One of the critical pieces of the self-driving puzzle is understanding the surroundings of a self-driving vehicle (SDV) and predicting how these surroundings will change in the near future. To address this task we propose MultiXNet, an end-to-end approach for detection and motion prediction based directly on lidar sensor data. This approach builds on prior work by handling multiple classes of traffic actors, adding a jointly trained second-stage trajectory refinement step, and producing a multimodal probability distribution over future actor motion that includes both multiple discrete traffic behaviors and calibrated continuous position uncertainties. The method was evaluated on large-scale, real-world data collected by a fleet of SDV s in several cities, with the results indicating that it outperforms existing state-of-the-art approaches.

An important problem in discrete graphical models is the maximum a posterior (MAP) inference problem. Recent research has been focusing on the development of parallel MAP inference algorithm, which scales to graphical models of millions of nodes. In this paper, we introduce a parallel implementation of the recently proposed Bethe-ADMM algorithm using Message Passing Interface (MPI), which allows us to fully utilize the computing power provided by the modern supercomputers with thousands of cores. Experimental results demonstrate that for a broad class of problems, our parallel implementation of Bethe-ADMM scales almost linearly even with thousands of cores.

We consider the problem of estimating sparse precision matrix of Gaussian copula distributions using samples with missing values in high dimensions. Existing approaches, primarily designed for Gaussian distributions, suggest using plugin estimators by disregarding the missing values. In this paper, we propose double plugin Gaussian (DoPinG) copula estimators to estimate the sparse precision matrix corresponding to \emphnon-paranormal distributions. DoPinG uses two plugin procedures and consists of three steps: (1) estimate nonparametric correlations based on observed values, including Kendall’s tau and Spearman’s rho; (2) estimate the non-paranormal correlation matrix; (3) plug into existing sparse precision estimators. We prove that DoPinG copula estimators consistently estimate the non-paranormal correlation matrix at a rate of O(\frac1(1-δ)\sqrt\frac\log pn), where δis the probability of missing values. We provide experimental results to illustrate the effect of sample size and percentage of missing data on the model performance. Experimental results show that DoPinG is significantly better than estimators like mGlasso, which are primarily designed for Gaussian data.

We consider the problem of sparse precision matrix estimation in high dimensions using the CLIME estimator, which has several desirable theoretical properties. We present an inexact alternating direction method of multiplier (ADMM) algorithm for CLIME, and establish rates of convergence for both the objective and optimality conditions. Further, we develop a large scale distributed framework for the computations, which scales to millions of dimensions and trillions of parameters, using hundreds of cores. The proposed framework solves CLIME in column-blocks and only involves elementwise operations and parallel matrix multiplications. We evaluate our algorithm on both shared-memory and distributed-memory architectures, which can use block cyclic distribution of data and parameters to achieve load balance and improve the efficiency in the use of memory hierarchies. Experimental results show that our algorithm is substantially more scalable than state-of-the-art methods and scales almost linearly with the number of cores.

Given their pervasive use, social media, such as Twitter, have become a leading source of breaking news. A key task in the automated identification of such news is the detection of novel documents from a voluminous stream of text documents in a scalable manner. Motivated by this challenge, we introduce the problem of online L1-dictionary learning where unlike traditional dictionary learning, which uses squared loss, the L1-penalty is used for measuring the reconstruction error. We present an efficient online algorithm for this problem based on alternating directions method of multipliers, and establish a sublinear regret bound for this algorithm. Empirical results on news-stream and Twitter data, shows that this online L1-dictionary learning algorithm for novel document detection gives more than an order of magnitude speedup over the previously known batch algorithm, without any significant loss in quality of results. Our algorithm for online L1-dictionary learning could be of independent interest.

We consider the problem of finding a suitable common low dimensional subspace for accurately representing a given set of covariance matrices. With one covariance matrix, this is principal component analysis (PCA). For multiple covariance matrices, we term the problem Common Component Analysis (CCA). While CCA can be posed as a tensor decomposition problem, standard approaches to tensor decompositions have two critical issues: (i) tensor decomposition methods are iterative and rely on the initialization; (ii) for a given level of approximation error, it is difficult to choose a suitable low dimensionality. In this paper, we present a detailed analysis of CCA that yields an effective initialization and iterative algorithms for the problem. The proposed methodology has provable approximation guarantees w.r.t. the global maximum and also allows one to choose the dimensionality for a given level of approximation error. We also establish conditions under which the methodology will achieve the global maximum. We illustrate the effectiveness of the proposed method through extensive experiments on synthetic data as well as on two real stock market datasets, where major financial events can be visualized in low dimensions.