Joint Active Learning with Feature Selection via CUR Matrix Decomposition
University of Electronic Science and Technology of China（电子科技大学）；Youedata（优易数据）；East China Normal University（华东师范大学）；Baidu Search（百度搜索）；Shanghai Jiao Tong University（上海交通大学）；Nanjing University of Information Science and Technology（南京信息工程大学）；Georgia Institute of Technology（佐治亚理工学院）
This paper presents an unsupervised learning approach for simultaneous sample and feature selection, which is in contrast to existing works which mainly tackle these two problems separately. In fact the two tasks are often interleaved with each other: noisy and high-dimensional features will bring adverse effect on sample selection, while informative or representative samples will be beneficial to feature selection. Specifically, we propose a framework to jointly conduct active learning and feature selection based on the CUR matrix decomposition. From the data reconstruction perspective, both the selected samples and features can best approximate the original dataset respectively, such that the selected samples characterized by the features are highly representative. In particular, our method runs in one-shot without the procedure of iterative sample selection for progressive labeling. Thus, our model is especially suitable when there are few labeled samples or even in the absence of supervision, which is a particular challenge for existing methods. As the joint learning problem is NP-hard, the proposed formulation involves a convex but non-smooth optimization problem. We solve it efficiently by an iterative algorithm, and prove its global convergence. Experimental results on publicly available datasets corroborate the efficacy of our method compared with the state-of-the-art.
University of Virginia（弗吉尼亚大学）；University of Minnesota（明尼苏达大学）
Feature selection by maximizing high-order mutual information between the selected feature vector and a target variable is the gold standard in terms of selecting the best subset of relevant features that maximizes the performance of prediction models. However, such an approach typically requires knowledge of the multivariate probability distribution of all features and the target, and involves a challenging combinatorial optimization problem. Recent work has shown that any joint Probability Mass Function (PMF) can be represented as a naive Bayes model, via Canonical Polyadic (tensor rank) Dec…
The problem of simultaneous column and row subset selection is addressed in this paper. The column space and row space of a matrix are spanned by its left and right singular vectors, respectively. However, the singular vectors are not within actual columns/rows of the matrix. In this paper, an iterative approach is proposed to capture the most structural information of columns/rows via selecting a subset of actual columns/rows. This algorithm is referred to as two-way spectrum pursuit (TWSP) which provides us with an accurate solution for the CUR matrix decomposition. TWSP is applicable in a w…
In this work, we study non-parametric estimation of joint probabilities of a given set of discrete and continuous random variables from their (empirically estimated) 2D marginals, under the assumption that the joint probability could be decomposed and approximated by a mixture of product densities/mass functions. The problem of estimating the joint probability density function (PDF) using semi-parametric techniques such as Gaussian Mixture Models (GMMs) is widely studied. However such techniques yield poor results when the underlying densities are mixtures of various other families of distribu…
Recently, there has been a trend to combine independent component analysis and canonical polyadic decomposition (ICA-CPD) for an enhanced robustness for the computation of CPD, and ICA-CPD could be further converted into CPD of a 5th-order partially symmetric tensor, by calculating the eigenmatrices of the 4th-order cumulant slices of a trilinear mixture. In this study, we propose a new 5th-order CPD algorithm constrained with partial symmetry based on joint diagonalization. As the main steps involved in the proposed algorithm undergo no updating iterations for the loading matrices, it is much…
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）
Matrix decomposition is a popular and fundamental approach in machine learning and data mining. It has been successfully applied into various fields. Most matrix decomposition methods focus on decomposing a data matrix from one single source. However, it is common that data are from different sources with heterogeneous noise. A few of matrix decomposition methods have been extended for such multi-view data integration and pattern discovery. While only few methods were designed to consider the heterogeneity of noise in such multi-view data for data integration explicitly. To this end, we propos…
Joint Projection Learning and Tensor Decomposition Based Incomplete Multi-view Clustering
Nanjing University（南京大学）；Nanjing Institute of Agricultural Mechanization, Ministry of Agriculture and Rural Affairs（农业农村部南京农业机械化研究所）；Nanjing University of Science and Technology（南京理工大学）
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Apple Inc.（苹果公司）
Inverse rendering is the problem of decomposing an image into its intrinsic components, i.e. albedo, normal and lighting. To solve this ill-posed problem from single image, state-of-the-art methods in shape from shading mostly resort to supervised training on all the components on either synthetic or real datasets. Here, we propose a new self-supervised training paradigm that 1) reduces the need for full supervision on the decomposition task and 2) takes into account the relighting task. We introduce new self-supervised loss terms that leverage the consistencies between multi-lit images (image…
East China Normal University（华东师范大学）；The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））；Shenzhen Institute of Artificial Intelligence and Robotics for Society（深圳人工智能与机器人研究院）
Non-stationarity is one thorny issue in cooperative multi-agent reinforcement learning (MARL). One of the reasons is the policy changes of agents during the learning process. Some existing works have discussed various consequences caused by non-stationarity with several kinds of measurement indicators. This makes the objectives or goals of existing algorithms are inevitably inconsistent and disparate. In this paper, we introduce a novel notion, the $δ$-measurement, to explicitly measure the non-stationarity of a policy sequence, which can be further proved to be bounded by the KL-divergence of…
Shaping Initial State Prevents Modality Competition in Multi-modal Fusion: A Two-stage Scheduling Framework via Fast Partial Information Decomposition
Institute of Medical Technology, Peking University Health Science Center（北京大学人民医院医学技术研究所）；National Institute of Health Data Science（国家健康数据科学研究院）；State Key Laboratory of General Artificial Intelligence, Peking University（北京大学通用人工智能国家重点实验室）；Wangxuan Institute of Computer Technology, Peking University（北京大学王轩计算机技术研究所）
Offline Multi-agent Reinforcement Learning via Sequential Score Decomposition
School of Data Science, The Chinese University of Hong Kong, Shenzhen, China（香港中文大学（深圳）数据科学学院）；School of Computer Science, Tongji University, Shanghai, China（同济大学计算机科学学院）；Vector Institute（向量研究所）
University of California Riverside（加州大学河滨分校）；Snap Inc.（Snap公司）
Distinguishing between misinformation and real information is one of the most challenging problems in today's interconnected world. The vast majority of the state-of-the-art in detecting misinformation is fully supervised, requiring a large number of high-quality human annotations. However, the availability of such annotations cannot be taken for granted, since it is very costly, time-consuming, and challenging to do so in a way that keeps up with the proliferation of misinformation. In this work, we are interested in exploring scenarios where the number of annotations is limited. In such scen…
Decomposition for Bayesian Networks: Local and Parallel Inference
School of Mathematics and Statistics and KLAS, Northeast Normal University（数学与统计学学院及KLAS，东北师范大学）；College of Mathematics and System Sciences, Xinjiang University（数学与系统科学学院，新疆大学）；Institute of Statistics and Data Science, Xinjiang University of Finance and Economics（统计与数据科学学院，新疆财经大学）
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；IBM T.J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Two-dimensional embeddings remain the dominant approach to visualize high dimensional data. The choice of embeddings ranges from highly non-linear ones, which can capture complex relationships but are difficult to interpret quantitatively, to axis-aligned projections, which are easy to interpret but are limited to bivariate relationships. Linear project can be considered as a compromise between complexity and interpretability, as they allow explicit axes labels, yet provide significantly more degrees of freedom compared to axis-aligned projections. Nevertheless, interpreting the axes direction…
KU Leuven（鲁汶大学）；University of Piraeus（比雷埃夫斯大学）；KU Leuven Kulak（鲁汶大学科特赖克校区）；Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
Data fusion refers to the joint analysis of multiple datasets which provide complementary views of the same task. In this preprint, the problem of jointly analyzing electroencephalography (EEG) and functional Magnetic Resonance Imaging (fMRI) data is considered. Jointly analyzing EEG and fMRI measurements is highly beneficial for studying brain function because these modalities have complementary spatiotemporal resolution: EEG offers good temporal resolution while fMRI is better in its spatial resolution. The fusion methods reported so far ignore the underlying multi-way nature of the data in …
The StarCraft II Multi-Agent Challenge (SMAC) was created to be a challenging benchmark problem for cooperative multi-agent reinforcement learning (MARL). SMAC focuses exclusively on the problem of StarCraft micromanagement and assumes that each unit is controlled individually by a learning agent that acts independently and only possesses local information; centralized training is assumed to occur with decentralized execution (CTDE). To perform well in SMAC, MARL algorithms must handle the dual problems of multi-agent credit assignment and joint action evaluation. This paper introduces a new a…
Explicit encoding of group actions in deep features makes it possible for convolutional neural networks (CNNs) to handle global deformations of images, which is critical to success in many vision tasks. This paper proposes to decompose the convolutional filters over joint steerable bases across the space and the group geometry simultaneously, namely a rotation-equivariant CNN with decomposed convolutional filters (RotDCF). This decomposition facilitates computing the joint convolution, which is proved to be necessary for the group equivariance. It significantly reduces the model size and compu…
Assigning Distinct Roles to Quantized and Low-Rank Matrices Toward Optimal Weight Decomposition
Department of Computer Science, Yonsei University（yonsei大学计算机科学系）；Department of Artificial Intelligence, Yonsei University（yonsei大学人工智能系）；Department of Electronic & Electrical Convergence Engineering, Hongik University（hongik大学电子与电气融合工程系）
University of California, Los Angeles（加州大学洛杉矶分校）；University of Texas at Arlington（德克萨斯大学阿灵顿分校）
Low rank tensor approximation is a fundamental tool in modern machine learning and data science. In this paper, we study the characterization, perturbation analysis, and an efficient sampling strategy for two primary tensor CUR approximations, namely Chidori and Fiber CUR. We characterize exact tensor CUR decompositions for low multilinear rank tensors. We also present theoretical error bounds of the tensor CUR approximations when (adversarial or Gaussian) noise appears. Moreover, we show that low cost uniform sampling is sufficient for tensor CUR approximations if the tensor has an incoherent…
