The concept of a random process has been recently extended to graph signals, whereby random graph processes are a class of multivariate stochastic processes whose coefficients are matrices with a \textit{graph-topological} structure. The system identification problem of a random graph process therefore revolves around determining its underlying topology, or mathematically, the graph shift operators (GSOs) i.e. an adjacency matrix or a Laplacian matrix. In the same work that introduced random graph processes, a \textit{batch} optimization method to solve for the GSO was also proposed for the random graph process based on a \textit{causal} vertex-time autoregressive model. To this end, the online version of this optimization problem was proposed via the framework of adaptive filtering. The modified stochastic gradient projection method was employed on the regularized least squares objective to create the filter. The recursion is divided into 3 regularized sub-problems to address issues like multi-convexity, sparsity, commutativity and bias. A discussion on convergence analysis is also included. Finally, experiments are conducted to illustrate the performance of the proposed algorithm, from traditional MSE measure to successful recovery rate regardless correct values, all of which to shed light on the potential, the limit and the possible research attempt of this work.
Lehigh University（理海大学）；Xiamen University of Technology（厦门理工学院）
Extreme multi-label text classification (XMTC) is a task for tagging a given text with the most relevant labels from an extremely large label set. We propose a novel deep learning method called APLC-XLNet. Our approach fine-tunes the recently released generalized autoregressive pretrained model (XLNet) to learn a dense representation for the input text. We propose Adaptive Probabilistic Label Clusters (APLC) to approximate the cross entropy loss by exploiting the unbalanced label distribution to form clusters that explicitly reduce the computational time. Our experiments, carried out on five b…
We constuct a sequential adaptive procedure for estimating the autoregressive function at a given point in nonparametric autoregression models with Gaussian noise. We make use of the sequential kernel estimators. The optimal adaptive convergence rate is given as well as the upper bound for the minimax risk.
Autoregressive generative models can estimate complex continuous data distributions, like trajectory rollouts in an RL environment, image intensities, and audio. Most state-of-the-art models discretize continuous data into several bins and use categorical distributions over the bins to approximate the continuous data distribution. The advantage is that the categorical distribution can easily express multiple modes and are straightforward to optimize. However, such approximation cannot express sharp changes in density without using significantly more bins, making it parameter inefficient. We pr…
We construct efficient robust truncated sequential estimators for the pointwise estimation problem in nonparametric autoregression models with smooth coefficients. For Gaussian models we propose an adaptive procedure based on the constructed sequential estimators. The minimax nonadaptive and adaptive convergence rates are established. It turns out that in this case these rates are the same as for regression models.
California Institute of Technology（加州理工学院）；Purdue University（普渡大学）
Autoregressive exogenous (ARX) systems are the general class of input-output dynamical systems used for modeling stochastic linear dynamical systems (LDS) including partially observable LDS such as LQG systems. In this work, we study the problem of system identification and adaptive control of unknown ARX systems. We provide finite-time learning guarantees for the ARX systems under both open-loop and closed-loop data collection. Using these guarantees, we design adaptive control algorithms for unknown ARX systems with arbitrary strongly convex or convex quadratic regulating costs. Under strong…
Conditional autoregressive (CAR) models are commonly used to capture spatial correlation in areal unit data, and are typically specified as a prior distribution for a set of random effects, as part of a hierarchical Bayesian model. The spatial correlation structure induced by these models is determined by geographical adjacency, so that two areas have correlated random effects if they share a common border. However, this correlation structure is too simplistic for real data, which are instead likely to include sub-regions of strong correlation as well as locations at which the response exhibit…
Linear Vector AutoRegressive (VAR) models where the innovations could be unconditionally heteroscedastic and serially dependent are considered. The volatility structure is deterministic and quite general, including breaks or trending variances as special cases. In this framework we propose Ordinary Least Squares (OLS), Generalized Least Squares (GLS) and Adaptive Least Squares (ALS) procedures. The GLS estimator requires the knowledge of the time-varying variance structure while in the ALS approach the unknown variance is estimated by kernel smoothing with the outer product of the OLS residual…
Online Graph Topology Learning via Time-Vertex Adaptive Filters: From Theory to Cardiac Fibrillation
Department of Electrical and Electronic Engineering, Imperial College London（帝国理工学院伦敦校区电子与电气工程系）；National Heart and Lung Institute, Imperial College London（帝国理工学院伦敦校区国家心脏和肺研究所）
Exponential mixing properties of nonlinear functional autoregressive models
Graduate School of Engineering Science, The University of Osaka（大阪大学工学研究科）；Center for Advanced Integrated Intelligence Research, RIKEN（理化学研究所先进集成智能研究中心）
The volatility modeling for autoregressive univariate time series is considered. A benchmark approach is the stationary ARCH model of Engle (1982). Motivated by real data evidence, processes with non constant unconditional variance and ARCH effects have been recently introduced. We take into account such possible non stationarity and propose simple testing procedures for ARCH effects. Adaptive McLeod and Li's portmanteau and ARCH-LM tests for checking for second order dynamics are provided. The standard versions of these tests, commonly used by practitioners, suppose constant unconditional var…
Multivariate Self-Exciting Threshold Autoregressive Models with eXogenous Input
European Doctorate in Economics–Erasmus Mundus (EDEEM) Centre d’Économie de la Sorbonne (CES) - CNRS : UMR8174 - Université Paris I - Panthéon Sorbonne Università Ca’Foscari of Venice, Department of Economics（欧洲经济学博士-伊拉斯谟世界（EDEEM）索邦经济中心（CES）- 法国国家科学研究中心：联合研究单位8174 - 巴黎第一大学 - 巴黎先贤祠-索邦大学 威尼斯卡福斯卡里大学，经济学系）
Center for Mathematical Modeling Universidad de Chile Email
Kernel adaptive filters, a class of adaptive nonlinear time-series models, are known by their ability to learn expressive autoregressive patterns from sequential data. However, for trivial monotonic signals, they struggle to perform accurate predictions and at the same time keep computational complexity within desired boundaries. This is because new observations are incorporated to the dictionary when they are far from what the algorithm has seen in the past. We propose a novel approach to kernel adaptive filtering that compares new observations against dictionary samples in terms of their uni…
We propose a parsimonious spatiotemporal model for time series data on a spatial grid. Our model is capable of dealing with high-dimensional time series data that may be collected at hundreds of locations and capturing the spatial non-stationarity. In essence, our model is a vector autoregressive model that utilizes the spatial structure to achieve parsimony of autoregressive matrices at two levels. The first level ensures the sparsity of the autoregressive matrices using a lagged-neighborhood scheme. The second level performs a spatial clustering of the non-zero autoregressive coefficients su…
We study the nonparametric covariance estimation of a stationary Gaussian field X observed on a regular lattice. In the time series setting, some procedures like AIC are proved to achieve optimal model selection among autoregressive models. However, there exists no such equivalent results of adaptivity in a spatial setting. By considering collections of Gaussian Markov random fields (GMRF) as approximation sets for the distribution of X, we introduce a novel model selection procedure for spatial fields. For all neighborhoods m in a given collection M, this procedure first amounts to computing …
Dynamic model averaging (DMA) combines the forecasts of a large number of dynamic linear models (DLMs) to predict the future value of a time series. The performance of DMA critically depends on the appropriate choice of two forgetting factors. The first of these controls the speed of adaptation of the coefficient vector of each DLM, while the second enables time variation in the model averaging stage. In this paper we develop a novel, adaptive dynamic model averaging (ADMA) methodology. The proposed methodology employs a stochastic optimisation algorithm that sequentially updates the forgettin…
