Towards Flexible Sparsity-Aware Modeling: Automatic Tensor Rank Learning Using The Generalized Hyperbolic Prior
Zhejiang University（浙江大学）；The University of Hong Kong（香港大学）；Tongji University（同济大学）；Shenzhen Research Institute of Big Data（深圳大数据研究院）；National and Kapodistrian University of Athens（雅典国立卡波迪斯特里安大学）；Aalborg University（奥尔堡大学）
Lei Cheng, Zhongtao Chen, Qingjiang Shi, Yik-Chung Wu, Sergios Theodoridis
Tensor rank learning for canonical polyadic decomposition (CPD) has long been deemed as an essential yet challenging problem. In particular, since the tensor rank controls the complexity of the CPD model, its inaccurate learning would cause overfitting to noise or underfitting to the signal sources, and even destroy the interpretability of model parameters. However, the optimal determination of a tensor rank is known to be a non-deterministic polynomial-time hard (NP-hard) task. Rather than exhaustively searching for the best tensor rank via trial-and-error experiments, Bayesian inference under the Gaussian-gamma prior was introduced in the context of probabilistic CPD modeling, and it was shown to be an effective strategy for automatic tensor rank determination. This triggered flourishing research on other structured tensor CPDs with automatic tensor rank learning. On the other side of the coin, these research works also reveal that the Gaussian-gamma model does not perform well for high-rank tensors and/or low signal-to-noise ratios (SNRs). To overcome these drawbacks, in this paper, we introduce a more advanced generalized hyperbolic (GH) prior to the probabilistic CPD model, which not only includes the Gaussian-gamma model as a special case, but also is more flexible to adapt to different levels of sparsity. Based on this novel probabilistic model, an algorithm is developed under the framework of variational inference, where each update is obtained in a closed-form. Extensive numerical results, using synthetic data and real-world datasets, demonstrate the significantly improved performance of the proposed method in learning both low as well as high tensor ranks even for low SNR cases.
Clustering is an effective technique in data mining to group a set of objects in terms of some attributes. Among various clustering approaches, the family of K-Means algorithms gains popularity due to simplicity and efficiency. However, most of existing K-Means based clustering algorithms cannot deal with outliers well and are difficult to efficiently solve the problem embedded the $L_0$-norm constraint. To address the above issues and improve the performance of clustering significantly, we propose a novel clustering algorithm, named REFCMFS, which develops a $L_{2,1}$-norm robust loss as the …
Motivating Next-Gen Accelerators with Flexible (N:M) Activation Sparsity via Benchmarking Lightweight Post-Training Sparsification Approaches
Applied AI（应用人工智能）；Artificial Intelligence Research Institute（人工智能研究所）；HSE University（俄罗斯高等经济大学）；Sb AI Lab（Sb人工智能实验室）；MWS AI（MWS人工智能）；Yandex；Independent Researcher（独立研究者）
Aston University（阿斯顿大学）；University of Sussex（萨塞克斯大学）；University of Birmingham（伯明翰大学）；Massachusetts Institute of Technology（麻省理工学院）
Ubiquitous linear Gaussian exploratory tools such as principle component analysis (PCA) and factor analysis (FA) remain widely used as tools for: exploratory analysis, pre-processing, data visualization and related tasks. However, due to their rigid assumptions including crowding of high dimensional data, they have been replaced in many settings by more flexible and still interpretable latent feature models. The Feature allocation is usually modelled using discrete latent variables assumed to follow either parametric Beta-Bernoulli distribution or Bayesian nonparametric prior. In this work we …
Sparse models are desirable for many applications across diverse domains as they can perform automatic variable selection, aid interpretability, and provide regularization. When fitting sparse models in a Bayesian framework, however, analytically obtaining a posterior distribution over the parameters of interest is intractable for all but the simplest cases. As a result practitioners must rely on either sampling algorithms such as Markov chain Monte Carlo or variational methods to obtain an approximate posterior. Mean field variational inference is a particularly simple and popular framework t…
The family of location and scale mixtures of Gaussians has the ability to generate a number of flexible distributional forms. It nests as particular cases several important asymmetric distributions like the Generalised Hyperbolic distribution. The Generalised Hyperbolic distribution in turn nests many other well known distributions such as the Normal Inverse Gaussian (NIG) whose practical relevance has been widely documented in the literature. In a multivariate setting, we propose to extend the standard location and scale mixture concept into a so called multiple scaled framework which has the…
Efficient modeling of relational data arising in physical, social, and information sciences is challenging due to complicated dependencies within the data. In this work, we build off of semi-implicit graph variational auto-encoders to capture higher-order statistics in a low-dimensional graph latent representation. We incorporate hyperbolic geometry in the latent space through a Poincare embedding to efficiently represent graphs exhibiting hierarchical structure. To address the naive posterior latent distribution assumptions in classical variational inference, we use semi-implicit hierarchical…
Robust clustering from incomplete data is an important topic because, in many practical situations, real data sets are heavy-tailed, asymmetric, and/or have arbitrary patterns of missing observations. Flexible methods and algorithms for model-based clustering are presented via mixture of the generalized hyperbolic distributions and its limiting case, the mixture of multivariate skew-t distributions. An analytically feasible EM algorithm is formulated for parameter estimation and imputation of missing values for mixture models employing missing at random mechanisms. The proposed methodologies a…
In this paper, we propose the realized Hyperbolic GARCH model for the joint-dynamics of lowfrequency returns and realized measures that generalizes the realized GARCH model of Hansen et al.(2012) as well as the FLoGARCH model introduced by Vander Elst (2015). This model is sufficiently flexible to capture both long memory and asymmetries related to leverage effects. In addition, we will study the strictly and weak stationarity conditions of the model. To evaluate its performance, experimental simulations, using the Monte Carlo method, are made to forecast the Value at Risk (VaR) and the Expect…
University of Science and Technology of China（中国科学技术大学）；meituan（美团）；Sichuan University（四川大学）
Learning hyperbolic embeddings for knowledge graph (KG) has gained increasing attention due to its superiority in capturing hierarchies. However, some important operations in hyperbolic space still lack good definitions, making existing methods unable to fully leverage the merits of hyperbolic space. Specifically, they suffer from two main limitations: 1) existing Graph Convolutional Network (GCN) methods in hyperbolic space rely on tangent space approximation, which would incur approximation error in representation learning, and 2) due to the lack of inner product operation definition in hype…
SlideSparse: Fast and Flexible (2N-2):2N Structured Sparsity
Peking University（北京大学）；South China University of Technology（南方科技大学）；Microsoft Research（微软研究院）；Shanghai Jiao Tong University（上海交通大学）；The Hong Kong University of Science and Technology（香港科技大学）
Sparser, Better, Faster, Stronger: Sparsity Detection for Efficient Automatic Differentiation
BIFOLD – Berlin Institute for the Foundations of Learning and Data（柏林学习与数据基础研究所）；Technical University of Berlin（柏林工业大学）；ENPC（巴黎高科路桥学校）；Institut Polytechnique de Paris（巴黎综合理工学院）；Univ Gustave Eiffel（古斯塔夫·埃菲尔大学）
Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University at Buffalo（布法罗大学）
A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. This success is largely attributed to the GP's analytical tractability, robustness, non-parametric structure, and natural inclusion of uncertainty quantification. Unfortunately, the use of exact GPs is prohibitively expensive for large datasets due to their unfavorable numerical complexity of $O(N^3)$ in computation and $O(N^2)$ in storage. All existing methods addressing this issue utilize some form of approximation -- usually considering subsets of the …
Purdue University（普渡大学）；Lawrence Berkeley Lab（劳伦斯伯克利实验室）；Yahoo! Research（雅虎研究院）；University of Electronic Science and Technology of China（电子科技大学）；University of Cambridge（剑桥大学）
Tensor factorization is a powerful tool to analyse multi-way data. Compared with traditional multi-linear methods, nonlinear tensor factorization models are capable of capturing more complex relationships in the data. However, they are computationally expensive and may suffer severe learning bias in case of extreme data sparsity. To overcome these limitations, in this paper we propose a distributed, flexible nonlinear tensor factorization model. Our model can effectively avoid the expensive computations and structural restrictions of the Kronecker-product in existing TGP formulations, allowing…
Sparsity Hurts: Simple Linear Adapter Can Boost Generalized Category Discovery
School of Computer Science and Engineering, Southeast University（东南大学计算机科学与工程学院）；Key Laboratory of Computer Network and Information Integration (Southeast University), Ministry of Education, China（计算机网络与信息集成重点实验室（东南大学），教育部，中国）
We introduce LL-RNNs (Log-Linear RNNs), an extension of Recurrent Neural Networks that replaces the softmax output layer by a log-linear output layer, of which the softmax is a special case. This conceptually simple move has two main advantages. First, it allows the learner to combat training data sparsity by allowing it to model words (or more generally, output symbols) as complex combinations of attributes without requiring that each combination is directly observed in the training data (as the softmax does). Second, it permits the inclusion of flexible prior knowledge in the form of a prior…
