In our previous works (1, 2), we have shown its potential in cluster analysis. Combinations of the IT structure with the Semi-Supervised learning concept (3), Rodriguez and Laio's "Decision Graph" (4), and Frey and Dueck's "Affinity Propagation" (AP) (5), have resulted in effective cluster analysis methods. For example, based on the IT structure, the application scope of AP was extended from spherical to nonspherical cluster detection (2). In this paper, we will show another potential of the IT structure: nonlinear dimensionality reduction, for which an effective combination is made with the "isometric mapping" (Isomap) proposed by Tenenbaum et al (6). Isomap is a simple and effective dimensionality reduction method which extends the application scope of multidimensional scaling (MDS) from linear to nonlinear structure. It contains three steps: first construct the K-nearest-neighborhood (KNN) graph, then compute the graph distances (the shortest path distances in the neighborhood graph) and lastly compute the low-dimensional embedding by classical MDS. In effect, the constructed KNN graph for data points is unfolded in the low-dimensional Euclidean space, which is effective especially for preserving in the embedding the topology relationship of data points on manifolds. The crux of the success for Isomap is that it takes as the input for classical MDS the graph distances, instead of the straight-line Euclidian ones, for all pairs of data points.

This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows mitigating the drawbacks of the high extrinsic dimensionality while avoiding the algorithm to evaluate points giving redundant information. It also alleviates constraints on bound selection for the embedded domain, thus improving the robustness, as illustrated with a test case with 25 variables and intrinsic dimension 6.

Recently, there has been focus on penalized log-likelihood covariance estimation for sparse inverse covariance (precision) matrices. The penalty is responsible for inducing sparsity, and a very common choice is the convex $l_1$ norm. However, the best estimator performance is not always achieved with this penalty. The most natural sparsity promoting "norm" is the non-convex $l_0$ penalty but its lack of convexity has deterred its use in sparse maximum likelihood estimation. In this paper we consider non-convex $l_0$ penalized log-likelihood inverse covariance estimation and present a novel cyclic descent algorithm for its optimization. Convergence to a local minimizer is proved, which is highly non-trivial, and we demonstrate via simulations the reduced bias and superior quality of the $l_0$ penalty as compared to the $l_1$ penalty.

In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in rewards in addition to maximizing a standard criterion. Variance related risk measures are among the most common risk-sensitive criteria in finance and operations research. However, optimizing many such criteria is known to be a hard problem. In this paper, we consider both discounted and average reward Markov decision processes. For each formulation, we first define a measure of variability for a policy, which in turn gives us a set of risk-sensitive criteria to optimize. For each of these criteria, we derive a formula for computing its gradient. We then devise actor-critic algorithms that operate on three timescales - a TD critic on the fastest timescale, a policy gradient (actor) on the intermediate timescale, and a dual ascent for Lagrange multipliers on the slowest timescale. In the discounted setting, we point out the difficulty in estimating the gradient of the variance of the return and incorporate simultaneous perturbation approaches to alleviate this. The average setting, on the other hand, allows for an actor update using compatible features to estimate the gradient of the variance. We establish the convergence of our algorithms to locally risk-sensitive optimal policies. Finally, we demonstrate the usefulness of our algorithms in a traffic signal control application.

We propose an improved LASSO estimation technique based on Stein-rule. We shrink classical LASSO estimator using preliminary test, shrinkage, and positive-rule shrinkage principle. Simulation results have been carried out for various configurations of correlation coefficients ($r$), size of the parameter vector ($\beta$), error variance ($\sigma^2$) and number of non-zero coefficients ($k$) in the model parameter vector. Several real data examples have been used to demonstrate the practical usefulness of the proposed estimators. Our study shows that the risk ordering given by LSE $>$ LASSO $>$ Stein-type LASSO $>$ Stein-type positive rule LASSO, remains the same uniformly in the divergence parameter $\Delta^2$ as in the traditional case.

We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the de-biasing technique with the composite quantile function to construct an estimator that is asymptotically normal. Hence it can be used to construct valid confidence intervals and conduct hypothesis tests. Our estimator is robust and does not require the existence of first or second moment of the noise distribution. It also preserves efficiency in the sense that the worst case efficiency loss is less than 30\% compared to the square-loss-based de-biased Lasso estimator. In many cases our estimator is close to or better than the latter, especially when the noise is heavy-tailed. Our de-biasing procedure does not require solving the $L_1$-penalized composite quantile regression. Instead, it allows for any first-stage estimator with desired convergence rate and empirical sparsity. The paper also provides new proof techniques for developing theoretical guarantees of inferential procedures with non-smooth loss functions. To establish the main results, we exploit the local curvature of the conditional expectation of composite quantile loss and apply empirical process theories to control the difference between empirical quantities and their conditional expectations. Our results are established under weaker assumptions compared to existing work on inference for high-dimensional quantile regression. Furthermore, we consider a high-dimensional simultaneous test for the regression parameters by applying the Gaussian approximation and multiplier bootstrap theories. We also study distributed learning and exploit the divide-and-conquer estimator to reduce computation complexity when the sample size is massive. Finally, we provide empirical results to verify the theory.

This paper presents a general vector-valued reproducing kernel Hilbert spaces (RKHS) framework for the problem of learning an unknown functional dependency between a structured input space and a structured output space. Our formulation encompasses both Vector-valued Manifold Regularization and Co-regularized Multi-view Learning, providing in particular a unifying framework linking these two important learning approaches. In the case of the least square loss function, we provide a closed form solution, which is obtained by solving a system of linear equations. In the case of Support Vector Machine (SVM) classification, our formulation generalizes in particular both the binary Laplacian SVM to the multi-class, multi-view settings and the multi-class Simplex Cone SVM to the semi-supervised, multi-view settings. The solution is obtained by solving a single quadratic optimization problem, as in standard SVM, via the Sequential Minimal Optimization (SMO) approach. Empirical results obtained on the task of object recognition, using several challenging datasets, demonstrate the competitiveness of our algorithms compared with other state-of-the-art methods.

The increase of dementia patients is one of the problems caused by aged population not only in Japan but in many developed countries. As cognitive enhancement method for prevention of dementia, coimagination method is proposed: designed group conversation whose themes are selected from recent topics for training of recent episodic memory functions, since recent episodic memory functions decline before the onset of dementia. It is known that people who are disuse particular cognitive functions have higher risk of loosing the functions. However, the participants of the conversations supported by coimagination method sometimes refer to past topics rather than recent topics. The method is required for analyzing whether the topics deal with recent or past for effective intervention, which has not been established. Purpose of this study is to propose method for analyzing the temporal characteristics of the topics during conversation. Mental time travel, or chronesthesia, is the ability to be aware of one’s present, past or future which has been evolved in humans in particular. In order to estimate the mental time of the speaker from topics during conversation supported by coimagination method, we propose mental time estimation method by analyzing tenses and senses. We applied the method to the scripts of conversation supported by coimagination method. The result suggests that it’s possible to estimate mental time from analysis of the topics in conversation. The ratio of the reference of past, present and future of each speaker was enumerated. The individual differences of the tendencies were demonstrated as the ratios.

We introduce the concept of Hypoelliptic Diffusion Maps (HDM), a framework generalizing Diffusion Maps in the context of manifold learning and dimensionality reduction. Standard non-linear dimensionality reduction methods (e.g., LLE, ISOMAP, Laplacian Eigenmaps, Diffusion Maps) focus on mining massive data sets using weighted affinity graphs; Orientable Diffusion Maps and Vector Diffusion Maps enrich these graphs by attaching to each node also some local geometry. HDM likewise considers a scenario where each node possesses additional structure, which is now itself of interest to investigate. Virtually, HDM augments the original data set with attached structures, and provides tools for studying and organizing the augmented ensemble. The goal is to obtain information on individual structures attached to the nodes and on the relationship between structures attached to nearby nodes, so as to study the underlying manifold from which the nodes are sampled. In this paper, we analyze HDM on tangent bundles, revealing its intimate connection with sub-Riemannian geometry and a family of hypoelliptic differential operators. In a later paper, we shall consider more general fibre bundles.

Latent tree graphical models are a popular class of latent variable models, where a probability distribution involving observed and hidden variables are Markovian on a tree. Due to the fact that structure of (observable and hidden) variable interactions are approximated as a tree, inference on latent trees can be carried out exactly through a simple belief propagation [Pea88]. Therefore, latent tree graphical models present a good tradeoff between model accuracy and computational complexity. They are applicable in many domains, where it is natural to expect hierarchical or sequential relationships among the variables (through a hidden-Markov model). For instance, latent tree models have been employed for phylogenetic reconstruction [DEKM99], object recognition [CTW12a, CTW12b] and human pose estimation [WL13]. In this paper, we use latent tree model for discovering a hierarchy among diseases based on comorbidities exhibited in patients' health records, i.e. co-occurrences of diseases in patients. In particular, two large healthcare datasets of 30K and 1.6M patients are used to build the latent disease trees, where clinically meaningful disease clusters are identified as shown in fig 3 and 4. The task of learning a latent tree models consists of two parts: learning the tree structure, and learning the parameters of the tree. There exist many challenges which prohibit efficient or guaranteed learning of the latent tree graphical model, which will be addressed in this paper: 1. The location and the number of latent variables are hidden and the marginalized graph over the observable variables no longer conforms to a tree structure.