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强化学习中的平稳性检验与变点检测AI 解读

We consider reinforcement learning (RL) in possibly nonstationary environments. Many existing RL algorithms in the literature rely on the stationarity assumption that requires the state transition and reward functions to be constant over time. However, this assumption is restrictive in practice and is likely to be violated in a number of applications, including traffic signal control, robotics and mobile health. In this paper, we develop a model-free test to assess the…

稳健最窄显著区间搜索：中位数多重变点推断AI 解读

We propose Robust Narrowest Significance Pursuit (RNSP), a methodology for detecting localized regions in data sequences which each must contain a change-point in the median, at a prescribed global significance level.RNSP works by fitting the postulated constant model over many regions of the data using a new signmultiresolution sup-norm-type loss, and greedily identifying the shortest intervals on which the constancy is significantly violated.By working with the signs of…

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.…

最窄显著区间搜寻：线性模型中的多变点推断AI 解读

We propose Narrowest Significance Pursuit (NSP), a general and flexible methodology for automatically detecting localised regions in data sequences which each must contain a change-point (understood as an abrupt change in the parameters of an underlying linear model), at a prescribed global significance level. NSP works with a wide range of distributional assumptions on the errors, and guarantees important stochastic bounds which directly yield exact desired coverage…

大型协方差矩阵中的多重结构断点检测AI 解读

This article studies multiple structural breaks in large contemporaneous covariance matrices of highdimensional time series satisfying an approximate factor model.The breaks in the second-order moment structure of the common components are due to sudden changes in either factor loadings or covariance of latent factors, requiring appropriate transformation of the factor models to facilitate estimation of the (transformed) common factors and factor loadings via the classical…

多重变点及类似变点特征的最窄超阈值检测AI 解读

Summary We propose a new, generic and flexible methodology for non-parametric function estimation, in which we first estimate the number and locations of any features that may be present in the function and then estimate the function parametrically between each pair of neighbouring detected features. Examples of features handled by our methodology include change points in the piecewise constant signal model, kinks in the piecewise linear signal model and other similar…

尾部贪心的自下而上数据分解与快速多变点检测AI 解读

This article proposes a “tail-greedy”, bottom-up transform for one-dimensional data, which results in a nonlinear but conditionally orthonormal, multiscale decomposition of the data with respect to an adaptively chosen unbalanced Haar wavelet basis. The “tail-greediness” of the decomposition algorithm, whereby multiple greedy steps are taken in a single pass through the data, both enables fast computation and makes the algorithm applicable in the problem of consistent…

高维时间序列的多变点检测与因子分析AI 解读

We propose the first comprehensive treatment of high-dimensional time series factor models with multiple change-points in their second-order structure. We operate under the most flexible definition of piecewise stationarity, and estimate the number and locations of change-points consistently as well as identifying whether they originate in the common or idiosyncratic components. Through the use of wavelets, we transform the problem of change-point detection in the…

通过稀疏化二元分割检测高维时间序列的多个变点AI 解读

Summary Time series segmentation, which is also known as multiple-change-point detection, is a well-established problem. However, few solutions have been designed specifically for high dimensional situations. Our interest is in segmenting the second-order structure of a high dimensional time series. In a generic step of a binary segmentation algorithm for multivariate time series, one natural solution is to combine cumulative sum statistics obtained from local periodograms…

用于多重变点检测的随机二元分割AI 解读

We propose a new technique, called wild binary segmentation (WBS), for consistent estimation of the number and locations of multiple change-points in data. We assume that the number of change-points can increase to infinity with the sample size. Due to a certain random localisation mechanism, WBS works even for very short spacings between the change-points and/or very small jump magnitudes, unlike standard binary segmentation. On the other hand, despite its use of…

通过倾斜相关进行高维变量选择AI 解读

Summary The paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations. High dimensionality of the data brings in many complications, such as (possibly spurious) high correlations between the variables, which result in marginal correlation being unreliable as a measure of association between the variables and the response. We propose a new way of measuring the contribution of each…

利用随机小波表示一致分类非平稳时间序列AI 解读

Consider the situation when we have training data containing many time series having known group membership and testing data with unknown group membership. The goals are to find timescale features (using training data) that can best separate the groups, and to use these highly discriminant features to classify test data. We propose a method for classification using a bias-corrected nondecimated wavelet transform. Wavelets are ideal for identifying highly discriminant local…

时变 ARCH 模型中的归一化最小二乘估计AI 解读

We investigate the time-varying ARCH (tvARCH) process. It is shown that it can be used to describe the slow decay of the sample autocorrelations of the squared returns often observed in financial time series, which warrants the further study of parameter estimation methods for the model. Since the parameters are changing over time, a successful estimator needs to perform well for small samples. We propose a kernel normalized-least-squares (kernel-NLS) estimator which has a…

非参数函数估计的非平衡Haar技术AI 解读

The discrete unbalanced Haar (UH) transform is a decomposition of one-dimensional data with respect to an orthonormal Haar-like basis where jumps in the basis vectors do not necessarily occur in the middle of their support. We introduce a multiscale procedure for estimation in Gaussian noise that consists of three steps: a UH transform, thresholding of the decomposition coefficients, and the inverse UH transform. We show that our estimator is mean squared consistent with…

用于局部平稳波动率估计的 Haar–Fisz 技术AI 解读

We consider a locally stationary model for financial log-returns whereby the returns are independent and the volatility is a piecewise-constant function with jumps of an unknown number and locations, defined on a compact interval to enable a meaningful estimation theory. We demonstrate that the model explains well the common characteristics of log-returns. We propose a new wavelet thresholding algorithm for volatility estimation in this model, in which Haar wavelets are…

演化小波谱的 Haar–Fisz 估计AI 解读

Summary We propose a new ‘Haar–Fisz’ technique for estimating the time-varying, piecewise constant local variance of a locally stationary Gaussian time series. We apply our technique to the estimation of the spectral structure in the locally stationary wavelet model. Our method combines Haar wavelets and the variance stabilizing Fisz transform. The resulting estimator is mean square consistent, rapidly computable and easy to implement, and performs well in practice. We also…

小波回归中跨尺度阈值的参数化建模AI 解读

We propose a parametric wavelet thresholding procedure for estimation in the ‘function plus independent, identically distributed Gaussian noise’ model. To reflect the decreasing sparsity of wavelet coefficients from finer to coarser scales, our thresholds also decrease. They retain the noise-free reconstruction property while being lower than the universal threshold, and are jointly parameterised by a single scalar parameter. We show that our estimator achieves near-optimal…