We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those at the remaining ones under a group penalty. We show that the proposed estimator can be computed by a fast convex optimization algorithm. We show that as the sample size increases, the estimated regression coefficients and the correct graphical structure are correctly estimated with probability tending to one. By extensive simulations, we show the superiority of the proposed method over comparable procedures. We apply the technique on two real datasets. The first one is to identify gene and protein networks showing up in cancer cell lines, and the second one is to reveal the connections among different industries in the US. 1 2 Introduction

This paper argues that there has not been enough discussion in the field of applications of Gaussian Process for the fast moving consumer goods industry. Yet, this technique can be important as it e.g., can provide automatic feature relevance determination and the posterior mean can unlock insights on the data. Significant challenges are the large size and high dimensionality of commercial data at a point of sale. The study reviews approaches in the Gaussian Processes modeling for large data sets, evaluates their performance on commercial sales and shows value of this type of models as a decision-making tool for management.

We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a latent variable that is used to modulate the covariance function over the training data. We show how our approach can be used to model multi-modal and non-stationary processes. We exemplify the approach on a set of synthetic data and provide results on real data from motion capture and geostatistics.

Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite number of loss functions. The present paper proposes a Riemannian stochastic quasi-Newton algorithm with variance reduction (R-SQN-VR). The key challenges of averaging, adding, and subtracting multiple gradients are addressed with notions of retraction and vector transport. We present convergence analyses of R-SQN-VR on both non-convex and retraction-convex functions under retraction and vector transport operators. The proposed algorithm is evaluated on the Karcher mean computation on the symmetric positive-definite manifold and the low-rank matrix completion on the Grassmann manifold. In all cases, the proposed algorithm outperforms the state-of-the-art Riemannian batch and stochastic gradient algorithms.

The random dot product graph (RDPG) is an independent-edge random graph that is analytically tractable and, simultaneously, either encompasses or can successfully approximate a wide range of random graphs, from relatively simple stochastic block models to complex latent position graphs. In this survey paper, we describe a comprehensive paradigm for statistical inference on random dot product graphs, a paradigm centered on spectral embeddings of adjacency and Laplacian matrices. We examine the analogues, in graph inference, of several canonical tenets of classical Euclidean inference: in particular, we summarize a body of existing results on the consistency and asymptotic normality of the adjacency and Laplacian spectral embeddings, and the role these spectral embeddings can play in the construction of single- and multi-sample hypothesis tests for graph data. We investigate several real-world applications, including community detection and classification in large social networks and the determination of functional and biologically relevant network properties from an exploratory data analysis of the Drosophila connectome. We outline requisite background and current open problems in spectral graph inference.

We extend the discussion on machine learning one step further and focus on predictive analysis offered in the ML domain. Prediction builds on classification and clustering techniques discussed previously and uses pattern detection and similarity features in data to estimate the future outcome. This is particularly relevant to finance where the ability of data groups to predict the values of less-liquid instruments is of high interest. We demonstrate the prediction using CDS data and show the application of non-regression models as superior methods for predictive analysis. Classification and clustering which we discussed in previous installments naturally extends into another field of data mining - prediction.

Connected vehicle technology is foreseen to play an important role in reducing the number of traffic accidents while being one of the main enabling components for autonomous driving. One of the application of such connection is to provide accurate information about the road condition such as friction level to drivers or the intelligent systems controlling the car. Road surface friction can be defined as the grip between car tyre and underlying surface. During winter times when the temperature decreases dramatically, friction level reduces substantially, which can increase the risk of car accidents. Studies indicate that road conditions such as surface temperature, type of road, and structure of the road sides play an important role in the measured friction level, and some of these conditions can vary significantly within short distances under specific weather situations. Road friction prediction based on the past sensor measurements available in the cars, e.g., temperature and sun light, has advantages of being independent of the road structure and surrounding infrastructure. Intelligent forecast systems rely on the availability of high quality data in order to allow their multiple actors to make correct decisions in diverse traffic situations. These systems have the potential to increase the safety of roads users by means of the timely sharing of road-related information. With the advances in car-to-car communication technology, today, Volvo cars are equipped with slippery road condition warning system to improve road safety and traffic flow.

Most popular word embedding techniques involve implicit or explicit factorization of a word co-occurrence based matrix into low rank factors. In this paper, we aim to generalize this trend by using numerical methods to factor higher-order word co-occurrence based arrays, or \textit{tensors}. We present four word embeddings using tensor factorization and analyze their advantages and disadvantages. One of our main contributions is a novel joint symmetric tensor factorization technique related to the idea of coupled tensor factorization. We show that embeddings based on tensor factorization can be used to discern the various meanings of polysemous words without being explicitly trained to do so, and motivate the intuition behind why this works in a way that doesn't with existing methods. We also modify an existing word embedding evaluation metric known as Outlier Detection [Camacho-Collados and Navigli, 2016] to evaluate the quality of the order-$N$ relations that a word embedding captures, and show that tensor-based methods outperform existing matrix-based methods at this task. Experimentally, we show that all of our word embeddings either outperform or are competitive with state-of-the-art baselines commonly used today on a variety of recent datasets. Suggested applications of tensor factorization-based word embeddings are given, and all source code and pre-trained vectors are publicly available online.

We introduce the speculate-correct method to derive error bounds for local classifiers. Using it, we show that k-nearest neighbor classifiers, in spite of their famously (fractured decision boundaries, have exponential error bounds (k) with O lnn)/n error bound range for n in-sample examples. Keywords: nearest neighbors, statistical learning, supervised learning, error bounds, generalization 2000 MSC: 62G99, 2000 MSC: 68Q32, 2000 MSC: 62M99 1. Introduction Local classifiers use only a small subset of their examples to classify each input. The best-known local classifier is the nearest neighbor classifier. To classify an example, a k-nearest neighbor (k-nn) classifier uses a majority vote over the k in-sample examples closest to the example. We assume k is odd, and we assume binary classification.

We propose a method for hand pose estimation based on a deep regressor trained on two different kinds of input. Raw depth data is fused with an intermediate representation in the form of a segmentation of the hand into parts. This intermediate representation contains important topological information and provides useful cues for reasoning about joint locations. The mapping from raw depth to segmentation maps is learned in a semi/weakly-supervised way from two different datasets: (i) a synthetic dataset created through a rendering pipeline including densely labeled ground truth (pixelwise segmentations); and (ii) a dataset with real images for which ground truth joint positions are available, but not dense segmentations. Loss for training on real images is generated from a patch-wise restoration process, which aligns tentative segmentation maps with a large dictionary of synthetic poses. The underlying premise is that the domain shift between synthetic and real data is smaller in the intermediate representation, where labels carry geometric and topological meaning, than in the raw input domain. Experiments on the NYU dataset show that the proposed training method decreases error on joints over direct regression of joints from depth data by 15.7%.