We propose a general modeling and algorithmic framework for discrete structure recovery that can be applied to a wide range of problems. Under this framework, we are able to study the recovery of clustering labels, ranks of players, and signs of regression coefficients from a unified perspective. A simple iterative algorithm is proposed for discrete structure recovery, which generalizes methods including Lloyd's algorithm and the iterative feature matching algorithm. A linear convergence result for the proposed algorithm is established in this paper under appropriate abstract conditions on stochastic errors and initialization. We illustrate our general theory by applying it on three representative problems: clustering in Gaussian mixture model, approximate ranking, and sign recovery in compressed sensing, and show that minimax rate is achieved in each case.

We consider the optimization problem: x arg max x X f (x), (1) where x is a d-dimensional vector and X is a compact (closed and bounded) set in R d . Given limited budget B, BO aims to search for the optimal x by itera-tively updating a surrogate model of f (x), where this surrogate is used to find the next design to evaluate. Typically, in BO, the surrogate model is a Gaussian process ( GP), due to its Bayesian interpretation and uncertainty quantification capability (see Rasmussen (2003) for more information). More specifically, given the current data D k, BO aims to determine the next informative sampling point x k 1 by solving the auxiliary problem: x k 1: x arg max x X Q k(x; D k). (2) where Q k is a acquisition/utility function that only involves evaluating the surrogate and not the expensive objective function f . Typically, evaluation of acquisition function is relatively cheap. The rationale is to seek design points that produce maximum increment of the objective function. After Eq. (2) is solved, the iterative algorithm proceeds by augmenting the current training data D k with a new observation to obtain D k 1 D k { (x k 1,y k 1) }. Popular choices of acquisition functions are entropy search (ES) (Hennig and Schuler, 2012), predictive entropy search (PES) (Hern andez-Lobato et al., 2014) and expectation improvement (EI) (Lam et al., 2016). All aforementioned functions exploit myopic strategies and ignore the future information.

Temporal prediction is critical for making intelligent and robust decisions in complex dynamic environments. Motion prediction needs to model the inherently uncertain future which often contains multiple potential outcomes, due to multi-agent interactions and the latent goals of others. Towards these goals, we introduce a probabilistic framework that efficiently learns latent variables to jointly model the multi-step future motions of agents in a scene. Our framework is data-driven and learns semantically meaningful latent variables to represent the multimodal future, without requiring explicit labels. Using a dynamic attention-based state encoder, we learn to encode the past as well as the future interactions among agents, efficiently scaling to any number of agents. Finally, our model can be used for planning via computing a conditional probability density over the trajectories of other agents given a hypothetical rollout of the 'self' agent. We demonstrate our algorithms by predicting vehicle trajectories of both simulated and real data, demonstrating the state-of-the-art results on several vehicle trajectory datasets.

Biomedical data are widely accepted in developing prediction models for identifying a specific tumor, drug discovery and classification of human cancers. However, previous studies usually focused on different classifiers, and overlook the class imbalance problem in real-world biomedical datasets. There are a lack of studies on evaluation of data pre-processing techniques, such as resampling and feature selection, on imbalanced biomedical data learning. The relationship between data pre-processing techniques and the data distributions has never been analysed in previous studies. This article mainly focuses on reviewing and evaluating some popular and recently developed resampling and feature selection methods for class imbalance learning. We analyse the effectiveness of each technique from data distribution perspective. Extensive experiments have been done based on five classifiers, four performance measures, eight learning techniques across twenty real-world datasets. Experimental results show that: (1) resampling and feature selection techniques exhibit better performance using support vector machine (SVM) classifier. However, resampling and Feature Selection techniques perform poorly when using C4.5 decision tree and Linear discriminant analysis classifiers; (2) for datasets with different distributions, techniques such as Random undersampling and Feature Selection perform better than other data pre-processing methods with T Location-Scale distribution when using SVM and KNN (K-nearest neighbours) classifiers. Random oversampling outperforms other methods on Negative Binomial distribution using Random Forest classifier with lower level of imbalance ratio; (3) Feature Selection outperforms other data pre-processing methods in most cases, thus, Feature Selection with SVM classifier is the best choice for imbalanced biomedical data learning.

This paper proposes a new method for determining similarity and anomalies between time series, most practically effective in large collections of (likely related) time series, with a particular focus on measuring distances between structural breaks within such a collection. We consolidate and generalise a class of semi-metric distance measures, which we term MJ distances. Experiments on simulated data demonstrate that our proposed family of distances uncover similarity within collections of time series more effectively than measures such as the Hausdorff and Wasserstein metrics. Although our class of distances do not necessarily satisfy the triangle inequality requirement of a metric, we analyse the transitivity properties of respective distance matrices in various contextual scenarios. There, we demonstrate a trade-off between robust performance in the presence of outliers, and the triangle inequality property. We show in experiments using real data that the contrived scenarios that severely violate the transitivity property rarely exhibit themselves in real data; instead, our family of measures satisfies all the properties of a metric most of the time. We illustrate three ways of analysing the distance and similarity matrices, via eigenvalue analysis, hierarchical clustering, and spectral clustering. The results from our hierarchical and spectral clustering experiments on simulated data demonstrate that the Hausdorff and Wasserstein metrics may lead to erroneous inference as to which time series are most similar with respect to their structural breaks, while our semi-metrics provide an improvement.

Communication and privacy are two critical concerns in distributed learning. Many existing works treat these concerns separately. In this work, we argue that a natural connection exists between methods for communication reduction and privacy preservation in the context of distributed machine learning. In particular, we prove that Count Sketch, a simple method for data stream summarization, has inherent differential privacy properties. Using these derived privacy guarantees, we propose a novel sketch-based framework (DiffSketch) for distributed learning, where we compress the transmitted messages via sketches to simultaneously achieve communication efficiency and provable privacy benefits. Our evaluation demonstrates that DiffSketch can provide strong differential privacy guarantees (e.g., $\varepsilon$= 1) and reduce communication by 20-50x with only marginal decreases in accuracy. Compared to baselines that treat privacy and communication separately, DiffSketch improves absolute test accuracy by 5%-50% while offering the same privacy guarantees and communication compression.

A main task in data analysis is to organize data points into coherent groups or clusters. The stochastic block model is a probabilistic model for the cluster structure. This model prescribes different probabilities for the presence of edges within a cluster and between different clusters. We assume that the cluster assignments are known for at least one data point in each cluster. In such a partially labeled stochastic block model, clustering amounts to estimating the cluster assignments of the remaining data points. We study total variation minimization as a method for this clustering task. We implement the resulting clustering algorithm as a highly scalable message passing protocol. We also provide a condition on the model parameters such that total variation minimization allows for accurate clustering.

Neural network based models for collaborative filtering have started to gain attention recently. One branch of research is based on using deep generative models to model user preferences where variational autoencoders were shown to produce state-of-the-art results. However, there are some potentially problematic characteristics of the current variational autoencoder for CF. The first is the too simplistic prior that VAEs incorporate for learning the latent representations of user preference. The other is the model's inability to learn deeper representations with more than one hidden layer for each network. Our goal is to incorporate appropriate techniques to mitigate the aforementioned problems of variational autoencoder CF and further improve the recommendation performance. Our work is the first to apply flexible priors to collaborative filtering and show that simple priors (in original VAEs) may be too restrictive to fully model user preferences and setting a more flexible prior gives significant gains. We experiment with the VampPrior, originally proposed for image generation, to examine the effect of flexible priors in CF. We also show that VampPriors coupled with gating mechanisms outperform SOTA results including the Variational Autoencoder for Collaborative Filtering by meaningful margins on 2 popular benchmark datasets (MovieLens & Netflix).

Thanks to its generality, RL has been widely studied in many areas, such as control theory, game theory, operations research, multi-agent systems, machine learning, artificial intelligence, and statistics [23]. In recent years, combining with deep learning, RL has demonstrated its great potential in addressing challenging practical control and optimization problems [17, 21]. Among all possible algorithms, the temporal difference (TD) learning has arguably become one of the most popular RL algorithms so far, which is further dominated by the celebrated TD(0) algorithm [22]. TD learning provides an iterative process to update an estimate of the so-termed value function v π(s) with respect to a given policy π based on temporally successive samples. Dealing with a finite state space, the classical version of the TD(0) algorithm adopts a tabular representation for v π(s), which stores entry-wise value estimates on a per state basis. J. Sun and Q. Yang are with the College of Control Science and Engineering, and the State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, China. G. Wang and G. B. Giannakis are with the Digital Technology Center and the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455, USA. Z. Yang is with the Department of Mechanical and Energy Engineering, Southern University of Science and Technology, Shenzhen, China.

Learning with rejection (LWR) allows development of machine learning systems with the ability to discard low confidence decisions generated by a prediction model. That is, just like human experts, LWR allows machine models to abstain from generating a prediction when reliability of the prediction is expected to be low. Several frameworks for this learning with rejection have been proposed in the literature. However, most of them work for classification problems only and regression with rejection has not been studied in much detail. In this work, we present a neural framework for LWR based on a generalized meta-loss function that involves simultaneous training of two neural network models: a predictor model for generating predictions and a rejecter model for deciding whether the prediction should be accepted or rejected. The proposed framework can be used for classification as well as regression and other related machine learning tasks. We have demonstrated the applicability and effectiveness of the method on synthetically generated data as well as benchmark datasets from UCI machine learning repository for both classification and regression problems. Despite being simpler in implementation, the proposed scheme for learning with rejection has shown to perform at par or better than previously proposed methods. Furthermore, we have applied the method to the problem of hurricane intensity prediction from satellite imagery. Significant improvement in performance as compared to conventional supervised methods shows the effectiveness of the proposed scheme in real-world regression problems.