Abstract: In our physically inspired in-tree (IT) based clustering algorithm and the series after it, there is only one free parameter involved in computing the potential value of each point. In this work, based on the Delaunay Triangulation or its dual Voronoi tessellation, we propose a nonparametric process to compute potential values by the local information. This computation, though nonparametric, is relatively very rough, and consequently, many local extreme points will be generated. However, unlike those gradient-based methods, our ITbased methods are generally insensitive to those local extremes. This positively demonstrates the superiority of these parametric (previous) and nonparametric (in this work) ITbased methods. 1 Introduction In (1), we proposed a physically inspired clustering algorithm, in which an in-tree (IT) structure was first constructed. This IT structure organizes the data points into the clusters with several undesired connections (edges) between them requiring to be removed.

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.

Speech to personal assistants (e.g., reminders, calendar entries, messaging, voice search) is often uttered under cognitive load, causing nonfinal pausing that can result in premature recognition cut-offs. Prior research suggests that prepausal features can discriminate final from nonfinal pauses, but it does not reveal how speakers would behave if given longer to pause. To this end, we collected and compared two elicitation corpora differing in naturalness and task complexity. The Template Corpus (4409 nonfinal pauses) uses keyword-based prompts; the Freeform Corpus (8061 nonfinal pauses) elicits open-ended speech. While nonfinal pauses are longer and twice as frequent in the Freeform data, prepausal feature modelling is roughly equally effective in both corpora. At a response latency of 100 ms, prepausal features modelled by an SVM reduced cut-off rates from 100% to 20% for both corpora. Results have implications for enhancing turn-taking efficiency and naturalness in personal-assistant technology.

We seek to develop a robot that will be capable of teaming with humans to accomplish physical exploration tasks that would not otherwise be possible in dynamic, dangerous environments. For such tasks, a human commander needs to be able to communicate with a robot that moves out of sight and relays information back to the commander. What is the best way to determine how a human commander would interact in a multi-modal spoken dialog with such a robot to accomplish tasks? In this paper, we describe our initial approach to discovering a principled basis for coordinating turn-taking, perception, and navigational behavior of a robot in communication with a commander, by identifying decision phases in dialogs collected in a WoZ framework. We present two types of utterance annotation with examples applied to task-oriented dialog between a human commander and a human ``robot navigator'' who controls the physical robot in a realistic environment similar to expected actual conditions. We discuss core robot capabilities that bear on the robot navigator's ability to take turns while performing a ``find the building doors'' task at hand. The paper concludes with a brief overview of ongoing work to implement these decision phases within an open-source dialog management framework, constructing a task tree specification and dialog control logic for our application domain.