每日简报

面向不规则间隔时间序列的子序列拓扑数据分析方法AI 解读

A time-delay embedding (TDE), grounded in the framework of Takens's Theorem, provides a mechanism to represent and analyze the inherent dynamics of time-series data. Recently, topological data analysis (TDA) methods have been applied to study this time series representation mainly through the lens of persistent homology. Current literature on the fusion of TDE and TDA are adept at analyzing uniformly-spaced time series observations. This work introduces a novel {\em…

HOUND：用于无参数多项式在线近似的高阶通用数值微分器AI 解读

This paper introduces a scalar numerical differentiator, represented as a system of nonlinear differential equations of any high order. We derive the explicit solution for this system and demonstrate that, with a suitable choice of differentiator order, the error converges to zero for polynomial signals with additive white noise. In more general cases, the error remains bounded, provided that the highest estimated derivative is also bounded. A notable advantage of this…

含长期与短期波动成分的 GARCH 期权估值：保证方差为正的新框架AI 解读

Christoffersen, Jacobs, Ornthanalai, and Wang (2008) (CJOW) proposed an improved Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model for valuing European options, where the return volatility is comprised of two distinct components. Empirical studies indicate that the model developed by CJOW outperforms widely-used single-component GARCH models and provides a superior fit to options data than models that combine conditional heteroskedasticity with…

具有两个波动成分和两个驱动因子的 GARCH 模型AI 解读

We introduce a novel GARCH model that integrates two sources of uncertainty to better capture the rich, multi-component dynamics often observed in the volatility of financial assets. This model provides a quasi closed-form representation of the characteristic function for future log-returns, from which semi-analytical formulas for option pricing can be derived. A theoretical analysis is conducted to establish sufficient conditions for strict stationarity and geometric…

利用 HeartSteps 微随机试验的纵向函数数据建模移动健康干预的时变效应AI 解读

To optimize mobile health interventions and advance domain knowledge on intervention design, it is critical to understand how the intervention effect varies over time and with contextual information. This study aims to assess how a push notification suggesting physical activity influences individuals' step counts using data from the HeartSteps micro-randomized trial (MRT). The statistical challenges include the time-varying treatments and longitudinal functional step count…

基于贝叶斯方法的倾向得分分层估计器AI 解读

Subclassification estimators are one of the methods used to estimate causal effects of interest using the propensity score. This method is more stable compared to other weighting methods, such as inverse probability weighting estimators, in terms of the variance of the estimators. In subclassification estimators, the number of strata is traditionally set at five, and this number is not typically chosen based on data information. Even when the number of strata is selected,…

从熵的视角估计波动率AI 解读

In the present paper, we first revisit the volatility estimation approach proposed by N. Kunitomo and S. Sato, and second, we show that the volatility estimator proposed by P. Malliavin and M.E. Mancino can be understood in a unified way by the approach. Third, we introduce an alternative estimator that might overcome the inconsistency caused by the microstructure noise of the initial observation.

基于结构因果关系的可泛化概念发现模型AI 解读

The rising need for explainable deep neural network architectures has utilized semantic concepts as explainable units. Several approaches utilizing disentangled representation learning estimate the generative factors and utilize them as concepts for explaining DNNs. However, even though the generative factors for a dataset remain fixed, concepts are not fixed entities and vary based on downstream tasks. In this paper, we propose a disentanglement mechanism utilizing a…

异质性处理效应估计中的缺失协变量问题AI 解读

Many applications of causal inference require using treatment effects estimated on a study population to make decisions in a separate target population. We consider the challenging setting where there are covariates that are observed in the target population that were not seen in the original study. Our goal is to estimate the tightest possible bounds on heterogeneous treatment effects conditioned on such newly observed covariates. We introduce a novel partial identification…

利用广义正态分布混合模型刻画金融收益AI 解读

This PhD Thesis presents an investigation into the analysis of financial returns using mixture models, focusing on mixtures of generalized normal distributions (MGND) and their extensions. The study addresses several critical issues encountered in the estimation process and proposes innovative solutions to enhance accuracy and efficiency. In Chapter 2, the focus lies on the MGND model and its estimation via expectation conditional maximization (ECM) and generalized…

二次型谱估计量的偏差校正AI 解读

The three cardinal, statistically consistent, families of non-parametric estimators to the power spectral density of a time series are lag-window, multitaper and Welch estimators. However, when estimating power spectral densities from a finite sample each can be subject to non-ignorable bias. Astfalck et al. (2024) developed a method that offers significant bias reduction for finite samples for Welch's estimator, which this article extends to the larger family of quadratic…

一般非线性过程的多谱均值估计AI 解读

Higher-order spectra (or polyspectra), defined as the Fourier Transform of a stationary process' autocumulants, are useful in the analysis of nonlinear and non Gaussian processes. Polyspectral means are weighted averages over Fourier frequencies of the polyspectra, and estimators can be constructed from analogous weighted averages of the higher-order periodogram (a statistic computed from the data sample's discrete Fourier Transform). We derive the asymptotic distribution of…

最大得分问题的贝叶斯视角AI 解读

This paper presents a Bayesian inference framework for a linear index threshold-crossing binary choice model that satisfies a median independence restriction. The key idea is that the model is observationally equivalent to a probit model with nonparametric heteroskedasticity. Consequently, Gibbs sampling techniques from Albert and Chib (1993) and Chib and Greenberg (2013) lead to a computationally attractive Bayesian inference procedure in which a Gaussian process forms a…

用图自回归模型从平稳信号推断潜在图AI 解读

Graphs are an intuitive way to represent relationships between variables in fields such as finance and neuroscience. However, these graphs often need to be inferred from data. In this paper, we propose a novel framework to infer a latent graph by treating the observed multidimensional data as graph-referenced stationary signals. Specifically, we introduce the graphical autoregressive model (GAR), where the inverse covariance matrix of the observed signals is expressed as a…

用自回归模型增强多变量传感器时间序列：故障预后应用AI 解读

This work presents a novel data augmentation solution for non-stationary multivariate time series and its application to failure prognostics. The method extends previous work from the authors which is based on time-varying autoregressive processes. It can be employed to extract key information from a limited number of samples and generate new synthetic samples in a way that potentially improves the performance of PHM solutions. This is especially valuable in situations of…

新型处理效应估计模型的消融研究AI 解读

Ablation studies are essential for understanding the contribution of individual components within complex models, yet their application in nonparametric treatment effect estimation remains limited. This paper emphasizes the importance of ablation studies by examining the Bayesian Causal Forest (BCF) model, particularly the inclusion of the estimated propensity score $\hatπ(x_i)$ intended to mitigate regularization-induced confounding (RIC). Through a partial ablation study…

基于自由度的统一因果分析AI 解读

Temporally evolving systems are typically modeled by dynamic equations. A key challenge in accurate modeling is understanding the causal relationships between subsystems, as well as identifying the presence and influence of unobserved hidden drivers on the observed dynamics. This paper presents a unified method capable of identifying fundamental causal relationships between pairs of systems, whether deterministic or stochastic. Notably, the method also uncovers hidden common…

无需显式雅可比矩阵的有效伪似然算法AI 解读

This study proposes a simple procedure to compute Efficient Pseudo Likelihood (EPL) estimator proposed by Dearing and Blevins (2024) for estimating dynamic discrete games, without computing Jacobians of equilibrium constraints. EPL estimator is efficient, convergent, and computationally fast. However, the original algorithm requires deriving and coding the Jacobians, which are cumbersome and prone to coding mistakes especially when considering complicated models. The current…

利用干预样本高效开展因果图的贝叶斯学习AI 解读

Causal discovery is a fundamental problem with applications spanning various areas in science and engineering. It is well understood that solely using observational data, one can only orient the causal graph up to its Markov equivalence class, necessitating interventional data to learn the complete causal graph. Most works in the literature design causal discovery policies with perfect interventions, i.e., they have access to infinite interventional samples. This study…

存在未测量中介—结局混杂时受控直接效应的稳健估计与模型选择AI 解读

Controlled Direct Effect (CDE) is one of the causal estimands used to evaluate both exposure and mediation effects on an outcome. When there are unmeasured confounders existing between the mediator and the outcome, the ordinary identification assumption does not work. In this manuscript, we consider an identification condition to identify CDE in the presence of unmeasured confounders. The key assumptions are: 1) the random allocation of the exposure, and 2) the existence of…

通货膨胀的国际脆弱性AI 解读

In a globalised world, inflation in a given country may be becoming less responsive to domestic economic activity, while being increasingly determined by international conditions. Consequently, understanding the international sources of vulnerability of domestic inflation is turning fundamental for policy makers. In this paper, we propose the construction of Inflation-at-risk and Deflation-at-risk measures of vulnerability obtained using factor-augmented quantile regressions…

结局与协变量信息不完整时 HIV 照护留存的贝叶斯反事实预测AI 解读

Like many chronic diseases, human immunodeficiency virus (HIV) is managed over time at regular clinic visits. At each visit, patient features are assessed, treatments are prescribed, and a subsequent visit is scheduled. There is a need for data-driven methods for both predicting retention and recommending scheduling decisions that optimize retention. Prediction models can be useful for estimating retention rates across a range of scheduling options. However, training such…

依赖数据下使用深度神经网络的部分线性模型推断AI 解读

I consider inference in a partially linear regression model under stationary $β$-mixing data after first stage deep neural network (DNN) estimation. Using the DNN results of Brown (2024), I show that the estimator for the finite dimensional parameter, constructed using DNN-estimated nuisance components, achieves $\sqrt{n}$-consistency and asymptotic normality. By avoiding sample splitting, I address one of the key challenges in applying machine learning techniques to…

利用核嵌入开展因果推断的研究概览AI 解读

Kernel embeddings have emerged as a powerful tool for representing probability measures in a variety of statistical inference problems. By mapping probability measures into a reproducing kernel Hilbert space (RKHS), kernel embeddings enable flexible representations of complex relationships between variables. They serve as a mechanism for efficiently transferring the representation of a distribution downstream to other tasks, such as hypothesis testing or causal effect…