As humans, we live in a remarkably complex social environment. One cognitive tool which helps us manage all this complexity is our theory of mind, the ability to reason about the mental states of others. By deducing what other people want, feel and think, we can understand their actions, predict how our actions will influence them, and decide how we should behave to be successful. Theory of mind is the cognitive capacity to understand and predict external behavior of others and oneself by attributing internal mental states, such as knowledge, beliefs, and intentions [17]. This is thought to be the pinnacle of social cognition.

Current studies about motor imagery based rehabilitation training systems for stroke subjects lack an appropriate analytic method, which can achieve a considerable classification accuracy, at the same time detects gradual changes of imagery patterns during rehabilitation process and disinters potential mechanisms about motor function recovery. In this study, we propose an adaptive boosting algorithm based on the cortex plasticity and spectral band shifts. This approach models the usually predetermined spatial-spectral configurations in EEG study into variable preconditions, and introduces a new heuristic of stochastic gradient boost for training base learners under these preconditions. We compare our proposed algorithm with commonly used methods on datasets collected from 2 months' clinical experiments. The simulation results demonstrate the effectiveness of the method in detecting the variations of stroke patients' EEG patterns. By chronologically reorganizing the weight parameters of the learned additive model, we verify the spatial compensatory mechanism on impaired cortex and detect the changes of accentuation bands in spectral domain, which may contribute important prior knowledge for rehabilitation practice.

Combining information from different sources is a common way to improve classification accuracy in Brain-Computer Interfacing (BCI). For instance, in small sample settings it is useful to integrate data from other subjects or sessions in order to improve the estimation quality of the spatial filters or the classifier. Since data from different subjects may show large variability, it is crucial to weight the contributions according to importance. Many multi-subject learning algorithms determine the optimal weighting in a separate step by using heuristics, however, without ensuring that the selected weights are optimal with respect to classification. In this work we apply Multiple Kernel Learning (MKL) to this problem. MKL has been widely used for feature fusion in computer vision and allows to simultaneously learn the classifier and the optimal weighting. We compare the MKL method to two baseline approaches and investigate the reasons for performance improvement.

The generic identification problem is to decide whether a stochastic process $(X_t)$ is a hidden Markov process and if yes to infer its parameters for all but a subset of parametrizations that form a lower-dimensional subvariety in parameter space. Partial answers so far available depend on extra assumptions on the processes, which are usually centered around stationarity. Here we present a general solution for binary-valued hidden Markov processes. Our approach is rooted in algebraic statistics hence it is geometric in nature. We find that the algebraic varieties associated with the probability distributions of binary-valued hidden Markov processes are zero sets of determinantal equations which draws a connection to well-studied objects from algebra. As a consequence, our solution allows for algorithmic implementation based on elementary (linear) algebraic routines.

Sequential decision-making problems with multiple objectives arise naturally in practice and pose unique challenges for research in decision-theoretic planning and learning, which has largely focused on single-objective settings. This article surveys algorithms designed for sequential decision-making problems with multiple objectives. Though there is a growing body of literature on this subject, little of it makes explicit under what circumstances special methods are needed to solve multi-objective problems. Therefore, we identify three distinct scenarios in which converting such a problem to a single-objective one is impossible, infeasible, or undesirable. Furthermore, we propose a taxonomy that classifies multi-objective methods according to the applicable scenario, the nature of the scalarization function (which projects multi-objective values to scalar ones), and the type of policies considered. We show how these factors determine the nature of an optimal solution, which can be a single policy, a convex hull, or a Pareto front. Using this taxonomy, we survey the literature on multi-objective methods for planning and learning. Finally, we discuss key applications of such methods and outline opportunities for future work.

Feature extraction and dimensionality reduction are important tasks in many fields of science dealing with signal processing and analysis. The relevance of these techniques is increasing as current sensory devices are developed with ever higher resolution, and problems involving multimodal data sources become more common. A plethora of feature extraction methods are available in the literature collectively grouped under the field of Multivariate Analysis (MVA). This paper provides a uniform treatment of several methods: Principal Component Analysis (PCA), Partial Least Squares (PLS), Canonical Correlation Analysis (CCA) and Orthonormalized PLS (OPLS), as well as their non-linear extensions derived by means of the theory of reproducing kernel Hilbert spaces. We also review their connections to other methods for classification and statistical dependence estimation, and introduce some recent developments to deal with the extreme cases of large-scale and low-sized problems. To illustrate the wide applicability of these methods in both classification and regression problems, we analyze their performance in a benchmark of publicly available data sets, and pay special attention to specific real applications involving audio processing for music genre prediction and hyperspectral satellite images for Earth and climate monitoring.

Many problems in machine learning, statistics and signal processing may be cast as convex optimization problems. In large-scale situations, simple gradient-based algorithms with potentially many cheap iterations are often preferred over methods, such as Newton's method or interior-point methods, that rely on fewer but more expensive iterations. The choice of a first-order method depends on the structure of the problem, in particular (a) the smoothness and/or strong convexity of the objective function, and (b) the computational efficiency of certain operations related to the non-smooth parts of the objective function, when it is decomposable in a smooth and a non-smooth part. In this paper, we consider two classical algorithms, namely (a) subgradient descent and its mirror descent extension [29, 24, 4], and (b) conditional gradient algorithms, sometimes referred to as Frank-Wolfe algorithms [16, 13, 15, 14, 19]. Subgradient algorithms are adapted to non-smooth unstructured situations, and after t steps have a convergence rate of O(1/ t) in terms of objective values.

We propose a voted dual averaging method for online classification problems with explicit regularization. This method employs the update rule of the regularized dual averaging (RDA) method, but only on the subsequence of training examples where a classification error is made. We derive a bound on the number of mistakes made by this method on the training set, as well as its generalization error rate. We also introduce the concept of relative strength of regularization, and show how it affects the mistake bound and generalization performance. We experimented with the method using $\ell_1$ regularization on a large-scale natural language processing task, and obtained state-of-the-art classification performance with fairly sparse models.

We consider the prediction of weak effects in a multiple-output regression setup, when covariates are expected to explain a small amount, less than $\approx 1%$, of the variance of the target variables. To facilitate the prediction of the weak effects, we constrain our model structure by introducing a novel Bayesian approach of sharing information between the regression model and the noise model. Further reduction of the effective number of parameters is achieved by introducing an infinite shrinkage prior and group sparsity in the context of the Bayesian reduced rank regression, and using the Bayesian infinite factor model as a flexible low-rank noise model. In our experiments the model incorporating the novelties outperformed alternatives in genomic prediction of rich phenotype data. In particular, the information sharing between the noise and regression models led to significant improvement in prediction accuracy.

The recently introduced continuous Skip-gram model is an efficient method for learning high-quality distributed vector representations that capture a large number of precise syntactic and semantic word relationships. In this paper we present several extensions that improve both the quality of the vectors and the training speed. By subsampling of the frequent words we obtain significant speedup and also learn more regular word representations. We also describe a simple alternative to the hierarchical softmax called negative sampling. An inherent limitation of word representations is their indifference to word order and their inability to represent idiomatic phrases. For example, the meanings of "Canada" and "Air" cannot be easily combined to obtain "Air Canada". Motivated by this example, we present a simple method for finding phrases in text, and show that learning good vector representations for millions of phrases is possible.