We propose a statistical learning model for classifying cognitive processes based on distributed patterns of neural activation in the brain, acquired via functional magnetic resonance imaging (fMRI). In the proposed learning method, local meshes are formed around each voxel. The distance between voxels in the mesh is determined by using a functional neighbourhood concept. In order to define the functional neighbourhood, the similarities between the time series recorded for voxels are measured and functional connectivity matrices are constructed. Then, the local mesh for each voxel is formed by including the functionally closest neighbouring voxels in the mesh. The relationship between the voxels within a mesh is estimated by using a linear regression model. These relationship vectors, called Functional Connectivity aware Local Relational Features (FC-LRF) are then used to train a statistical learning machine. The proposed method was tested on a recognition memory experiment, including data pertaining to encoding and retrieval of words belonging to ten different semantic categories. Two popular classifiers, namely k-nearest neighbour (k-nn) and Support Vector Machine (SVM), are trained in order to predict the semantic category of the item being retrieved, based on activation patterns during encoding. The classification performance of the Functional Mesh Learning model, which range in 62%-71% is superior to the classical multi-voxel pattern analysis (MVPA) methods, which range in 40%-48%, for ten semantic categories.

In this survey we present different approaches that allow an intelligent agent to explore autonomous its environment to gather information and learn multiple tasks. Different communities proposed different solutions, that are in many cases, similar and/or complementary. These solutions include active learning, exploration/exploitation, online-learning and social learning. The common aspect of all these approaches is that it is the agent to selects and decides what information to gather next. Applications for these approaches already include tutoring systems, autonomous grasping learning, navigation and mapping and human-robot interaction. We discuss how these approaches are related, explaining their similarities and their differences in terms of problem assumptions and metrics of success. We consider that such an integrated discussion will improve inter-disciplinary research and applications.

With the rapid development of social media sharing, people often need to manage the growing volume of multimedia data such as large scale video classification and annotation, especially to organize those videos containing human activities. Recently, manifold regularized semi-supervised learning (SSL), which explores the intrinsic data probability distribution and then improves the generalization ability with only a small number of labeled data, has emerged as a promising paradigm for semiautomatic video classification. In addition, human action videos often have multi-modal content and different representations. To tackle the above problems, in this paper we propose multiview Hessian regularized logistic regression (mHLR) for human action recognition. Compared with existing work, the advantages of mHLR lie in three folds: (1) mHLR combines multiple Hessian regularization, each of which obtained from a particular representation of instance, to leverage the exploring of local geometry; (2) mHLR naturally handle multi-view instances with multiple representations; (3) mHLR employs a smooth loss function and then can be effectively optimized. We carefully conduct extensive experiments on the unstructured social activity attribute (USAA) dataset and the experimental results demonstrate the effectiveness of the proposed multiview Hessian regularized logistic regression for human action recognition.

We develop a framework for post model selection inference, via marginal screening, in linear regression. At the core of this framework is a result that characterizes the exact distribution of linear functions of the response $y$, conditional on the model being selected (``condition on selection" framework). This allows us to construct valid confidence intervals and hypothesis tests for regression coefficients that account for the selection procedure. In contrast to recent work in high-dimensional statistics, our results are exact (non-asymptotic) and require no eigenvalue-like assumptions on the design matrix $X$. Furthermore, the computational cost of marginal regression, constructing confidence intervals and hypothesis testing is negligible compared to the cost of linear regression, thus making our methods particularly suitable for extremely large datasets. Although we focus on marginal screening to illustrate the applicability of the condition on selection framework, this framework is much more broadly applicable. We show how to apply the proposed framework to several other selection procedures including orthogonal matching pursuit, non-negative least squares, and marginal screening+Lasso.

We study the robustness properties of $\ell_1$ norm minimization for the classical linear regression problem with a given design matrix and contamination restricted to the dependent variable. We perform a fine error analysis of the $\ell_1$ estimator for measurements errors consisting of outliers coupled with noise. We introduce a new estimation technique resulting from a regularization of $\ell_1$ minimization by inf-convolution with the $\ell_2$ norm. Concerning robustness to large outliers, the proposed estimator keeps the breakdown point of the $\ell_1$ estimator, and reduces to least squares when there are not outliers. We present a globally convergent forward-backward algorithm for computing our estimator and some numerical experiments confirming its theoretical properties.

In this paper, we address the challenging problem of selecting tuning parameters for high-dimensional sparse regression. We propose a simple and computationally efficient method, called path thresholding (PaTh), that transforms any tuning parameter-dependent sparse regression algorithm into an asymptotically tuning-free sparse regression algorithm. More specifically, we prove that, as the problem size becomes large (in the number of variables and in the number of observations), PaTh performs accurate sparse regression, under appropriate conditions, without specifying a tuning parameter. In finite-dimensional settings, we demonstrate that PaTh can alleviate the computational burden of model selection algorithms by significantly reducing the search space of tuning parameters.

We consider the high-dimensional sparse linear regression problem of accurately estimating a sparse vector using a small number of linear measurements that are contaminated by noise. It is well known that the standard cadre of computationally tractable sparse regression algorithms---such as the Lasso, Orthogonal Matching Pursuit (OMP), and their extensions---perform poorly when the measurement matrix contains highly correlated columns. To address this shortcoming, we develop a simple greedy algorithm, called SWAP, that iteratively swaps variables until convergence. SWAP is surprisingly effective in handling measurement matrices with high correlations. In fact, we prove that SWAP outputs the true support, the locations of the non-zero entries in the sparse vector, under a relatively mild condition on the measurement matrix. Furthermore, we show that SWAP can be used to boost the performance of any sparse regression algorithm. We empirically demonstrate the advantages of SWAP by comparing it with several state-of-the-art sparse regression algorithms.

In this paper, a new descriptor selection method for selecting an optimal combination of important descriptors of sulfonamide derivatives data, named self tuned reweighted sampling (STRS), is developed. descriptors are defined as the descriptors with large absolute coefficients in a multivariate linear regression model such as partial least squares(PLS). In this study, the absolute values of regression coefficients of PLS model are used as an index for evaluating the importance of each descriptor Then, based on the importance level of each descriptor, STRS sequentially selects N subsets of descriptors from N Monte Carlo (MC) sampling runs in an iterative and competitive manner. In each sampling run, a fixed ratio (e.g. 80%) of samples is first randomly selected to establish a regresson model. Next, based on the regression coefficients, a two-step procedure including rapidly decreasing function (RDF) based enforced descriptor selection and self tuned sampling (STS) based competitive descriptor selection is adopted to select the important descriptorss. After running the loops, a number of subsets of descriptors are obtained and root mean squared error of cross validation (RMSECV) of PLS models established with subsets of descriptors is computed. The subset of descriptors with the lowest RMSECV is considered as the optimal descriptor subset. The performance of the proposed algorithm is evaluated by sulfanomide derivative dataset. The results reveal an good characteristic of STRS that it can usually locate an optimal combination of some important descriptors which are interpretable to the biologically of interest. Additionally, our study shows that better prediction is obtained by STRS when compared to full descriptor set PLS modeling, Monte Carlo uninformative variable elimination (MC-UVE).

We study the task of retrieving relevant experiments given a query experiment. By experiment, we mean a collection of measurements from a set of `covariates' and the associated `outcomes'. While similar experiments can be retrieved by comparing available `annotations', this approach ignores the valuable information available in the measurements themselves. To incorporate this information in the retrieval task, we suggest employing a retrieval metric that utilizes probabilistic models learned from the measurements. We argue that such a metric is a sensible measure of similarity between two experiments since it permits inclusion of experiment-specific prior knowledge. However, accurate models are often not analytical, and one must resort to storing posterior samples which demands considerable resources. Therefore, we study strategies to select informative posterior samples to reduce the computational load while maintaining the retrieval performance. We demonstrate the efficacy of our approach on simulated data with simple linear regression as the models, and real world datasets.

Can we make Bayesian posterior MCMC sampling more efficient when faced with very large datasets? We argue that computing the likelihood for N datapoints in the Metropolis-Hastings (MH) test to reach a single binary decision is computationally inefficient. We introduce an approximate MH rule based on a sequential hypothesis test that allows us to accept or reject samples with high confidence using only a fraction of the data required for the exact MH rule. While this method introduces an asymptotic bias, we show that this bias can be controlled and is more than offset by a decrease in variance due to our ability to draw more samples per unit of time.