With recent advancement in data collection and storage, we have large amounts of information at our disposal, especially with respect to the number of explanatory variables or'features'. When these features contain redundant or noisy information, estimating the functional connection between the response and these features can become quite challenging, and that often hampers the quality of learning. One way to overcome this is by finding a smaller set of features or explanatory variables that can perform the learning task sufficiently well. In this paper, we discuss feature elimination in statistical learning with kernel machines. Kernel machines (KM) are a class of learning methods for pattern analysis and regression, under transformations of the input feature space, of which the linear support vector machine (SVM) is the simplest case. In general, the term'kernel machine' is reserved for the more general version of the SVM problem with nonlinear transformation of the feature space. The popularity of these algorithms is motivated by the fact that these are easyto-compute techniques that enable estimation under weak or no assumptions on the distribution [see Steinwart and Chirstmann, 2008].

We survey concepts at the frontier of research connecting artificial, animal and human cognition to computation and information processing---from the Turing test to Searle's Chinese Room argument, from Integrated Information Theory to computational and algorithmic complexity. We start by arguing that passing the Turing test is a trivial computational problem and that its pragmatic difficulty sheds light on the computational nature of the human mind more than it does on the challenge of artificial intelligence. We then review our proposed algorithmic information-theoretic measures for quantifying and characterizing cognition in various forms. These are capable of accounting for known biases in human behavior, thus vindicating a computational algorithmic view of cognition as first suggested by Turing, but this time rooted in the concept of algorithmic probability, which in turn is based on computational universality while being independent of computational model, and which has the virtue of being predictive and testable as a model theory of cognitive behavior.

We present a domain-general account of causation that applies to settings in which macro-level causal relations between two systems are of interest, but the relevant causal features are poorly understood and have to be aggregated from vast arrays of micro-measurements. Our approach generalizes that of Chalupka et al. (2015) to the setting in which the macro-level effect is not specified. We formalize the connection between micro- and macro-variables in such situations and provide a coherent framework describing causal relations at multiple levels of analysis. We present an algorithm that discovers macro-variable causes and effects from micro-level measurements obtained from an experiment. We further show how to design experiments to discover macro-variables from observational micro-variable data. Finally, we show that under specific conditions, one can identify multiple levels of causal structure. Throughout the article, we use a simulated neuroscience multi-unit recording experiment to illustrate the ideas and the algorithms.

We show that the objective function of conventional k-means clustering can be expressed as the Frobenius norm of the difference of a data matrix and a low rank approximation of that data matrix. In short, we show that k-means clustering is a matrix factorization problem. These notes are meant as a reference and intended to provide a guided tour towards a result that is often mentioned but seldom made explicit in the literature.

A widely applied approach to causal inference from a non-experimental time series $X$, often referred to as "(linear) Granger causal analysis", is to regress present on past and interpret the regression matrix $\hat{B}$ causally. However, if there is an unmeasured time series $Z$ that influences $X$, then this approach can lead to wrong causal conclusions, i.e., distinct from those one would draw if one had additional information such as $Z$. In this paper we take a different approach: We assume that $X$ together with some hidden $Z$ forms a first order vector autoregressive (VAR) process with transition matrix $A$, and argue why it is more valid to interpret $A$ causally instead of $\hat{B}$. Then we examine under which conditions the most important parts of $A$ are identifiable or almost identifiable from only $X$. Essentially, sufficient conditions are (1) non-Gaussian, independent noise or (2) no influence from $X$ to $Z$. We present two estimation algorithms that are tailored towards conditions (1) and (2), respectively, and evaluate them on synthetic and real-world data. We discuss how to check the model using $X$.

Active learning (AL) is a learning paradigm where an active learner has to train a model (e.g., a classifier) which is in principal trained in a supervised way, but in AL it has to be done by means of a data set with initially unlabeled samples. To get labels for these samples, the active learner has to ask an oracle (e.g., a human expert) for labels. The goal is to maximize the performance of the model and to minimize the number of queries at the same time. In this article, we first briefly discuss the state of the art and own, preliminary work in the field of AL. Then, we propose the concept of collaborative active learning (CAL). With CAL, we will overcome some of the harsh limitations of current AL. In particular, we envision scenarios where an expert may be wrong for various reasons, there might be several or even many experts with different expertise, the experts may label not only samples but also knowledge at a higher level such as rules, and we consider that the labeling costs depend on many conditions. Moreover, in a CAL process human experts will profit by improving their own knowledge, too.

The efficiency of deep machine learning for automatic delineation of tumor areas has been demonstrated for intraoperative neuronavigation using active IR-mapping with the use of the cold test. The proposed approach employs a matrix IR-imager to remotely register the space-time distribution of surface temperature pattern, which is determined by the dynamics of local cerebral blood flow. The advantages of this technique are non-invasiveness, zero risks for the health of patients and medical staff, low implementation and operational costs, ease and speed of use. Traditional IR-diagnostic technique has a crucial limitation - it involves a diagnostician who determines the boundaries of tumor areas, which gives rise to considerable uncertainty, which can lead to diagnosis errors that are difficult to control. The current study demonstrates that implementing deep learning algorithms allows to eliminate the explained drawback.

Gaussian latent tree models, or more generally, Gaussian latent forest models have Fisher-information matrices that become singular along interesting submodels, namely, models that correspond to subforests. For these singularities, we compute the real log-canonical thresholds (also known as stochastic complexities or learning coefficients) that quantify the large-sample behavior of the marginal likelihood in Bayesian inference. This provides the information needed for a recently introduced generalization of the Bayesian information criterion. Our mathematical developments treat the general setting of Laplace integrals whose phase functions are sums of squared differences between monomials and constants. We clarify how in this case real log-canonical thresholds can be computed using polyhedral geometry, and we show how to apply the general theory to the Laplace integrals associated with Gaussian latent tree and forest models. In simulations and a data example, we demonstrate how the mathematical knowledge can be applied in model selection.

Mode clustering is a nonparametric method for clustering that defines clusters using the basins of attraction of a density estimator's modes. We provide several enhancements to mode clustering: (i) a soft variant of cluster assignment, (ii) a measure of connectivity between clusters, (iii) a technique for choosing the bandwidth, (iv) a method for denoising small clusters, and (v) an approach to visualizing the clusters. Combining all these enhancements gives us a complete procedure for clustering in multivariate problems. We also compare mode clustering to other clustering methods in several examples

Specifying and implementing flexible human-computer dialogs, such as those used in kiosks and smart phone apps, is challenging because of the numerous and varied directions in which each user might steer a dialog. The objective of this research is to improve dialog specification and implementation. To do so we enriched a notation based on concepts from programming languages, especially partial evaluation, for specifying a variety of unsolicited reporting, mixed-initiative dialogs in a concise representation that serves as a design for dialog implementation. We also built a dialog mining system that extracts a specification in this notation from requirements. To demonstrate that such a specification provides a design for dialog implementation, we built a system that automatically generates an implementation of the dialog, called a stager, from it. These two components constitute a dialog modeling toolkit that automates dialog specification and implementation. These results provide a proof of concept and demonstrate the study of dialog specification and implementation from a programming languages perspective. The ubiquity of dialogs in domains such as travel, education, and health care combined with the demand for smart phone apps provide a landscape for further investigation of these results.