Statistical machine learning methods are increasingly used for neuroimaging data analysis. Their main virtue is their ability to model high-dimensional datasets, e.g. multivariate analysis of activation images or resting-state time series. Supervised learning is typically used in decoding or encoding settings to relate brain images to behavioral or clinical observations, while unsupervised learning can uncover hidden structures in sets of images (e.g. resting state functional MRI) or find sub-populations in large cohorts. By considering different functional neuroimaging applications, we illustrate how scikit-learn, a Python machine learning library, can be used to perform some key analysis steps. Scikit-learn contains a very large set of statistical learning algorithms, both supervised and unsupervised, and its application to neuroimaging data provides a versatile tool to study the brain.

This paper addresses how a recursive neural network model can automatically leave out useless information and emphasize important evidence, in other words, to perform "weight tuning" for higher-level representation acquisition. We propose two models, Weighted Neural Network (WNN) and Binary-Expectation Neural Network (BENN), which automatically control how much one specific unit contributes to the higher-level representation. The proposed model can be viewed as incorporating a more powerful compositional function for embedding acquisition in recursive neural networks. Experimental results demonstrate the significant improvement over standard neural models.

Feature learning forms the cornerstone for tackling challenging learning problems in domains such as speech, computer vision and natural language processing. In this paper, we consider a novel class of matrix and tensor-valued features, which can be pre-trained using unlabeled samples. We present efficient algorithms for extracting discriminative information, given these pre-trained features and labeled samples for any related task. Our class of features are based on higher-order score functions, which capture local variations in the probability density function of the input. We establish a theoretical framework to characterize the nature of discriminative information that can be extracted from score-function features, when used in conjunction with labeled samples. We employ efficient spectral decomposition algorithms (on matrices and tensors) for extracting discriminative components. The advantage of employing tensor-valued features is that we can extract richer discriminative information in the form of an overcomplete representations. Thus, we present a novel framework for employing generative models of the input for discriminative learning.

In the multiple changepoint setting, various search methods have been proposed which involve optimising either a constrained or penalised cost function over possible numbers and locations of changepoints using dynamic programming. Such methods are typically computationally intensive. Recent work in the penalised optimisation setting has focussed on developing a pruning-based approach which gives an improved computational cost that, under certain conditions, is linear in the number of data points. Such an approach naturally requires the specification of a penalty to avoid under/over-fitting. Work has been undertaken to identify the appropriate penalty choice for data generating processes with known distributional form, but in many applications the model assumed for the data is not correct and these penalty choices are not always appropriate. Consequently it is desirable to have an approach that enables us to compare segmentations for different choices of penalty. To this end we present a method to obtain optimal changepoint segmentations of data sequences for all penalty values across a continuous range. This permits an evaluation of the various segmentations to identify a suitably parsimonious penalty choice. The computational complexity of this approach can be linear in the number of data points and linear in the difference between the number of changepoints in the optimal segmentations for the smallest and largest penalty values. This can be orders of magnitude faster than alternative approaches that find optimal segmentations for a range of the number of changepoints.

The first part of the paper presents a reinforcement learning (adaptive filtering) algorithm that facilitates learning an equilibrium by resorting to diffusion cooperation strategies in a social network. Agents form homophilic social groups, within which they exchange past experiences over an undirected graph. It is shown that, if all agents follow the proposed algorithm, their global behavior is attracted to the correlated equilibria set of the game. The second part of the paper provides a test to detect if the actions of agents are consistent with play from the equilibrium of a concave potential game. The theory of revealed preference from microeconomics is used to construct a nonparametric decision test and statistical test which only require the probe and associated actions of agents. A stochastic gradient algorithm is given to optimize the probe in real time to minimize the Type-II error probabilities of the detection test subject to specified Type-I error probability. We provide a real-world example using the energy market, and a numerical example to detect malicious agents in an online social network. Index Terms--Multi-agent signal processing, non-cooperative games, social networks, correlated equilibrium, diffusion cooperation, homophily behavior, revealed preferences, Afriat's theorem, stochastic approximation algorithm.

The paper gives a systematic study of the approximate versions of three greedy-type algorithms that are widely used in convex optimization. By approximate version we mean the one where some of evaluations are made with an error. Importance of such versions of greedy-type algorithms in convex optimization and in approximation theory was emphasized in previous literature.

Bayesian methods suffer from the problem of how to specify prior beliefs. One interesting idea is to consider worst-case priors. This requires solving a stochastic zero-sum game. In this paper, we extend well-known results from bandit theory in order to discover minimax-Bayes policies and discuss when they are practical.

We present a new approach for transferring knowledge from groups to individuals that comprise them. We evaluate our method in text, by inferring the ratings of individual sentences using full-review ratings. This approach, which combines ideas from transfer learning, deep learning and multi-instance learning, reduces the need for laborious human labelling of fine-grained data when abundant labels are available at the group level.

This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive `error indicators' to a distribution over the true error. The variance of this distribution can be interpreted as the (epistemic) uncertainty introduced by the reduced-order model. To model normed errors, the method employs existing rigorous error bounds and residual norms as indicators; numerical experiments show that the method leads to a near-optimal expected effectivity in contrast to typical error bounds. To model errors in general outputs, the method uses dual-weighted residuals---which are amenable to uncertainty control---as indicators. Experiments illustrate that correcting the reduced-order-model output with this surrogate can improve prediction accuracy by an order of magnitude; this contrasts with existing `multifidelity correction' approaches, which often fail for reduced-order models and suffer from the curse of dimensionality. The proposed error surrogates also lead to a notion of `probabilistic rigor', i.e., the surrogate bounds the error with specified probability.

In this paper we consider the problem of minimizing a convex function using a randomized block coordinate descent method. One of the key steps at each iteration of the algorithm is determining the update to a block of variables. Existing algorithms assume that in order to compute the update, a particular subproblem is solved exactly. In his work we relax this requirement, and allow for the subproblem to be solved inexactly, leading to an inexact block coordinate descent method. Our approach incorporates the best known results for exact updates as a special case. Moreover, these theoretical guarantees are complemented by practical considerations: the use of iterative techniques to determine the update as well as the use of preconditioning for further acceleration.