Brain-Computer Interfaces can suffer from a large variance of the subject conditions withinand across sessions. For example vigilance fluctuations in the individual, variabletask involvement, workload etc. alter the characteristics of EEG signals and thus challenge a stable BCI operation. In the present work we aim to define features based on a variant of the common spatial patterns (CSP) algorithm that are constructed invariant with respect to such nonstationarities. We enforce invariance properties by adding terms to the denominator of a Rayleigh coefficient representation of CSP such as disturbance covariance matrices from fluctuations in visual processing. In this manner physiological prior knowledge can be used to shape the classification engine for BCI. As a proof of concept we present a BCI classifier that is robust to changes in the level of parietal α-activity. In other words, the EEG decoding still works when there are lapses in vigilance.

We first compare these models on a formal level.

We study the rates of growth of the regret in online convex optimization. First, we show that a simple extension of the algorithm of Hazan et al eliminates the need for a priori knowledge of the lower bound on the second derivatives of the observed functions. We then provide an algorithm, Adaptive Online Gradient Descent, which interpolates between the results of Zinkevich for linear functions and of Hazan et al for strongly convex functions, achieving intermediate rates between T and log T . Furthermore, we show strong optimality of the algorithm. Finally, we provide an extension of our results to general norms.

We present a new analysis for the combination of binary classifiers. We propose a theoretical framework based on the Neyman-Pearson lemma to analyze combinations of classifiers. In particular, we give a method for finding the optimal decision rule for a combination of classifiers and prove that it has the optimal ROC curve. We also show how our method generalizes and improves on previous work on combining classifiers and generating ROC curves.

We present a novel linear clustering framework (Diffrac) which relies on a linear discriminative cost function and a convex relaxation of a combinatorial optimization problem. The large convex optimization problem is solved through a sequence of lower dimensional singular value decompositions. This framework has several attractive properties: (1) although apparently similar to K-means, it exhibits superior clustering performance than K-means, in particular in terms of robustness to noise. (2) It can be readily extended to non linear clustering if the discriminative cost function is based on positive definite kernels, and can then be seen as an alternative to spectral clustering. (3) Prior information on the partition is easily incorporated, leading to state-of-the-art performance for semi-supervised learning, for clustering or classification. We present empirical evaluations of our algorithms on synthetic and real medium-scale datasets.

We combine two threads of research on approximate dynamic programming: random sampling of states and using local trajectory optimizers to globally optimize a policy and associated value function. This combination allows us to replace a dense multidimensional grid with a much sparser adaptive sampling of states. Our focus is on finding steady state policies for the deterministic time invariant discrete time control problems with continuous states and actions often found in robotics. In this paper we show that we can now solve problems we couldn't solve previously with regular grid-based approaches.

Learning the common structure shared by a set of supervised tasks is an important practical and theoretical problem. Knowledge of this structure may lead to better generalizationperformance on the tasks and may also facilitate learning new tasks. We propose a framework for solving this problem, which is based on regularization withspectral functions of matrices. This class of regularization problems exhibits appealing computational properties and can be optimized efficiently by an alternating minimization algorithm. In addition, we provide a necessary and sufficient condition for convexity of the regularizer.

We consider continuous state, continuous action batch reinforcement learning where the goal is to learn a good policy from a sufficiently rich trajectory generated by another policy. We study a variant of fitted Q-iteration, where the greedy action selection is replaced by searching for a policy in a restricted set of candidate policies by maximizing the average action values. We provide a rigorous theoretical analysis of this algorithm, proving what we believe is the first finite-time bounds for value-function based algorithms for continuous state- and action-space problems.

There has been an explosion of interest in statistical models for analyzing network data, and considerable interest in the class of exponential random graph (ERG) models, especially in connection with difficulties in computing maximum likelihood estimates. The issues associated with these difficulties relate to the broader structure of discrete exponential families. This paper re-examines the issues in two parts. First we consider the closure of $k$-dimensional exponential families of distribution with discrete base measure and polyhedral convex support $\mathrm{P}$. We show that the normal fan of $\mathrm{P}$ is a geometric object that plays a fundamental role in deriving the statistical and geometric properties of the corresponding extended exponential families. We discuss its relevance to maximum likelihood estimation, both from a theoretical and computational standpoint. Second, we apply our results to the analysis of ERG models. In particular, by means of a detailed example, we provide some characterization of the properties of ERG models, and, in particular, of certain behaviors of ERG models known as degeneracy.

We have proposed a model based upon flocking on a complex network, and then developed two clustering algorithms on the basis of it. In the algorithms, firstly a \textit{k}-nearest neighbor (knn) graph as a weighted and directed graph is produced among all data points in a dataset each of which is regarded as an agent who can move in space, and then a time-varying complex network is created by adding long-range links for each data point. Furthermore, each data point is not only acted by its \textit{k} nearest neighbors but also \textit{r} long-range neighbors through fields established in space by them together, so it will take a step along the direction of the vector sum of all fields. It is more important that these long-range links provides some hidden information for each data point when it moves and at the same time accelerate its speed converging to a center. As they move in space according to the proposed model, data points that belong to the same class are located at a same position gradually, whereas those that belong to different classes are away from one another. Consequently, the experimental results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the rates of convergence of clustering algorithms are fast enough. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.