论文检索

高维随机森林的渐近性质AI 解读

As a flexible nonparametric learning tool, the random forests algorithm has been widely applied to various real applications with appealing empirical performance, even in the presence of high-dimensional feature space. Unveiling the underlying mechanisms has led to some important recent theoretical results on the consistency of the random forests algorithm and its variants. However, to our knowledge, almost all existing works concerning random forests consistency in a…

平均奖励马尔可夫决策过程中的批量策略学习AI 解读

We consider the batch (off-line) policy learning problem in the infinite horizon Markov Decision Process. Motivated by mobile health applications, we focus on learning a policy that maximizes the long-term average reward. We propose a doubly robust estimator for the average reward and show that it achieves semiparametric efficiency. Further we develop an optimization algorithm to compute the optimal policy in a parameterized stochastic policy class. The performance of the…

高斯过程协方差参数的贝叶斯固定域渐近理论AI 解读

Gaussian process models typically contain finite-dimensional parameters in the covariance function that need to be estimated from the data. We study the Bayesian fixed-domain asymptotics for the covariance parameters in a universal kriging model with an isotropic Matérn covariance function, which has many applications in spatial statistics. We show that when the dimension of domain is less than or equal to three, the joint posterior distribution of the microergodic parameter…

主题模型中稀疏主题分布的似然估计及 Wasserstein 文档距离应用AI 解读

This paper studies the estimation of high-dimensional, discrete, possibly sparse, mixture models in the context of topic models. The data consists of observed multinomial counts of p words across n independent documents. In topic models, the p×n expected word frequency matrix is assumed to be factorized as a p×K word-topic matrix A and a K×n topic-document matrix T. Since columns of both matrices represent conditional probabilities belonging to probability simplices, columns…

协方差核的补全AI 解读

We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain Ω of a rectangular domain I×I to a covariance kernel on the entire domain I×I. For a broad class of domains Ω called serrated domains, we are able to present a complete theory. Namely, we demonstrate that a canonical completion always exists and can be explicitly constructed. We characterise all possible completions as suitable perturbations of…

稳健马尔可夫决策过程的理论理解：样本复杂度与渐近性质AI 解读

In this paper, we study the nonasymptotic and asymptotic performances of the optimal robust policy and value function of robust Markov Decision Processes (MDPs), where the optimal robust policy and value function are estimated from a generative model. While prior work focusing on nonasymptotic performances of robust MDPs is restricted in the setting of the KL uncertainty set and (s,a)-rectangular assumption, we improve their results and also consider other uncertainty sets,…

公平统计决策问题的优化层级AI 解读

Data-driven decision making has drawn scrutiny from policy makers due to fears of potential discrimination, and a growing literature has begun to develop fair statistical techniques. However, these techniques are often specialized to one model context and based on ad hoc arguments, which makes it difficult to perform theoretical analysis. This paper develops an optimization hierarchy, which is a sequence of optimization problems with an increasing number of constraints, for…

复杂结构模型的近似最大似然估计AI 解读

Indirect Inference (I-I) is a popular technique for estimating complex parametric models whose likelihood function is intractable, however, the statistical efficiency of I-I estimation is questionable. While the efficient method of moments, Gallant and Tauchen (1996), promises efficiency, the price to pay for this efficiency is a loss of parsimony and thereby a potential lack of robustness to model misspecification. This stands in contrast to simpler I-I estimation…

具有偶尔约束生效机制的结构VARAI 解读

We develop a structural VAR in which an occasionally-binding constraint generates censoring of one of the dependent variables. Once the censoring mechanism is triggered, we allow some of the coefficients for the remaining variables to change. We show that a necessary condition for a unique reduced form is that regression functions for the non-censored variables are continuous at the censoring point and that parameters satisfy some mild restrictions. In our application the…

预测模型之间的条件轮换AI 解读

We establish conditions under which forecasting performance can be improved by rotating between a set of underlying forecasts whose predictive accuracy is tracked using a set of time-varying monitoring instruments. We characterize the properties that the monitoring instruments must possess to be useful for identifying, at each point in time, the best forecast and show that these reflect both the accuracy of the predictors used by the underlying forecasting models and the…

VAR 模型中脉冲响应的联合贝叶斯推断AI 解读

We derive the Bayes estimator of vectors of structural VAR impulse responses under a range of alternative loss functions. We also discuss the construction of joint credible regions for vectors of impulse responses as the lowest posterior risk region under the same loss functions. We show that conventional impulse response estimators such as the posterior median response function or the posterior mean response function are not in general the Bayes estimator of the impulse…

金融交易税与金融市场的信息效率：结构估计AI 解读

We develop a new methodology to estimate the impact of a financial transaction tax (FTT) on financial market outcomes. In our sequential trading model, there are price-elastic noise and informed traders. We estimate the model through maximum likelihood for a sample of 60 NYSE stocks in 2017. We quantify the effect of introducing an FTT given the parameter estimates. An FTT increases the proportion of informed trading, improves information aggregation, but lowers trading…

收益预测回归的一致局部谱推断AI 解读

This paper studies the properties of predictive regressions for asset returns in economic systems governed by persistent vector autoregressive dynamics. In particular, we allow for the state variables to be fractionally integrated, potentially of different orders, and for the returns to have a latent persistent conditional mean, whose memory is difficult to estimate consistently by standard techniques in finite samples. Moreover, the predictors may be endogenous and…

大型网络扩散的分解分析AI 解读

Diffusion over a network refers to the phenomenon of a change of state of a cross-sectional unit in one period leading to a change of state of its neighbors in the network in the next period. One may estimate or test for diffusion by estimating a cross-sectionally aggregated correlation between neighbors over time from data. However, the estimated diffusion can be misleading if the diffusion is confounded by omitted covariates. This paper focuses on the measure of diffusion…

谱金融计量经济学AI 解读

We survey the literature on spectral regression estimation. We present a cohesive framework designed to model dependence on frequency in the response of economic time series to changes in the explanatory variables. Our emphasis is on the statistical structure and on the economic interpretation of time-domain specifications needed to obtain horizon effects over frequencies , over scales , or upon aggregation . To this end, we articulate our discussion around the role played…

平均密度估计量：效率与自助法一致性AI 解读

This paper highlights a tension between semiparametric efficiency and bootstrap consistency in the context of a canonical semiparametric estimation problem, namely the problem of estimating the average density. It is shown that although simple plug-in estimators suffer from bias problems preventing them from achieving semiparametric efficiency under minimal smoothness conditions, the nonparametric bootstrap automatically corrects for this bias and that, as a result, these…

含误分类且内生二元解释变量的回归模型识别AI 解读

We study identification in nonparametric regression models with a misclassified and endogenous binary regressor when an instrument is correlated with misclassification error. We show that the regression function is nonparametrically identified if one binary instrument variable and one binary covariate satisfy the following conditions. The instrumental variable corrects endogeneity; the instrumental variable must be correlated with the unobserved true underlying binary…

次高斯随机矩阵算子范数的一致界及其应用AI 解读

For an $N \times T$ random matrix $X(\beta )$ with weakly dependent uniformly sub-Gaussian entries $x_{it}(\beta )$ that may depend on a possibly infinite-dimensional parameter $\beta \in \mathbf {B}$ , we obtain a uniform bound on its operator norm of the form $\mathbb {E} \sup _{\beta \in \mathbf {B}} ||X(\beta )|| \leq CK \left (\sqrt {\max (N,T)} + \gamma _2(\mathbf {B},d_{\mathbf {B}})\right )$ , where C is an absolute constant, K controls the tail behavior of (the…

高维二元回归中可扩展且准确的变分贝叶斯方法AI 解读

Summary Modern methods for Bayesian regression beyond the Gaussian response setting are often computationally impractical or inaccurate in high dimensions. In fact, as discussed in recent literature, bypassing such a trade-off is still an open problem even in routine binary regression models, and there is limited theory on the quality of variational approximations in high-dimensional settings. To address this gap, we study the approximation accuracy of routinely used…

边际因果效应估计中未测混杂的敏感性分析AI 解读

Summary One of the main threats to the validity of causal effect estimates from observational data is the existence of unmeasured confounders. A plethora of methods has been proposed to quantify deviation from conditional exchangeability, which arises when confounding is not properly accounted for, with each method having its own set of limitations and underlying assumptions. Few methods both scale well with the increasing complexity of potential measured confounders and…

随机森林的平均准确率下降：不一致性与 Sobol-MDA 解决方案AI 解读

Summary Variable importance measures are the main tools used to analyse the black-box mechanisms of random forests. Although the mean decrease accuracy is widely accepted as the most efficient variable importance measure for random forests, little is known about its statistical properties. In fact, the definition of mean decrease accuracy varies across the main random forest software. In this article, our objective is to rigorously analyse the behaviour of the main mean…

基于似然的稀疏协方差估计：近端距离算法AI 解读

Summary This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes the distance from the covariance estimate to a symmetric sparsity set. This formulation avoids unwanted shrinkage induced by more common norm penalties, and enables optimization of the resulting nonconvex objective by solving a…

通过隐式正则化进行高维线性回归AI 解读

Summary Many statistical estimators for high-dimensional linear regression are $M$-estimators, formed through minimizing a data-dependent square loss function plus a regularizer. This work considers a new class of estimators implicitly defined through a discretized gradient dynamic system under overparameterization. We show that, under suitable restricted isometry conditions, overparameterization leads to implicit regularization: if we directly apply gradient descent to the…

部分干扰下网络处理效应的有效半参数估计AI 解读

Summary Although many estimators for network treatment effects have been proposed, their optimality properties, in terms of semiparametric efficiency, have yet to be resolved. We present a simple yet flexible asymptotic framework for deriving the efficient influence function and the semiparametric efficiency lower bound for a family of network causal effects under partial interference. An important corollary of our results is that one existing estimator, that proposed by Liu…