A regularized risk minimization procedure for regression function estimation is introduced that achieves near optimal accuracy and confidence under general conditions, including heavy-tailed predictor and response variables. The procedure is based on median-of-means tournaments, introduced by the authors in [8]. It is shown that the new procedure outperforms standard regularized empirical risk minimization procedures such as lasso or slope in heavy-tailed problems.

Demanding sparsity in estimated models has become a routine practice in statistics. In many situations, we wish to require that the sparsity patterns attained honor certain problem-specific constraints. Hierarchical sparse modeling (HSM) refers to situations in which these constraints specify that one set of parameters be set to zero whenever another is set to zero. In recent years, numerous papers have developed convex regularizers for this form of sparsity structure, which arises in many areas of statistics including interaction modeling, time series analysis, and covariance estimation. In this paper, we observe that these methods fall into two frameworks, the group lasso (GL) and latent overlapping group lasso (LOG), which have not been systematically compared in the context of HSM. The purpose of this paper is to provide a side-by-side comparison of these two frameworks for HSM in terms of their statistical properties and computational efficiency. We call special attention to GL's more aggressive shrinkage of parameters deep in the hierarchy, a property not shared by LOG. In terms of computation, we introduce a finite-step algorithm that exactly solves the proximal operator of LOG for a certain simple HSM structure; we later exploit this to develop a novel path-based block coordinate descent scheme for general HSM structures. Both algorithms greatly improve the computational performance of LOG. Finally, we compare the two methods in the context of covariance estimation, where we introduce a new sparsely-banded estimator using LOG, which we show achieves the statistical advantages of an existing GL-based method but is simpler to express and more efficient to compute.

There are 2 aspects of this research that are worth highlighting: (1) we showed that micro-structural extra-hippocampal abnormalities are consistent enough across medial temporal lobe epilepsy (TLE) patients that they can be used to predict TLE, and (2) we obtained regularization values for the models trained on this sparse data in an unusual but effective manner. Our input data consisted of 3 different diffusion imaging modalities: mean diffusivity (MD), fractional anisotropy (FA), and mean kurtosis (MK). Predictive models trained with MK proved to be the most accurate: .82 Also, the highest coefficients of these linear models were located within the inferior medial aspect of the temporal lobes. These locations have complex fiber anatomy with many crossings. Diffusion kurtosis imaging (DKI) is more apt than diffusion tensor imaging (DTI) at capturing fiber crossings due to the presence of non-Gaussian water diffusion.

If you haven't heard yet, Data Science is all in Fashion. Courses, posts, and schools are jumping up all around. No withstanding, every time I investigate one of those offerings, I see that a considerable measure of accentuation is put on particular learning algorithms. Obviously, seeing how calculated Deep learning is cool, however once you begin working with Data, you discover that there are different things similarly essential, or perhaps more. I can't generally accuse these courses that concentrate especially on Learning Algorithms.

Wisdom of the crowd, the collective intelligence derived from responses of multiple human or machine individuals to the same questions, can be more accurate than each individual, and improve social decision-making and prediction accuracy. This can also integrate multiple programs or datasets, each as an individual, for the same predictive questions. Crowd wisdom estimates each individual's independent error level arising from their limited knowledge, and finds the crowd consensus that minimizes the overall error. However, previous studies have merely built isolated, problem-specific models with limited generalizability, and mainly for binary (yes/no) responses. Here we show with simulation and real-world data that the crowd wisdom problem is analogous to one-dimensional unsupervised dimension reduction in machine learning. This provides a natural class of crowd wisdom solutions, such as principal component analysis and Isomap, which can handle binary and also continuous responses, like confidence levels, and consequently can be more accurate than existing solutions. They can even outperform supervised-learning-based collective intelligence that is calibrated on historical performance of individuals, e.g. penalized linear regression and random forest. This study unifies crowd wisdom and unsupervised dimension reduction, and thereupon introduces a broad range of highly-performing and widely-applicable crowd wisdom methods. As the costs for data acquisition and processing rapidly decrease, this study will promote and guide crowd wisdom applications in the social and natural sciences, including data fusion, meta-analysis, crowd-sourcing, and committee decision making.

Outlier detection plays an essential role in many data-driven applications to identify isolated instances that are different from the majority. While many statistical learning and data mining techniques have been used for developing more effective outlier detection algorithms, the interpretation of detected outliers does not receive much attention. Interpretation is becoming increasingly important to help people trust and evaluate the developed models through providing intrinsic reasons why the certain outliers are chosen. It is difficult, if not impossible, to simply apply feature selection for explaining outliers due to the distinct characteristics of various detection models, complicated structures of data in certain applications, and imbalanced distribution of outliers and normal instances. In addition, the role of contrastive contexts where outliers locate, as well as the relation between outliers and contexts, are usually overlooked in interpretation. To tackle the issues above, in this paper, we propose a novel Contextual Outlier INterpretation (COIN) method to explain the abnormality of existing outliers spotted by detectors. The interpretability for an outlier is achieved from three aspects: outlierness score, attributes that contribute to the abnormality, and contextual description of its neighborhoods. Experimental results on various types of datasets demonstrate the flexibility and effectiveness of the proposed framework compared with existing interpretation approaches.

Nesterov's accelerated gradient descent (AGD), an instance of the general family of "momentum methods", provably achieves faster convergence rate than gradient descent (GD) in the convex setting. However, whether these methods are superior to GD in the nonconvex setting remains open. This paper studies a simple variant of AGD, and shows that it escapes saddle points and finds a second-order stationary point in $\tilde{O}(1/\epsilon^{7/4})$ iterations, faster than the $\tilde{O}(1/\epsilon^{2})$ iterations required by GD. To the best of our knowledge, this is the first Hessian-free algorithm to find a second-order stationary point faster than GD, and also the first single-loop algorithm with a faster rate than GD even in the setting of finding a first-order stationary point. Our analysis is based on two key ideas: (1) the use of a simple Hamiltonian function, inspired by a continuous-time perspective, which AGD monotonically decreases per step even for nonconvex functions, and (2) a novel framework called improve or localize, which is useful for tracking the long-term behavior of gradient-based optimization algorithms. We believe that these techniques may deepen our understanding of both acceleration algorithms and nonconvex optimization.

We propose a flexible nonparametric regression method for ultrahigh-dimensional data. As a first step, we propose a fast screening method based on the favored smoothing bandwidth of the marginal local constant regression. Then, an iterative procedure is developed to recover both the important covariates and the regression function. Theoretically, we prove that the favored smoothing bandwidth based screening possesses the model selection consistency property.

The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function defined over the nodes of a network. This work presents a versatile kernel-based framework for tackling this inference problem that naturally subsumes and generalizes the reconstruction approaches put forth recently by the signal processing on graphs community. Both the static and the dynamic settings are considered along with effective modeling approaches for addressing real-world problems. The herein analytical discussion is complemented by a set of numerical examples, which showcase the effectiveness of the presented techniques, as well as their merits related to state-of-the-art methods.

Object ranking or "learning to rank" is an important problem in the realm of preference learning. On the basis of training data in the form of a set of rankings of objects represented as feature vectors, the goal is to learn a ranking function that predicts a linear order of any new set of objects. In this paper, we propose a new approach to object ranking based on principles of analogical reasoning. More specifically, our inference pattern is formalized in terms of so-called analogical proportions and can be summarized as follows: Given objects $A,B,C,D$, if object $A$ is known to be preferred to $B$, and $C$ relates to $D$ as $A$ relates to $B$, then $C$ is (supposedly) preferred to $D$. Our method applies this pattern as a main building block and combines it with ideas and techniques from instance-based learning and rank aggregation. Based on first experimental results for data sets from various domains (sports, education, tourism, etc.), we conclude that our approach is highly competitive. It appears to be specifically interesting in situations in which the objects are coming from different subdomains, and which hence require a kind of knowledge transfer.