than the distance between any two instances from different classes,then a nearest neighbor classifier could achieve perfect performance with a single training example. We therefore suggest a two stage strategy.

Device mismatch in VLSI degrades the accuracy of analog arithmetic circuits and lowers the learning performance of large-scale neural networks implementedin this technology. We show compact, low-power on-chip calibration techniques that compensate for device mismatch. Our techniques enable large-scale analog VLSI neural networks with learning performanceon the order of 10 bits. We demonstrate our techniques on a 64-synapse linear perceptron learning with the Least-Mean-Squares (LMS) algorithm, and fabricated in a 0.35µm CMOS process.

We present an algorithm to overcome the local maxima problem in estimating theparameters of mixture models. It combines existing approaches fromboth EM and a robust fitting algorithm, RANSAC, to give a data-driven stochastic learning scheme. Minimal subsets of data points, sufficient to constrain the parameters of the model, are drawn from proposal densitiesto discover new regions of high likelihood. The proposal densities are learnt using EM and bias the sampling toward promising solutions. The algorithm is computationally efficient, as well as effective at escaping from local maxima. We compare it with alternative methods, including EM and RANSAC, on both challenging synthetic data and the computer vision problem of alpha-matting.

We address the problem of identifying specific instances of a class (cars) from a set of images all belonging to that class. Although we cannot build a model for any particular instance (as we may be provided with only one "training" example of it), we can use information extracted from observing othermembers of the class. We pose this task as a learning problem, in which the learner is given image pairs, labeled as matching or not, and must discover which image features are most consistent for matching instances anddiscriminative for mismatches. We explore a patch based representation, where we model the distributions of similarity measurements definedon the patches. Finally, we describe an algorithm that selects the most salient patches based on a mutual information criterion. This algorithm performs identification well for our challenging dataset of car images, after matching only a few, well chosen patches.

We introduce a new algorithm based on linear programming that approximates the differential value function of an average-cost Markov decision process via a linear combination of pre-selected basis functions. The algorithm carries out a form of cost shaping and minimizes a version of Bellman error. We establish an error bound that scales gracefully with the number of states without imposing the (strong) Lyapunov condition required by its counterpart in[6]. We propose a path-following method that automates selection of important algorithm parameters which represent counterparts tothe "state-relevance weights" studied in [6].

We describe a method that can make a scanned, handwritten mediaeval latin manuscript accessible to full text search. A generalized HMM is fitted, using transcribed latin to obtain a transition model and one example eachof 22 letters to obtain an emission model. We show results for unigram, bigram and trigram models.

It has been suggested that the primary goal of the sensory system is to represent input in such a way as to reduce the high degree of redundancy. Givena noisy neural representation, however, solely reducing redundancy is not desirable, since redundancy is the only clue to reduce the effects of noise. Here we propose a model that best balances redundancy reductionand redundant representation. Like previous models, our model accounts for the localized and oriented structure of simple cells, but it also predicts a different organization for the population. With noisy, limited-capacity units, the optimal representation becomes an overcomplete, multi-scalerepresentation, which, compared to previous models, is in closer agreement with physiological data. These results offer a new perspective on the expansion of the number of neurons from retina to V1 and provide a theoretical model of incorporating useful redundancy into efficient neural representations.

X-ray crystallography is currently the most common way protein structures are elucidated. One of the most time-consuming steps in the crystallographic process is interpretation of the electron density map, a task that involves finding patterns in a three-dimensional picture of a protein. This paper describes DEFT (DEFormable Template), an algorithm using pictorial structures to build a flexible protein model from the protein's amino-acid sequence. Matching this pictorial structure into the density map is a way of automating density-map interpretation. Also described are several extensions to the pictorial structure matching algorithm necessary for this automated interpretation. DEFT is tested on a set of density maps ranging from 2 to 4Å resolution, producing rootmean-squared errorsranging from 1.38 to 1.84Å.