论文检索

高维张量时间序列的 CP 因子分解与双重投影迭代AI 解读

Abstract We adopt the canonical polyadic (CP) decomposition to model high-dimensional tensor time series. Our primary goal is to identify and estimate the factor loadings in the CP decomposition. We propose a one-pass estimation procedure through standard eigen-analysis for a matrix constructed based on the serial dependence structure of the data. The asymptotic properties of the proposed estimator are established under a general setting as long as the factor loading vectors…

超越均值：无限均值自回归条件持续时间的极限理论与检验AI 解读

Abstract Integrated autoregressive conditional duration (ACD) models serve as counterparts to integrated generalized autoregressive conditional heteroskedastic models used for financial returns. However, despite their resemblance, asymptotic theory for ACD is still incomplete. Central challenges arise from the facts that (i) integrated ACD processes imply durations with infinite expectation and (ii) conventional asymptotic approaches break down due to the randomness in the…

用于变点检测的在线核 CUSUM 方法AI 解读

Abstract We present a computationally efficient online kernel Cumulative Sum method for change-point detection that utilizes the maximum over a set of kernel statistics to account for the unknown change-point location. Our approach exhibits increased sensitivity to small changes compared to existing kernel-based change-point detection methods, including the Scan-B statistic, corresponding to a non-parametric Shewhart chart-type procedure. We provide accurate analytic…

ART：具有有限样本保证的分布无关、模型无关变点检测AI 解读

Abstract We introduce ART, a distribution-free and model-agnostic framework for changepoint analysis with finite-sample guarantees. ART transforms independent observations into real-valued scores via a symmetric function; under the null hypothesis of no changepoint these scores are exchangeable. Ranking and aggregating the scores yields test statistics whose null distribution is known exactly from the permutation law of ranks, enabling exact finite-sample Type I error…

Markov 状态切换扩散的精确贝叶斯推断AI 解读

Abstract We develop the first exact Bayesian methodology for the problem of inference in discretely observed regime switching diffusions. Switching diffusion models extend ordinary diffusions by allowing for jumps in instantaneous drift and volatility. The jumps are driven by a latent, continuous-time Markov switching process. We address the problem through an MCMC and an MCEM algorithm that target the exact posterior of diffusion parameters and the latent regime process.…

带人工动态的自组织状态空间模型AI 解读

Abstract We consider the problem of performing parameter and state inference in a state-space model (SSM) parametrized by a static parameter θ. A popular idea to address this problem consists of incorporating θ in the state of the system and allowing its time evolution, modelled as a Markov chain (θt)t≥1. This proxy model defines a so-called self-organizing SSM (SO-SSM) to which one may apply standard particle filters. However, the practical implementation of this idea in a…

基于二阶特征的局部平稳时间序列结构分类AI 解读

Abstract Time series classification is crucial for numerous scientific and engineering applications. In this article, we present a numerically efficient, practically competitive, and theoretically rigorous classification method for distinguishing between two classes of locally stationary time series based on their time-domain, second-order characteristics. Our approach builds on the autoregressive approximation for locally stationary time series, imposes no requirement on…

含局部测量误差的非平稳函数型时间序列结构变化推断AI 解读

Abstract We study the problem of detecting and localizing change points for a general class of locally stationary functional time series. To accommodate the nonstationarity and other possible complex features, such as discontinuous trajectories, and heterogeneous partial measurement error of contemporary functional data, we propose methods that do not rest on the preprocessing techniques of presmoothing and dimension-reduction, which would be less accurate without the…

序贯变点定位的检测后推断AI 解读

Abstract This article addresses a fundamental but largely unexplored challenge in sequential changepoint analysis: conducting inference following a detected change. We develop a very general framework to construct confidence sets for the unknown changepoint using only the data observed up to a data-dependent stopping time at which an arbitrary sequential detection algorithm declares a change. Our framework is nonparametric, making no assumption on the composite postchange…

朱福康与郭祥宇对《流形假说的统计探索》的讨论AI 解读

We congratulate the authors on their introducing theoretical explanations and applications of the manifold hypothesis in statistics based on the latent metric space model. Using the continuity of the mean correlation kernel in the latent metric space model, the authors employ a feature map to connect the metric space of latent variables to a Euclidean space. This links the geometric and statistical properties of the model. Furthermore, the smoothness of the mean correlation…

基于稀疏张量分解的高维时间序列谱变点估计AI 解读

Abstract Multivariate time series may be subject to partial structural changes over certain frequency band, for instance, in neuroscience. We study the change point detection problem with high-dimensional time series, within the framework of frequency domain. The overarching goal is to locate all change points and delineate which series are activated by the change, over which frequencies. In practice, the number of activated series per change and frequency could span from a…

基于分块极大值估计量的自助法AI 解读

Abstract The block maxima method is a standard approach for analyzing the extremal behaviour of a potentially multivariate time series. It has recently been found that the classical approach based on disjoint block maxima may be universally improved by considering sliding block maxima instead. However, the asymptotic variance formula for estimators based on sliding block maxima involves an integral over the covariance of a certain family of multivariate extreme value…

利用计算几何联系进行在线多元变点检测AI 解读

Abstract The increasing volume of data streams poses significant computational challenges for detecting changepoints online. Likelihood-based methods are effective, but a naive sequential implementation becomes impractical online due to high computational costs. We develop an online algorithm that exactly calculates the likelihood ratio test for a single changepoint in p-dimensional data streams by leveraging a fascinating connection with computational geometry. This…

Abstract For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be exactly sparse segment-wise, which enables many existing methods to estimate the parameters locally via ℓ1-regularized maximum-likelihood-type estimation and then contrast them for change point detection. Contrary to this common practice, we show that the exact sparsity of neither regression parameters nor their differences, a.k.a. differential…

动态张量的 CP 因子模型AI 解读

Abstract Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach, in a form similar to tensor CANDECOMP/PARAFAC (CP) decomposition, to the analysis of high-dimensional dynamic tensor time series. As the loading vectors are uniquely defined but not necessarily orthogonal, it is significantly…

Rajendra Bhansali 对《因果模型的参数化与模拟》的讨论意见AI 解读

Contribution: My own introduction to the subject area of this paper is through the notion of Granger causality, a topic which has attracted much attention in time series analysis and related disciplines, including signal processing. The authors have proposed a new approach to causal models. However, this involves working with full density functions. It seems to me that, from a data analysis point of view, the authors’ approach might be a bit too general, and it might be…

关于“通过深度学习自动检测时间序列变点”讨论的作者回复AI 解读

Detecting change points in data is challenging because of the range of possible types of change and types of behaviour of data when there is no change. Statistically efficient methods for detecting a change will depend on both of these features, and it can be difficult for a practitioner to develop an appropriate detection method for their application of interest. We show how to automatically generate new offline detection methods based on training a neural network. Our…

基于深度学习的时间序列自动变点检测AI 解读

Abstract Detecting change points in data is challenging because of the range of possible types of change and types of behaviour of data when there is no change. Statistically efficient methods for detecting a change will depend on both of these features, and it can be difficult for a practitioner to develop an appropriate detection method for their application of interest. We show how to automatically generate new offline detection methods based on training a neural network.…

van Lieshout 与 Lu 对机器学习概率统计讨论会论文的讨论意见AI 解读

We congratulate Professors Li, Fearnhead, Fryzlewics, and Wang on their fine work that represents classic test statistics for change-point detection as a neural network-based classifier and develops improved offline detection algorithms for historical, labelled data. The paper focuses on real-valued observation vectors in a temporal regression model with training data being either labelled historical data or obtained by simulation from a model. In many applications, though,…

Cribben 与 Anastasiou 对机器学习概率统计讨论会论文的评论AI 解读

We extend our congratulations to the authors for their innovative contribution. Here, we address three key points: change-point labelling, handling imbalanced datasets, and computational complexity. Change-point labelling in datasets has many flaws and challenges. The primary flaw is the subjectivity inherent in the task as it often relies on human judgement. This subjectivity introduces biases and inconsistencies. One challenge is the lack of a universally accepted standard…

Hernando Ombao 对机器学习概率与统计讨论会论文的评论AI 解读

I congratulate the authors for their fundamental contribution that demonstrates how the existing tests for change-points can be represented by a neural network. The major consequence is that with sufficient data, the performance of these neural networks should be at par with these existing tests. This formulation is very insightful and inspired me to revisit the previous work on models for non-stationary time series that use time-localized representations such as wavelets,…

洪永淼、Oliver Linton、孙佳静与朱美婷对机器学习概率与统计讨论会的评论AI 解读

This paper proposes a neural network-based approach for automating offline change-point detection. The authors show that cumulative sum (CUSUM) and generalized CUSUM are a special case of their neural network class. They emphasize misclassification error rates and their theoretical contribution is to establish some elegant results for these under i.i.d. unit variance Gaussian data with a possible change in mean. Their theoretical results outline the conditions on the…

Shakeel Gavioli-Akilagun 对机器学习概率与统计讨论会论文的评论AI 解读

We congratulate the authors for the interesting and thought provoking paper. Lemma 3.2 shows that the generalized likelihood ratio (GLR) test for stability of a linear regression can be viewed as a simple feed forward neural network. However, close inspection of the lemma reveals that the setup rules out several common change point problems. Consider the piecewise polynomial regression: For ξ ’s distributed i.i.d. N(0,1)⁠, the likelihood ratio statistic for a change at…

贝叶斯预测决策综合AI 解读

Abstract Decision-guided perspectives on model uncertainty expand traditional statistical thinking about managing, comparing, and combining inferences from sets of models. Bayesian predictive decision synthesis (BPDS) advances conceptual and theoretical foundations, and defines new methodology that explicitly integrates decision-analytic outcomes into the evaluation, comparison, and potential combination of candidate models. BPDS extends recent theoretical and practical…