We present an algorithm based on convex optimization for constructing kernels for semi-supervised learning. The kernel matrices are derived from the spectral decomposition of graph Laplacians, and combine labeled and unlabeled data in a systematic fashion. Unlike previous work using diffusion kernels and Gaussian random field kernels, a nonparametric kernel approach is presented that incorporates order constraints during optimization. This results in flexible kernels and avoids the need to choose among different parametric forms. Our approach relies on a quadratically constrained quadratic program (QCQP), and is computationally feasible for large datasets. We evaluate the kernels on real datasets using support vector machines, with encouraging results.

This paper investigates the effect of Kernel Principal Component Analysis (KPCA)within the classification framework, essentially the regularization propertiesof this dimensionality reduction method. KPCA has been previously used as a pre-processing step before applying an SVM but we point out that this method is somewhat redundant from a regularization pointof view and we propose a new algorithm called Kernel Projection Machine to avoid this redundancy, based on an analogy with the statistical framework of regression for a Gaussian white noise model. Preliminary experimental results show that this algorithm reaches the same performances as an SVM.

Multiple realizations of continuous-valued time series from a stochastic process often contain systematic variations in rate and amplitude. To leverage the information contained in such noisy replicate sets, we need to align them in an appropriate way (for example, to allow the data to be properly combined by adaptive averaging). We present the Continuous Profile Model (CPM), a generative model in which each observed time series is a non-uniformly subsampled version of a single latent trace, to which local rescaling and additive noise are applied. After unsupervised training, the learned trace represents a canonical, high resolution fusion of all the replicates. As well, an alignment in time and scale of each observation to this trace can be found by inference in the model. We apply CPM to successfully align speech signals from multiple speakers and sets of Liquid Chromatography-Mass Spectrometry proteomic data.

We consider an MDP setting in which the reward function is allowed to change during each time step of play (possibly in an adversarial manner), yet the dynamics remain fixed. Similar to the experts setting, we address the question of how well can an agent do when compared to the reward achieved under the best stationary policy over time. We provide efficient algorithms, which have regret bounds with no dependence on the size of state space. Instead, these bounds depend only on a certain horizon time of the process and logarithmically on the number of actions. We also show that in the case that the dynamics change over time, the problem becomes computationally hard.

As animals interact with their environments, they must constantly update estimates about their states. Bayesian models combine prior probabilities, adynamical model and sensory evidence to update estimates optimally. Thesemodels are consistent with the results of many diverse psychophysical studies. However, little is known about the neural representation andmanipulation of such Bayesian information, particularly in populations of spiking neurons. We consider this issue, suggesting a model based on standard neural architecture and activations. We illustrate theapproach on a simple random walk example, and apply it to a sensorimotor integration task that provides a particularly compelling example of dynamic probabilistic computation. Bayesian models have been used to explain a gamut of experimental results in tasks which require estimates to be derived from multiple sensory cues.

We study a number of open issues in spectral clustering: (i) Selecting the appropriate scale of analysis, (ii) Handling multi-scale data, (iii) Clustering withirregular background clutter, and, (iv) Finding automatically the number of groups. We first propose that a'local' scale should be used to compute the affinity between each pair of points. This local scaling leads to better clustering especially when the data includes multiple scales and when the clusters are placed within a cluttered background. We further suggest exploiting the structure of the eigenvectors to infer automatically the number of groups. This leads to a new algorithm in which the final randomly initialized k-means stage is eliminated.

Classification algorithms typically induce population-wide models that are trained to perform well on average on expected future instances. We introduce a Bayesian framework for learning instance-specific models from data that are optimized to predict well for a particular instance. Based on this framework, we present a lazy instance-specific algorithm called ISA that performs selective model averaging over a restricted class of Bayesian networks. On experimental evaluation, this algorithm shows superior performance over model selection. We intend to apply such instance-specific algorithms to improve the performance of patient-specific predictive models induced from medical data.

We prove generalization error bounds for predicting entries in a partially observed matrix by fitting the observed entries with a low-rank matrix. In justifying the analysis approach we take to obtain the bounds, we present an example of a class of functions of finite pseudodimension such that the sums of functions from this class have unbounded pseudodimension.

The equivalent kernel [1] is a way of understanding how Gaussian process regressionworks for large sample sizes based on a continuum limit. In this paper we show (1) how to approximate the equivalent kernel of the widely-used squared exponential (or Gaussian) kernel and related kernels, and(2) how analysis using the equivalent kernel helps to understand the learning curves for Gaussian processes.

Most existing tracking algorithms construct a representation of a target object prior to the tracking task starts, and utilize invariant features to handle appearance variation of the target caused by lighting, pose, and view angle change. In this paper, we present an efficient and effective onlinealgorithm that incrementally learns and adapts a low dimensional eigenspacerepresentation to reflect appearance changes of the target, thereby facilitating the tracking task. Furthermore, our incremental method correctly updates the sample mean and the eigenbasis, whereas existing incremental subspace update methods ignore the fact the sample mean varies over time. The tracking problem is formulated as a state inference problem within a Markov Chain Monte Carlo framework and a particle filter is incorporated for propagating sample distributions over time. Numerous experiments demonstrate the effectiveness of the proposed trackingalgorithm in indoor and outdoor environments where the target objects undergo large pose and lighting changes.