Although non-parametric tests have already been proposed for that purpose, statistical significance tests for non-standard measures (different from the classification error) are less often used in the literature. This paper is an attempt at empirically verifying how these tests compare with more classical tests, on various conditions. More precisely, using a very large dataset to estimate the whole "population", we analyzed the behavior of several statistical test, varying the class unbalance, the compared models, the performance measure, and the sample size. The main result is that providing big enough evaluation sets non-parametric tests are relatively reliable in all conditions.

Lasso regression tends to assign zero weights to most irrelevant or redundant features, and hence is a promising technique for feature selection. Its limitation, however, is that it only offers solutions to linear models. Kernel machines with feature scaling techniques have been studied for feature selection with non-linear models. However, such approaches require to solve hard non-convex optimization problems. This paper proposes a new approach named the Feature Vector Machine (FVM). It reformulates the standard Lasso regression into a form isomorphic to SVM, and this form can be easily extended for feature selection with non-linear models by introducing kernels defined on feature vectors.

An increasing number of projects in neuroscience requires the sta- tistical analysis of high dimensional data sets, as, for instance, in predicting behavior from neural firing or in operating artificial de- vices from brain recordings in brain-machine interfaces. Linear analysis techniques remain prevalent in such cases, but classical linear regression approaches are often numerically too fragile in high dimensions. In this paper, we address the question of whether EMG data collected from arm movements of monkeys can be faith- fully reconstructed with linear approaches from neural activity in primary motor cortex (M1). To achieve robust data analysis, we develop a full Bayesian approach to linear regression that auto- matically detects and excludes irrelevant features in the data, reg- ularizing against overfitting. In comparison with ordinary least squares, stepwise regression, partial least squares, LASSO regres- sion and a brute force combinatorial search for the most predictive input features in the data, we demonstrate that the new Bayesian method offers a superior mixture of characteristics in terms of reg- ularization against overfitting, computational efficiency and ease of use, demonstrating its potential as a drop-in replacement for other linear regression techniques.

We extend radial basis function (RBF) networks to the scenario in which multiple correlated tasks are learned simultaneously, and present the cor- responding learning algorithms. We develop the algorithms for learn- ing the network structure, in either a supervised or unsupervised manner. Training data may also be actively selected to improve the network's gen- eralization to test data. Experimental results based on real data demon- strate the advantage of the proposed algorithms and support our conclu- sions.

We present an improvement to the DP-SLAM algorithm for simultane- ous localization and mapping (SLAM) that maintains multiple hypothe- ses about densely populated maps (one full map per particle in a par- ticle 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 parti- cles. We also 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.

While classical kernel-based learning algorithms are based on a single kernel, in practice it is often desirable to use multiple kernels. Lankriet et al. (2004) considered conic combinations of kernel matrices for classi- fication, leading to a convex quadratically constraint quadratic program. We show that it can be rewritten as a semi-infinite linear program that can be efficiently solved by recycling the standard SVM implementa- tions. Moreover, we generalize the formulation and our method to a larger class of problems, including regression and one-class classifica- tion. Experimental results show that the proposed algorithm helps for automatic model selection, improving the interpretability of the learn- ing result and works for hundred thousands of examples or hundreds of kernels to be combined.

We present an algorithm for learning a quadratic Gaussian metric (Maha- lanobis distance) for use in classification tasks. Our method relies on the simple geometric intuition that a good metric is one under which points in the same class are simultaneously near each other and far from points in the other classes. We construct a convex optimization problem whose solution generates such a metric by trying to collapse all examples in the same class to a single point and push examples in other classes infinitely far away. We show that when the metric we learn is used in simple clas- sifiers, it yields substantial improvements over standard alternatives on a variety of problems. We also discuss how the learned metric may be used to obtain a compact low dimensional feature representation of the original input space, allowing more efficient classification with very little reduction in performance. The problem of learning a distance measure (metric) over an input space is of fundamental importance in machine learning [10, 9], both supervised and unsupervised.

We show how to learn a Mahanalobis distance metric for k -nearest neighbor (kNN) classification by semidefinite programming. The metric is trained with the goal that the k -nearest neighbors always belong to the same class while examples from different classes are separated by a large margin. On seven data sets of varying size and difficulty, we find that metrics trained in this way lead to significant improvements in kNN classification--for example, achieving a test error rate of 1.3% on the MNIST handwritten digits. As in support vector machines (SVMs), the learning problem reduces to a convex optimization based on the hinge loss. Unlike learning in SVMs, however, our framework requires no modification or extension for problems in multiway (as opposed to binary) classification.

We study the problem of maximum entropy density estimation in the presence of known sample selection bias. We propose three bias cor- rection approaches. The first one takes advantage of unbiased sufficient statistics which can be obtained from biased samples. The second one es- timates the biased distribution and then factors the bias out. The third one approximates the second by only using samples from the sampling distri- bution.

We determine the asymptotic limit of the function computed by support vector machines (SVM) and related algorithms that minimize a regularized empirical convex 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. Non-asymptotic convergence bounds to this limit in the L2 sense are provided, together with upper bounds on the classification error that is shown to converge to the Bayes risk, therefore proving the Bayes-consistency of a variety of methods although the regularization term does not vanish. These results are particularly relevant to the one-class SVM, for which the regularization can not vanish by construction, and which is shown for the first time to be a consistent density level set estimator.