We introduce a novel framework for estimating vector fields using sparse basis field expansions (S-FLEX). The notion of basis fields, which are an extension of scalar basis functions, arises naturally in our framework from a rotational invariance requirement. We consider a regression setting as well as inverse problems. All variants discussed lead to second-order cone programming formulations. While our framework is generally applicable to any type of vector field, we focus in this paper on applying it to solving the EEG/MEG inverse problem. It is shown that significantly more precise and neurophysiologically more plausible location and shape estimates of cerebral current sources from EEG/MEG measurements become possible with our method when comparing to the state-of-the-art.

The standard assumption of identically distributed training and test data can be violated when an adversary can exercise some control over the generation of the test data. In a prediction game, a learner produces a predictive model while an adversary may alter the distribution of input data. We study single-shot prediction games in which the cost functions of learner and adversary are not necessarily antagonistic. We identify conditions under which the prediction game has a unique Nash equilibrium, and derive algorithms that will find the equilibrial prediction models. In a case study, we explore properties of Nash-equilibrial prediction models for email spam filtering empirically.

Many motor skills in humanoid robotics can be learned using parametrized motor primitives as done in imitation learning. However, most interesting motor learning problems are high-dimensional reinforcement learning problems often beyond the reach of current methods. In this paper, we extend previous work on policy learning from the immediate reward case to episodic reinforcement learning. We show that this results into a general, common framework also connected to policy gradient methods and yielding a novel algorithm for policy learning by assuming a form of exploration that is particularly well-suited for dynamic motor primitives. The resulting algorithm is an EM-inspired algorithm applicable in complex motor learning tasks. We compare this algorithm to alternative parametrized policy search methods and show that it outperforms previous methods. We apply it in the context of motor learning and show that it can learn a complex Ball-in-a-Cup task using a real Barrett WAM robot arm.

In this paper we propose a new incremental spike sorting model that automatically eliminates refractory period violations, accounts for action potential waveform drift, and can handle appearance" and "disappearance" of neurons. Our approach is to augment a known time-varying Dirichlet process that ties together a sequence of infinite Gaussian mixture models, one per action potential waveform observation, with an interspike-interval-dependent likelihood that prohibits refractory period violations. We demonstrate this model by showing results from sorting two publicly available neural data recordings for which the a partial ground truth labeling is known."

The relative merits of different population coding schemes have mostly been analyzed in the framework of stimulus reconstruction using Fisher Information. Here, we consider the case of stimulus discrimination in a two alternative forced choice paradigm and compute neurometric functions in terms of the minimal discrimination error and the Jensen-Shannon information to study neural population codes. We first explore the relationship between minimum discrimination error, Jensen-Shannon Information and Fisher Information and show that the discrimination framework is more informative about the coding accuracy than Fisher Information as it defines an error for any pair of possible stimuli. In particular, it includes Fisher Information as a special case. Second, we use the framework to study population codes of angular variables. Specifically, we assess the impact of different noise correlations structures on coding accuracy in long versus short decoding time windows. That is, for long time window we use the common Gaussian noise approximation. To address the case of short time windows we analyze the Ising model with identical noise correlation structure. In this way, we provide a new rigorous framework for assessing the functional consequences of noise correlation structures for the representational accuracy of neural population codes that is in particular applicable to short-time population coding.

We consider multi-armed bandit problems where the number of arms is larger than the possible number of experiments. We make a stochastic assumption on the mean-reward of a new selected arm which characterizes its probability of being anear-optimal arm. Our assumption is weaker than in previous works. We describe algorithms based on upper-confidence-bounds applied to a restricted set of randomly selected arms and provide upper-bounds on the resulting expected regret. We also derive a lower-bound which matches (up to a logarithmic factor) the upper-bound in some cases.

Embeddings of random variables in reproducing kernel Hilbert spaces (RKHSs) may be used to conduct statistical inference based on higher order moments. For sufficiently rich (characteristic) RKHSs, each probability distribution has a unique embedding, allowing all statistical properties of the distribution to be taken into consideration. Necessary and sufficient conditions for an RKHS to be characteristic exist for $\R^n$. In the present work, conditions are established for an RKHS to be characteristic on groups and semigroups. Illustrative examples are provided, including characteristic kernels on periodic domains, rotation matrices, and $\R^n_+$.

We show how improved sequences for magnetic resonance imaging can be found through automated optimization of Bayesian design scores. Combining recent advances in approximate Bayesian inference and natural image statistics with high-performance numerical computation, we propose the first scalable Bayesian experimental design framework for this problem of high relevance to clinical and brain research. Our solution requires approximate inference for dense, non-Gaussian models on a scale seldom addressed before. We propose a novel scalable variational inference algorithm, and show how powerful methods of numerical mathematics can be modified to compute primitives in our framework. Our approach is evaluated on a realistic setup with raw data from a 3T MR scanner.

We consider the problem of estimating the graph structure associated with a Gaussian Markov random field (GMRF) from i.i.d.

We develop the syntactic topic model (STM), a nonparametric Bayesian model of parsed documents. The STM generates words that are both thematically and syntactically constrained, which combines the semantic insights of topic models with the syntactic information available from parse trees. Each word of a sentence is generated by a distribution that combines document-specific topic weights and parse-tree-specific syntactic transitions. Words are assumed to be generated in an order that respects the parse tree. We derive an approximate posterior inference method based on variational methods for hierarchical Dirichlet processes, and we report qualitative and quantitative results on both synthetic data and hand-parsed documents.