We introduce two methods to improve convergence of the Kernel Hebbian Algorithm (KHA) for iterative kernel PCA. KHA has a scalar gain parameter which is either held constant or decreased as 1/t, leading to slow convergence. Our KHA/et algorithm accelerates KHA by incorporating the reciprocal of the current estimated eigenvalues as a gain vector. We then derive and apply Stochastic Meta-Descent (SMD) to KHA/et; this further speeds convergence by performing gain adaptation in RKHS. Experimental results for kernel PCA and spectral clustering of USPS digits as well as motion capture and image de-noising problems confirm that our methods converge substantially faster than conventional KHA.

Blind source separation, i.e. the extraction of unknown sources from a set of given signals, is relevant for many applications. A special case of this problem is dimension reduction, where the goal is to approximate a given set of signals by superpositions of a minimal number of sources. Since in this case the signals outnumber the sources the problem is over-determined. Most popular approaches for addressing this problem are based on purely linear mixing models. However, many applications like the modeling of acoustic signals, EMG signals, or movement trajectories, require temporal shift-invariance of the extracted components. This case has only rarely been treated in the computational literature, and specifically for the case of dimension reduction almost no algorithms have been proposed. We present a new algorithm for the solution of this problem, which is based on a timefrequency transformation (Wigner-Ville distribution) of the generative model. We show that this algorithm outperforms classical source separation algorithms for linear mixtures, and also a related method for mixtures with delays. In addition, applying the new algorithm to trajectories of human gaits, we demonstrate that it is suitable for the extraction of spatiotemporal components that are easier to interpret than components extracted with other classical algorithms.

Pyramid intersection is an efficient method for computing an approximate partial matching between two sets of feature vectors. We introduce a novel pyramid embedding based on a hierarchy of non-uniformly shaped bins that takes advantage of the underlying structure of the feature space and remains accurate even for sets with high-dimensional feature vectors. The matching similarity is computed in linear time and forms a Mercer kernel. Whereas previous matching approximation algorithms suffer from distortion factors that increase linearly with the feature dimension, we demonstrate that our approach can maintain constant accuracy even as the feature dimension increases. When used as a kernel in a discriminative classifier, our approach achieves improved object recognition results over a state-of-the-art set kernel.

This work presents a method for estimating human facial attractiveness, based on supervised learning techniques. Numerous facial features that describe facial geometry, color and texture, combined with an average human attractiveness score for each facial image, are used to train various predictors. Facial attractiveness ratings produced by the final predictor are found to be highly correlated with human ratings, markedly improving previous machine learning achievements. Simulated psychophysical experiments with virtually manipulated images reveal preferences in the machine's judgments which are remarkably similar to those of humans. These experiments shed new light on existing theories of facial attractiveness such as the averageness, smoothness and symmetry hypotheses. It is intriguing to find that a machine trained explicitly to capture an operational performance criteria such as attractiveness rating, implicitly captures basic human psychophysical biases characterizing the perception of facial attractiveness in general.

For example, muscle response can change because of fatigue, a condition where the disturbance has a fast timescale or because of disease where the disturbance is much slower. Here we hypothesize that the nervous system adapts in a way that reflects the temporal properties of such potential disturbances. According to a Bayesian formulation of this idea, movement error results in a credit assignment problem: what timescale is responsible for this disturbance? The adaptation schedule influences the behavior of the optimal learner, changing estimates at different timescales as well as the uncertainty. A system that adapts in this way predicts many properties observed in saccadic gain adaptation. It well predicts the timecourses of motor adaptation in cases of partial sensory deprivation and reversals of the adaptation direction.

We focus on the problem of estimating the graph structure associated with a discrete Markov random field.

In previous studies, quadratic modelling of natural images has resulted in cell models that react strongly to edges and bars. Here we apply quadratic Independent Component Analysis to natural image patches, and show that up to a small approximation error, the estimated components are computing conjunctions of two linear features. These conjunctive features appear to represent not only edges and bars, but also inherently two-dimensional stimuli, such as corners. In addition, we show that for many of the components, the underlying linear features have essentially V1 simple cell receptive field characteristics. Our results indicate that the development of the V2 cells preferring angles and corners may be partly explainable by the principle of unsupervised sparse coding of natural images.

We present a generalization of dynamic Bayesian networks to concisely describe complex probability distributions such as in problems with multiple interacting variable-length streams of random variables. Our framework incorporates recent graphical model constructs to account for existence uncertainty, value-specific independence, aggregation relationships, and local and global constraints, while still retaining a Bayesian network interpretation and efficient inference and learning techniques. We introduce one such general technique, which is an extension of Value Elimination, a backtracking search inference algorithm. Multi-dynamic Bayesian networks are motivated by our work on Statistical Machine Translation (MT). We present results on MT word alignment in support of our claim that MDBNs are a promising framework for the rapid prototyping of new MT systems.

Finite mixture model is a powerful tool in many statistical learning problems. In this paper, we propose a general, structure-preserving approach to reduce its model complexity, which can bring significant computational benefits in many applications. The basic idea is to group the original mixture components into compact clusters, and then minimize an upper bound on the approximation error between the original and simplified models.

We present a general model-independent approach to the analysis of data in cases when these data do not appear in the form of co-occurrence of two variables X,Y, but rather as a sample of values of an unknown (stochastic) function Z(X,Y). For example, in gene expression data, the expression level Z is a function of gene X and condition Y; or in movie ratings data the rating Z is a function of viewer X and movie Y. The approach represents a consistent extension of the Information Bottleneck method that has previously relied on the availability of co-occurrence statistics. By altering the relevance variable we eliminate the need in the sample of joint distribution of all input variables. This new formulation also enables simple MDL-like model complexity control and prediction of missing values of Z. The approach is analyzed and shown to be on a par with the best known clustering algorithms for a wide range of domains. For the prediction of missing values (collaborative filtering) it improves the currently best known results.