Sparse convex clustering is to cluster observations and conduct variable selection simultaneously in the framework of convex clustering. Although the weighted $L_1$ norm as the regularization term is usually employed in the sparse convex clustering, this increases the dependence on the data and reduces the estimation accuracy if the sample size is not sufficient. To tackle these problems, this paper proposes a Bayesian sparse convex clustering via the idea of Bayesian lasso and global-local shrinkage priors. We introduce Gibbs sampling algorithms for our method using scale mixtures of normals. The effectiveness of the proposed methods is shown in simulation studies and a real data analysis.

Critical incident stages identification and reasonable prediction of traffic incident duration are essential in traffic incident management. In this paper, we propose a traffic incident duration prediction model that simultaneously predicts the impact of the traffic incidents and identifies the critical groups of temporal features via a multi-task learning framework. First, we formulate a sparsity optimization problem that extracts low-level temporal features based on traffic speed readings and then generalizes higher level features as phases of traffic incidents. Second, we propose novel constraints on feature similarity exploiting prior knowledge about the spatial connectivity of the road network to predict the incident duration. The proposed problem is challenging to solve due to the orthogonality constraints, non-convexity objective, and non-smoothness penalties. We develop an algorithm based on the alternating direction method of multipliers (ADMM) framework to solve the proposed formulation. Extensive experiments and comparisons to other models on real-world traffic data and traffic incident records justify the efficacy of our model.

The graph-based semi-supervised label propagation algorithm has delivered impressive classification results. However, the estimated soft labels typically contain mixed signs and noise, which cause inaccurate predictions due to the lack of suitable constraints. Moreover, available methods typically calculate the weights and estimate the labels in the original input space, which typically contains noise and corruption. Thus, the en-coded similarities and manifold smoothness may be inaccurate for label estimation. In this paper, we present effective schemes for resolving these issues and propose a novel and robust semi-supervised classification algorithm, namely, the tri-ple-matrix-recovery-based robust auto-weighted label propa-gation framework (ALP-TMR). Our ALP-TMR introduces a triple matrix recovery mechanism to remove noise or mixed signs from the estimated soft labels and improve the robustness to noise and outliers in the steps of assigning weights and pre-dicting the labels simultaneously. Our method can jointly re-cover the underlying clean data, clean labels and clean weighting spaces by decomposing the original data, predicted soft labels or weights into a clean part plus an error part by fitting noise. In addition, ALP-TMR integrates the au-to-weighting process by minimizing reconstruction errors over the recovered clean data and clean soft labels, which can en-code the weights more accurately to improve both data rep-resentation and classification. By classifying samples in the recovered clean label and weight spaces, one can potentially improve the label prediction results. The results of extensive experiments demonstrated the satisfactory performance of our ALP-TMR.

This paper studies the theoretical predictive properties of classes of forecast combination methods. The study is motivated by the recently developed Bayesian framework for synthesizing predictive densities: Bayesian predictive synthesis. A novel strategy based on continuous time stochastic processes is proposed and developed, where the combined predictive error processes are expressed as stochastic differential equations, evaluated using Ito's lemma. We show that a subclass of synthesis functions under Bayesian predictive synthesis, which we categorize as non-linear synthesis, entails an extra term that "corrects" the bias from misspecification and dependence in the predictive error process, effectively improving forecasts. Theoretical properties are examined and shown that this subclass improves the expected squared forecast error over any and all linear combination, averaging, and ensemble of forecasts, under mild conditions. We discuss the conditions for which this subclass outperforms others, and its implications for developing forecast combination methods. A finite sample simulation study is presented to illustrate our results.

Graph representation learning is to learn universal node representations that preserve both node attributes and structural information. The derived node representations can be used to serve various downstream tasks, such as node classification and node clustering. When a graph is heterogeneous, the problem becomes more challenging than the homogeneous graph node learning problem. Inspired by the emerging information theoretic-based learning algorithm, in this paper we propose an unsupervised graph neural network Heterogeneous Deep Graph Infomax (HDGI) for heterogeneous graph representation learning. We use the meta-path structure to analyze the connections involving semantics in heterogeneous graphs and utilize graph convolution module and semantic-level attention mechanism to capture local representations. By maximizing local-global mutual information, HDGI effectively learns high-level node representations that can be utilized in downstream graph-related tasks. Experiment results show that HDGI remarkably outperforms state-of-the-art unsupervised graph representation learning methods on both classification and clustering tasks. By feeding the learned representations into a parametric model, such as logistic regression, we even achieve comparable performance in node classification tasks when comparing with state-of-the-art supervised end-to-end GNN models.

We propose a new nonlinear factorization model for graphs that are with topological structures, and optionally, node attributes. This model is based on a pseudometric called Gromov-Wasserstein (GW) discrepancy, which compares graphs in a relational way. It estimates observed graphs as GW barycenters constructed by a set of atoms with different weights. By minimizing the GW discrepancy between each observed graph and its GW barycenter-based estimation, we learn the atoms and their weights associated with the observed graphs. The model achieves a novel and flexible factorization mechanism under GW discrepancy, in which both the observed graphs and the learnable atoms can be un-aligned and with different sizes. We design an effective approximate algorithm for learning this Gromov-Wasserstein factorization (GWF) model, unrolling loopy computations as stacked modules and computing gradients with backpropaga-tion. The stacked modules can be with two different architectures, which correspond to the proximal point algorithm (PP A) and Bregman alternating direction method of multipliers (BADMM), respectively. Experiments show that our model obtains encouraging results on clustering graphs. Introduction As an important methodology for machine learning, factorization models explore intrinsic structures of high-dimensional observations explicitly, which have been widely used in many learning tasks, e.g., data clustering (Ng, Jordan, and Weiss 2002), dimensionality reduction (Cand es et al. 2011), recommendation systems (Wang and Blei 2011), etc. In particular, factorization models decompose high-dimensional observations into a set of atoms under specific criteria and achieve their latent representations accordingly.

However, unsupervised clustering remains one of the most fundamental challenges in machine learning because of high dimensionality of data and high complexities of their hidden structures. Long-established approaches for unsupervised clustering including K-means [15] and Gaussian Mixture Model (GMM) [3] are still the building blocks for numerous applications due to their efficiency and simplicity. However, their distance metrics are limited to data space, making them ineffective for high-dimensional data such as images. Therefore, considerable efforts have been put into obtaining a good feature embedding of data, usually of low dimensionality, for effective clustering [37]. However, the representation obtained by standalone data embedding typically can-Tian Han is the corresponding author not capture the latent structure and variation of the observed data which may be ineffective for clustering. We believe the good representation for clustering should also be able to compactly represent the observed data distribution to encode all necessary characteristics of the observation. Deep generative models (a.k.a the generator models) have shown great promise in learning latent representations for high-dimensional signals such as images and videos [32, 24, 11]. Generator models parameterized by deep neural networks specify a nonlinear mapping from latent variables to observed data.

November 20, 2019 A BSTRACT This paper presents a model that uses the information that sellers publish in real estate market websites to predict whether a property has higher or lower price than the average price of its similar properties. The model learns the correlation between price and information (text descriptions and features) of real estate properties through automatic identification of latent semantic content given by a machine learning model based on doc2vec and xgboost. The proposed model was evaluated with a data set of 57,516 publications of real estate properties collected from 2016 to 2018 of Bogot a city. Results show that the accuracy of a classifier that involves text descriptions is slightly higher than a classifier that only uses features of the real estate properties, as text descriptions tends to contain detailed information about the property. K eywords housing price prediction · real estate property · machine learning · doc2vec · xgboost 1 Introduction A fairly popular way for property sellers to advertise a property for sale is through a real estate market website which guarantees many more possible buyers than just the street for sale sign.

Background: Overweight and obesity are an increasing phenomenon worldwide. Predicting future overweight or obesity early in the childhood reliably could enable a successful intervention by experts. While a lot of research has been done using explanatory modeling methods, capability of machine learning, and predictive modeling, in particular, remain mainly unexplored. In predictive modeling models are validated with previously unseen examples, giving a more accurate estimate of their performance and generalization ability in real-life scenarios. Objective: To find and review existing overweight or obesity research from the perspective of employing childhood data and predictive modeling methods. Methods: The initial phase included bibliographic searches using relevant search terms in PubMed, IEEE database and Google Scholar. The second phase consisted of iteratively searching references of potential studies and recent research that cite the potential studies. Results: Eight research articles and three review articles were identified as relevant for this review. Conclusions: Prediction models with high performance either have a relatively short time period to predict or/and are based on late childhood data. Logistic regression is currently the most often used method in forming the prediction models. In addition to child's own weight and height information, maternal weight status or body mass index was often used as predictors in the models.

A BSTRACT Recent advances in deep learning theory have evoked the study of generalizabil-ity across different local minima of deep neural networks (DNNs). While current work focused on either discovering properties of good local minima or developing regularization techniques to induce good local minima, no approach exists that can tackle both problems. We achieve these two goals successfully in a unified manner. Specifically, based on the Fisher information we propose a metric both strongly indicative of generalizability of local minima and effectively applied as a practical regularizer. We provide theoretical analysis including a generalization bound and empirically demonstrate the success of our approach in both capturing and improving the generalizability of DNNs. Experiments are performed on CIFAR-10 and CIFAR-100 for various network architectures. 1 I NTRODUCTION Recently, there has been a surge in the interest of acquiring a theoretical understanding over deep neural network's behavior. Breakthroughs have been made in characterizing the optimization process, showing that learning algorithms such as stochastic gradient descent (SGD) tend to end up in one of the many local minima which have close-to-zero training loss (Choromanska et al., 2015; Dauphin et al., 2014; Kawaguchi, 2016; Nguyen & Hein, 2018; Du et al., 2018). It is, therefore, natural to ask two closely related questions: (a) What kind of local minima can generalize better? To our knowledge, existing work focused only on one of the two questions. For the "what" question, various definitions of "flatness/sharpness" have been introduced and analyzed (Keskar et al., 2017; Neyshabur et al., 2018; 2017; Wu et al., 2017; Liang et al., 2017).