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基于指数倾斜经验似然的风险最小化贝叶斯推断AI 解读

Abstract The celebrated Bernstein von-Mises theorem ensures credible regions from a Bayesian posterior to be well-calibrated when the model is correctly-specified, in the frequentist sense that their coverage probabilities tend to the nominal values as data accrue. However, this conventional Bayesian framework is known to lack robustness when the model is misspecified or partly specified, for example, in quantile regression, risk minimization based supervised/unsupervised…

变点检测后的均值变化检验AI 解读

Abstract While many methods are available to detect structural changes in a time series, few procedures are available to quantify the uncertainty of these estimates post-detection. In this work, we fill this gap by proposing a new framework to test the null hypothesis that there is no change in mean around an estimated changepoint. We further show that it is possible to efficiently carry out this framework in the case of changepoints estimated by binary segmentation and its…

贝叶斯因子调整稀疏回归AI 解读

Many sparse regression methods rely on an assumption that the covariates are weakly correlated, which hardly holds in many economic and financial datasets. To relax this assumption, we model the strongly correlated covariates by a factor structure: strong correlations among covariates are modeled by common factors, while the remaining variations of covariates are modeled as idiosyncratic components. We then propose a factor-adjusted sparse regression model and develop a…

条件随机化检验与knockoff的高维功效分析AI 解读

Summary In many scientific applications, researchers aim to relate a response variable $Y$ to a set of potential explanatory variables $X = (X_1,\dots,X_p)$, and start by trying to identify variables that contribute to this relationship. In statistical terms, this goal can be understood as trying to identify those $X_j$ on which $Y$ is conditionally dependent. Sometimes it is of value to simultaneously test for each $j$, which is more commonly known as variable selection.…

分位数趋势滤波的风险界AI 解读

Summary We study quantile trend filtering, a recently proposed method for nonparametric quantile regression, with the goal of generalizing existing risk bounds for the usual trend-filtering estimators that perform mean regression. We study both the penalized and the constrained versions, of order $r \geqslant 1$, of univariate quantile trend filtering. Our results show that both the constrained and the penalized versions of order $r \geqslant 1$ attain the minimax rate up to…

最小范数插值估计与正则化经验风险最小化的稳健性AI 解读

This article develops a general theory for minimum norm interpolating estimators and regularized empirical risk minimizers (RERM) in linear models in the presence of additive, potentially adversarial, errors. In particular, no conditions on the errors are imposed. A quantitative bound for the prediction error is given, relating it to the Rademacher complexity of the covariates, the norm of the minimum norm interpolator of the errors and the size of the subdifferential around…

二元响应下高维个体化阈值的非正则与极小极大估计AI 解读

Given a large number of covariates Z, we consider the estimation of a high-dimensional parameter θ in an individualized linear threshold θTZ for a continuous variable X, which minimizes the disagreement between sign(X−θTZ) and a binary response Y. While the problem can be formulated into the M-estimation framework, minimizing the corresponding empirical risk function is computationally intractable due to discontinuity of the sign function. Moreover, estimating θ even in the…

惩罚回归学习动态治疗方案的泛化误差界AI 解读

A dynamic treatment regime (DTR) is a sequence of decision rules, one per stage of intervention, that maps up-to-date patient information to a recommended treatment. Discovering an appropriate DTR for a given disease is a challenging issue especially when a large set of prognostic variables are observed. To address this problem, we propose penalized regression-based learning methods with l1 penalty to estimate the optimal DTR that would maximize the expected outcome if…

预测回归中的 LASSO 方法AI 解读

Explanatory variables in a predictive regression typically exhibit low signal strength and various degrees of persistence. Variable selection in such a context is of great importance. In this paper, we explore the pitfalls and possibilities of the LASSO methods in this predictive regression framework. In the presence of stationary, local unit root, and cointegrated predictors, we show that the adaptive LASSO cannot asymptotically eliminate all cointegrating variables with…

随机系数模型的非参数估计：弹性网方法AI 解读

This paper investigates and extends the computationally attractive nonparametric random coefficients estimator of Fox et al. (2011). We show that their estimator is a special case of the nonnegative LASSO, explaining its sparse nature observed in many applications. Recognizing this link, we extend the estimator, transforming it into a special case of the nonnegative elastic net. The extension improves the estimator’s recovery of the true support and allows for more accurate…

机器学习如何帮助宏观经济预测？AI 解读

Summary We move beyond Is Machine Learning Useful for Macroeconomic Forecasting? by adding the how . The current forecasting literature has focused on matching specific variables and horizons with a particularly successful algorithm. To the contrary, we study the usefulness of the underlying features driving ML gains over standard macroeconometric methods. We distinguish four so‐called features (nonlinearities, regularization, cross‐validation, and alternative loss function)…

基于张量分解的高维向量自回归时间序列建模AI 解读

The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of time series and lag order are even moderately large. This article proposes to rearrange the transition matrices of the model into a tensor form such that the parameter space can be restricted along three directions simultaneously via tensor decomposition. In contrast, the reduced-rank regression method can restrict…

稀疏先验下高维线性回归的变分贝叶斯方法AI 解读

We study a mean-field spike and slab variational Bayes (VB) approximation to Bayesian model selection priors in sparse high-dimensional linear regression. Under compatibility conditions on the design matrix, oracle inequalities are derived for the mean-field VB approximation, implying that it converges to the sparse truth at the optimal rate and gives optimal prediction of the response vector. The empirical performance of our algorithm is studied, showing that it works…

异步纵向函数型与标量数据的回归分析AI 解读

Many modern large-scale longitudinal neuroimaging studies, such as the Alzheimer’s Disease Neuroimaging Initiative (ADNI) study, have collected/are collecting asynchronous scalar and functional variables that are measured at distinct time points. The analyses of temporally asynchronous functional and scalar variables pose major technical challenges to many existing statistical approaches. We propose a class of generalized functional partial-linear varying-coefficient models…

控制错误符号率的高维交互项筛选AI 解读

Identifying interaction effects is fundamentally important in many scientific discoveries and contemporary applications, but it is challenging since the number of pairwise interactions increases quadratically with the number of covariates and that of higher-order interactions grows even faster. Although there is a growing literature on interaction detection, little work has been done on the prediction and false sign rate on interaction detection in ultrahigh-dimensional…

期权价格隐含状态价格密度的直接半参数估计AI 解读

We present a model for direct semi-parametric estimation of the state price density (SPD) implied by quoted option prices. We treat the observed prices as expected values of possible pay-offs at maturity, weighted by the unknown probability density function. We model the logarithm of the latter as a smooth function, using P-splines, while matching the expected values of the potential pay-offs with the observed prices. This leads to a special case of the penalized composite…

基于分位数相关的变量选择AI 解读

This article is concerned with identifying important features in high-dimensional data analysis, especially when there are complex relationships among predictors. Without any specification of an actual model, we first introduce a multiple testing procedure based on the quantile correlation to select important predictors in high dimensionality. The quantile-correlation statistic is able to capture a wide range of dependence. A stepwise procedure is studied for further…

机器学习时间序列回归及其即时预测应用AI 解读

This article introduces structured machine learning regressions for high-dimensional time series data potentially sampled at different frequencies. The sparse-group LASSO estimator can take advantage of such time series data structures and outperforms the unstructured LASSO. We establish oracle inequalities for the sparse-group LASSO estimator within a framework that allows for the mixing processes and recognizes that the financial and the macroeconomic data may have heavier…

Kuldeep Kumar 对《广义线性模型参数的弱假设推断》的讨论AI 解读

According to Leo Breiman (2001), there are two broad cultures for analysing and modelling to reach conclusions from the data. The first one is data modelling culture where the value of the parameters are estimated from the data and then the model is used for information and/or prediction. The second one is algorithmic modelling culture, where the approach is to find a function f(x) using an algorithm that operates on x to predict y. In the first case, statistical tools like…

Ian Hunt 对《广义线性模型参数的少假设推断》的讨论AI 解读

This paper offers a generic and principled addition to conventional statistical modelling. It is a real advance in applicable methodology. But there is no need in the paper for the following claims: that statisticians routinely use ‘dishonest’ modelling assumptions, that statisticians should aim for ‘purely evidence-based’ inferences and that modelling assumptions are ‘almost always a pure mathematical convenience’. These sorts of claims are redundant or misleading for three…

异质缺失下的高维变点估计AI 解读

Abstract We propose a new method for changepoint estimation in partially observed, high-dimensional time series that undergo a simultaneous change in mean in a sparse subset of coordinates. Our first methodological contribution is to introduce a ‘MissCUSUM’ transformation (a generalisation of the popular cumulative sum statistics), that captures the interaction between the signal strength and the level of missingness in each coordinate. In order to borrow strength across the…

Abstract Modern high-dimensional methods often adopt the ‘bet on sparsity’ principle, while in supervised multivariate learning statisticians may face ‘dense’ problems with a large number of nonzero coefficients. This paper proposes a novel clustered reduced-rank learning (CRL) framework that imposes two joint matrix regularizations to automatically group the features in constructing predictive factors. CRL is more interpretable than low-rank modelling and relaxes the…

用于评估重复研究成功的怀疑贝叶斯因子AI 解读

Abstract Replication studies are increasingly conducted but there is no established statistical criterion for replication success. We propose a novel approach combining reverse-Bayes analysis with Bayesian hypothesis testing: a sceptical prior is determined for the effect size such that the original finding is no longer convincing in terms of a Bayes factor. This prior is then contrasted to an advocacy prior (the reference posterior of the effect size based on the original…

重新审视岭回归：去偏、阈值化与自助法AI 解读

The success of the Lasso in the era of high-dimensional data can be attributed to its conducting an implicit model selection, that is, zeroing out regression coefficients that are not significant. By contrast, classical ridge regression cannot reveal a potential sparsity of parameters, and may also introduce a large bias under the high-dimensional setting. Nevertheless, recent work on the Lasso involves debiasing and thresholding, the latter in order to further enhance the…