每日简报

向量自回归移动平均模型综述AI 解读

Vector AutoRegressive Moving Average (VARMA) models form a powerful and general model class for analyzing dynamics among multiple time series. While VARMA models encompass the Vector AutoRegressive (VAR) models, their popularity in empirical applications is dominated by the latter. Can this phenomenon be explained fully by the simplicity of VAR models? Perhaps many users of VAR models have not fully appreciated what VARMA models can provide. The goal of this review is to…

CausalFormer：用于时间因果发现的可解释 TransformerAI 解读

Temporal causal discovery is a crucial task aimed at uncovering the causal relations within time series data. The latest temporal causal discovery methods usually train deep learning models on prediction tasks to uncover the causality between time series. They capture causal relations by analyzing the parameters of some components of the trained models, e.g., attention weights and convolution weights. However, this is an incomplete mapping process from the model parameters…

向量自回归模型中的反事实干预AI 解读

Counterfactual reasoning allows us to explore hypothetical scenarios in order to explain the impacts of our decisions. However, addressing such inquires is impossible without establishing the appropriate mathematical framework. In this work, we introduce the problem of counterfactual reasoning in the context of vector autoregressive (VAR) processes. We also formulate the inference of a causal model as a joint regression task where for inference we use both data with and…

从非干预复杂系统中解析干预型动力因果关系AI 解读

Detecting and quantifying causality is a focal topic in the fields of science, engineering, and interdisciplinary studies. However, causal studies on non-intervention systems attract much attention but remain extremely challenging. Delay-embedding technique provides a promising approach. In this study, we propose a framework named Interventional Dynamical Causality (IntDC) in contrast to the traditional Constructive Dynamical Causality (ConDC). ConDC, including Granger…

存在变点与近弱识别时的高效两样本工具变量估计AI 解读

We consider estimation and inference in a linear model with endogenous regressors where the parameters of interest change across two samples. If the first-stage is common, we show how to use this information to obtain more efficient two-sample GMM estimators than the standard split-sample GMM, even in the presence of near-weak instruments. We also propose two tests to detect change points in the parameters of interest, depending on whether the first-stage is common or not.…

贝叶斯时间双聚类及其在多受试者神经科学研究中的应用AI 解读

We consider the problem of analyzing multivariate time series collected on multiple subjects, with the goal of identifying groups of subjects exhibiting similar trends in their recorded measurements over time as well as time-varying groups of associated measurements. To this end, we propose a Bayesian model for temporal biclustering featuring nested partitions, where a time-invariant partition of subjects induces a time-varying partition of measurements. Our approach allows…

线性过程频域因果效应估计的渐近不确定性AI 解读

Structural vector autoregressive (SVAR) processes are commonly used time series models to identify and quantify causal interactions between dynamically interacting processes from observational data. The causal relationships between these processes can be effectively represented by a finite directed process graph - a graph that connects two processes whenever there is a direct delayed or simultaneous effect between them. Recent research has introduced a framework for…

具有 2＋ε 阶矩的椭圆因子模型下高维协方差矩阵的次高斯率估计AI 解读

We study the estimation of high-dimensional covariance matrices under elliptical factor models with 2 + εth moment. For such heavy-tailed data, robust estimators like the Huber-type estimator in Fan, Liu and Wang (2018) can not achieve sub-Gaussian convergence rate. In this paper, we develop an idiosyncratic-projected self-normalization (IPSN) method to remove the effect of heavy-tailed scalar parameter, and propose a robust pilot estimator for the scatter matrix that…

过程图上的因果推断（二）：因果结构与效应识别AI 解读

A structural vector autoregressive (SVAR) process is a linear causal model for variables that evolve over a discrete set of time points and between which there may be lagged and instantaneous effects. The qualitative causal structure of an SVAR process can be represented by its finite and directed process graph, in which a directed link connects two processes whenever there is a lagged or instantaneous effect between them. At the process graph level, the causal structure of…

如何构建潜在马尔可夫模型：时间与空间的作用AI 解读

Statistical models that involve latent Markovian state processes have become immensely popular tools for analysing time series and other sequential data. However, the plethora of model formulations, the inconsistent use of terminology, and the various inferential approaches and software packages can be overwhelming to practitioners, especially when they are new to this area. With this review-like paper, we thus aim to provide guidance for both statisticians and practitioners…

在线分布回归AI 解读

Large-scale streaming data are common in modern machine learning applications and have led to the development of online learning algorithms. Many fields, such as supply chain management, weather and meteorology, energy markets, and finance, have pivoted toward probabilistic forecasting. This results in the need not only for accurate learning of the expected value but also for learning the conditional heteroskedasticity and conditional moments. Against this backdrop, we…

潜在因子模型协方差矩阵的结构化先验AI 解读

Factor models are widely used for dimension reduction in the analysis of multivariate data. This is achieved through decomposition of a p x p covariance matrix into the sum of two components. Through a latent factor representation, they can be interpreted as a diagonal matrix of idiosyncratic variances and a shared variation matrix, that is, the product of a p x k factor loadings matrix and its transpose. If k << p, this defines a parsimonious factorisation of the covariance…

干扰参数不确定性对实用数据科学模型统计推断的影响AI 解读

For multiple reasons -- such as avoiding overtraining from one data set or because of having received numerical estimates for some parameters in a model from an alternative source -- it is sometimes useful to divide a model's parameters into one group of primary parameters and one group of nuisance parameters. However, uncertainty in the values of nuisance parameters is an inevitable factor that impacts the model's reliability. This paper examines the issue of uncertainty…

大型近似因子模型中主成分与拟极大似然估计的渐近等价性AI 解读

This paper investigates the properties of Quasi Maximum Likelihood estimation of an approximate factor model for an $n$-dimensional vector of stationary time series. We prove that the factor loadings estimated by Quasi Maximum Likelihood are asymptotically equivalent, as $n\to\infty$, to those estimated via Principal Components. Both estimators are, in turn, also asymptotically equivalent, as $n\to\infty$, to the unfeasible Ordinary Least Squares estimator we would have if…

错设 Copula 模型中的反馈切断AI 解读

In copula models the marginal distributions and copula function are specified separately. We treat these as two modules in a modular Bayesian inference framework, and propose conducting modified Bayesian inference by "cutting feedback". Cutting feedback limits the influence of potentially misspecified modules in posterior inference. We consider two types of cuts. The first limits the influence of a misspecified copula on inference for the marginals, which is a Bayesian…