Brain has intrigued researchers since the beginning of scientific endeavors. Firstly, beginning of computers saw the advent of exciting developments which culminated to the development of the new discipline of artificial neural networks (ANN). ANNs have been through several generations of major developments, with the recent phase consisting of spiking neural networks based works [1]. Another parallel field of computational neuroscience has been the bio-inspired cognitive architectures (BICA) [2] a field which got major thrust in development. Cognitive architecture (CA) in general and BICA in particular also has a long history and the efforts have been devoted towards trying to emulate the functioning of brain. CAs like SOAR and ACT-R have been under development for many decades and have been applied in various studies [3, 4].

Alzheimer's disease is a major cause of dementia. Its diagnosis requires accurate biomarkers that are sensitive to disease stages. In this respect, we regard probabilistic classification as a method of designing a probabilistic biomarker for disease staging. Probabilistic biomarkers naturally support the interpretation of decisions and evaluation of uncertainty associated with them. In this paper, we obtain probabilistic biomarkers via Gaussian Processes. Gaussian Processes enable probabilistic kernel machines that offer flexible means to accomplish Multiple Kernel Learning. Exploiting this flexibility, we propose a new variation of Automatic Relevance Determination and tackle the challenges of high dimensionality through multiple kernels. Our research results demonstrate that the Gaussian Process models are competitive with or better than the well-known Support Vector Machine in terms of classification performance even in the cases of single kernel learning. Extending the basic scheme towards the Multiple Kernel Learning, we improve the efficacy of the Gaussian Process models and their interpretability in terms of the known anatomical correlates of the disease. For instance, the disease pathology starts in and around the hippocampus and entorhinal cortex. Through the use of Gaussian Processes and Multiple Kernel Learning, we have automatically and efficiently determined those portions of neuroimaging data. In addition to their interpretability, our Gaussian Process models are competitive with recent deep learning solutions under similar settings.

Traditional statistical theory assumes that the analysis to be performed on a given data set is selected independently of the data themselves. This assumption breaks downs when data are re-used across analyses and the analysis to be performed at a given stage depends on the results of earlier stages. Such dependency can arise when the same data are used by several scientific studies, or when a single analysis consists of multiple stages. How can we draw statistically valid conclusions when data are re-used? This is the focus of a recent and active line of work. At a high level, these results show that limiting the information revealed by earlier stages of analysis controls the bias introduced in later stages by adaptivity. Here we review some known results in this area and highlight the role of information-theoretic concepts, notably several one-shot notions of mutual information.

Foot-mounted inertial positioning (FMIP) can face problems of inertial drifts and unknown initial states in real applications, which renders the estimated trajectories inaccurate and not obtained in a well defined coordinate system for matching trajectories of different users. In this paper, an approach adopting received signal strength (RSS) measurements for Wifi access points (APs) are proposed to align and calibrate the trajectories estimated from foot mounted inertial measurement units (IMUs). A crowd-sourced radio map (RM) can be built subsequently and can be used for fingerprinting based Wifi indoor positioning (FWIP). The foundation of the proposed approach is graph based simultaneously localization and mapping (SLAM). The nodes in the graph denote users poses and the edges denote the pairwise constrains between the nodes. The constrains are derived from: (1) inertial estimated trajectories; (2) vicinity in the RSS space. With these constrains, an error functions is defined. By minimizing the error function, the graph is optimized and the aligned/calibrated trajectories along with the RM are acquired. The experimental results have corroborated the effectiveness of the approach for trajectory alignment, calibration as well as RM construction.

Canonical correlation analysis was proposed by Hotelling [6] and it measures linear relationship between two multidimensional variables. In high dimensional setting, the classical canonical correlation analysis breaks down. We propose a sparse canonical correlation analysis by adding l1 constraints on the canonical vectors and show how to solve it efficiently using linearized alternating direction method of multipliers (ADMM) and using TFOCS as a black box. We illustrate this idea on simulated data.

Measuring conditional dependencies among the variables of a network is of great interest to many disciplines. This paper studies some shortcomings of the existing dependency measures in detecting direct causal influences or their lack of ability for group selection to capture strong dependencies and accordingly introduces a new statistical dependency measure to overcome them. This measure is inspired by Dobrushin's coefficients and based on the fact that there is no dependency between $X$ and $Y$ given another variable $Z$, if and only if the conditional distribution of $Y$ given $X=x$ and $Z=z$ does not change when $X$ takes another realization $x'$ while $Z$ takes the same realization $z$. We show the advantages of this measure over the related measures in the literature. Moreover, we establish the connection between our measure and the integral probability metric (IPM) that helps to develop estimators of the measure with lower complexity compared to other relevant information theoretic based measures. Finally, we show the performance of this measure through numerical simulations.

This paper deals with a new filter algorithm for selecting the smallest subset of features carrying all the information content of a data set (i.e. for removing redundant features). It is an advanced version of the fractal dimension reduction technique, and it relies on the recently introduced Morisita estimator of Intrinsic Dimension (ID). Here, the ID is used to quantify dependencies between subsets of features, which allows the effective processing of highly non-linear data. The proposed algorithm is successfully tested on simulated and real world case studies. Different levels of sample size and noise are examined along with the variability of the results. In addition, a comprehensive procedure based on random forests shows that the data dimensionality is significantly reduced by the algorithm without loss of relevant information. And finally, comparisons with benchmark feature selection techniques demonstrate the promising performance of this new filter.

We propose a geometric assumption on nonnegative data matrices such that under this assumption, we are able to provide upper bounds (both deterministic and probabilistic) on the relative error of nonnegative matrix factorization (NMF). The algorithm we propose first uses the geometric assumption to obtain an exact clustering of the columns of the data matrix; subsequently, it employs several rank-one NMFs to obtain the final decomposition. When applied to data matrices generated from our statistical model, we observe that our proposed algorithm produces factor matrices with comparable relative errors vis-\`a-vis classical NMF algorithms but with much faster speeds. On face image and hyperspectral imaging datasets, we demonstrate that our algorithm provides an excellent initialization for applying other NMF algorithms at a low computational cost. Finally, we show on face and text datasets that the combinations of our algorithm and several classical NMF algorithms outperform other algorithms in terms of clustering performance.

In statistical learning for real-world large-scale data problems, one must often resort to "streaming" algorithms which operate sequentially on small batches of data. In this work, we present an analysis of the information-theoretic limits of mini-batch inference in the context of generalized linear models and low-rank matrix factorization. In a controlled Bayes-optimal setting, we characterize the optimal performance and phase transitions as a function of mini-batch size. We base part of our results on a detailed analysis of a mini-batch version of the approximate message-passing algorithm (Mini-AMP), which we introduce. Additionally, we show that this theoretical optimality carries over into real-data problems by illustrating that Mini-AMP is competitive with standard streaming algorithms for clustering.

The 'conjunction fallacy' has been extensively debated by scholars in cognitive science and, in recent times, the discussion has been enriched by the proposal of modeling the fallacy using the quantum formalism. Two major quantum approaches have been put forward: the first assumes that respondents use a two-step sequential reasoning and that the fallacy results from the presence of 'question order effects'; the second assumes that respondents evaluate the cognitive situation as a whole and that the fallacy results from the 'emergence of new meanings', as an 'effect of overextension' in the conceptual conjunction. Thus, the question arises as to determine whether and to what extent conjunction fallacies would result from 'order effects' or, instead, from 'emergence effects'. To help clarify this situation, we propose to use the World Wide Web as an 'information space' that can be interrogated both in a sequential and non-sequential way, to test these two quantum approaches. We find that 'emergence effects', and not 'order effects', should be considered the main cognitive mechanism producing the observed conjunction fallacies.