We present an improvement to the DP-SLAM algorithm for simultaneous localizationand mapping (SLAM) that maintains multiple hypotheses about densely populated maps (one full map per particle in a particle filter)in time that is linear in all significant algorithm parameters and takes constant (amortized) time per iteration. This means that the asymptotic complexity of the algorithm is no greater than that of a pure localization algorithm using a single map and the same number of particles. Wealso present a hierarchical extension of DP-SLAM that uses a two level particle filter which models drift in the particle filtering process itself. The hierarchical approach enables recovery from the inevitable drift that results from using a finite number of particles in a particle filter and permits the use of DP-SLAM in more challenging domains, while maintaining linear time asymptotic complexity.

We study the statistical convergence and consistency of regularized Boosting methods, where the samples are not independent and identically distributed(i.i.d.) but come from empirical processes of stationary β-mixing sequences. Utilizing a technique that constructs a sequence of independent blocks close in distribution to the original samples, we prove the consistency of the composite classifiers resulting from a regularization achievedby restricting the 1-norm of the base classifiers' weights. When compared to the i.i.d.

In this paper, we show that the hinge loss can be interpreted as the neg-log-likelihood of a semi-parametric model of posterior probabilities. From this point of view, SVMs represent the parametric component of a semi-parametric model fitted by a maximum a posteriori estimation procedure. Thisconnection enables to derive a mapping from SVM scores to estimated posterior probabilities. Unlike previous proposals, the suggested mappingis interval-valued, providing a set of posterior probabilities compatible with each SVM score. This framework offers a new way to adapt the SVM optimization problem to unbalanced classification, whendecisions result in unequal (asymmetric) losses. Experiments show improvements over state-of-the-art procedures.

We propose a new linear method for dimension reduction to identify non-Gaussian components in high dimensional data. Our method, NGCA (non-Gaussian component analysis), uses a very general semi-parametric framework. In contrast to existing projection methods we define what is uninteresting (Gaussian): by projecting out uninterestingness, we can estimate therelevant non-Gaussian subspace. We show that the estimation error of finding the non-Gaussian components tends to zero at a parametric rate.Once NGCA components are identified and extracted, various tasks can be applied in the data analysis process, like data visualization, clustering, denoising or classification. A numerical study demonstrates the usefulness of our method.

Finally we provide very encouraging experimental results.

In this paper we propose a new receiver for digital communications. We focus on the application of Gaussian Processes (GPs) to the multiuser detection (MUD) in code division multiple access (CDMA) systems to solve the near-far problem. Hence, we aim to reduce the interference from other users sharing the same frequency band. While usual approaches minimizethe mean square error (MMSE) to linearly retrieve the user of interest, we exploit the same criteria but in the design of a nonlinear MUD. Since the optimal solution is known to be nonlinear, the performance of this novel method clearly improves that of the MMSE detectors. Furthermore,the GP based MUD achieves excellent interference suppression even for short training sequences. We also include some experiments toillustrate that other nonlinear detectors such as those based on Support Vector Machines (SVMs) exhibit a worse performance.

We present a nonlinear, simple, yet effective, feature subset selection method for regression and use it in analyzing cortical neural activity. Our algorithm involves a feature-weighted version of the k-nearest-neighbor algorithm. It is able to capture complex dependency of the target function onits input and makes use of the leave-one-out error as a natural regularization. We explain the characteristics of our algorithm on synthetic problemsand use it in the context of predicting hand velocity from spikes recorded in motor cortex of a behaving monkey. By applying feature selectionwe are able to improve prediction quality and suggest a novel way of exploring neural data.

We determine the asymptotic limit of the function computed by support vector machines (SVM) and related algorithms that minimize a regularized empiricalconvex loss function in the reproducing kernel Hilbert space of the Gaussian RBF kernel, in the situation where the number of examples tends to infinity, the bandwidth of the Gaussian kernel tends to 0, and the regularization parameter is held fixed.

Active learning is the problem in supervised learning to design the locations oftraining input points so that the generalization error is minimized. Existing active learning methods often assume that the model used for learning is correctly specified, i.e., the learning target function can be expressed bythe model at hand. In many practical situations, however, this assumption may not be fulfilled. In this paper, we first show that the existing activelearning method can be theoretically justified under slightly weaker condition: the model does not have to be correctly specified, but slightly misspecified models are also allowed. However, it turns out that the weakened condition is still restrictive in practice.

The parameters of the model are learned using contrastive divergence and an optimization procedure for finding appropriate marginal directions.