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Abstract Cross-validation is the de facto standard for predictive model evaluation and selection. In proper use, it provides an unbiased estimate of a model's predictive performance. However, data sets often undergo various forms of data-dependent preprocessing, such as mean-centring, rescaling, dimensionality reduction and outlier removal. It is often believed that such preprocessing stages, if done in an unsupervised manner (that does not incorporate the class labels or…

谱嵌入的统计解释：广义随机点积图AI 解读

Abstract Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph. This paper proposes a generalisation of the latent position network model known as the random dot product graph, to allow interpretation of those vector representations as latent position estimates. The generalisation is needed to model heterophilic connectivity (e.g. ‘opposites attract’) and to cope with negative eigenvalues more generally. We show that,…

主分层可忽略性下因果效应的多重稳健估计AI 解读

Abstract Causal inference concerns not only the average effect of the treatment on the outcome but also the underlying mechanism through an intermediate variable of interest. Principal stratification characterizes such a mechanism by targeting subgroup causal effects within principal strata, which are defined by the joint potential values of an intermediate variable. Due to the fundamental problem of causal inference, principal strata are inherently latent, rendering it…

函数型数据的超阈值极值分析AI 解读

Abstract Peaks-over-threshold analysis using the generalised Pareto distribution is widely applied in modelling tails of univariate random variables, but much information may be lost when complex extreme events are studied using univariate results. In this paper, we extend peaks-over-threshold analysis to extremes of functional data. Threshold exceedances defined using a functional r are modelled by the generalised r-Pareto process, a functional generalisation of the…

分层抽样下半监督预测规则的高效评估AI 解读

Abstract In many contemporary applications, large amounts of unlabelled data are readily available while labelled examples are limited. There has been substantial interest in semi-supervised learning (SSL) which aims to leverage unlabelled data to improve estimation or prediction. However, current SSL literature focuses primarily on settings where labelled data are selected uniformly at random from the population of interest. Stratified sampling, while posing additional…

S 形函数的非参数免调参估计AI 解读

Abstract We consider the nonparametric estimation of an S-shaped regression function. The least squares estimator provides a very natural, tuning-free approach, but results in a non-convex optimization problem, since the inflection point is unknown. We show that the estimator may nevertheless be regarded as a projection onto a finite union of convex cones, which allows us to propose a mixed primal-dual bases algorithm for its efficient, sequential computation. After…

贝叶斯上下文树：离散时间序列建模与精确推断AI 解读

Abstract We develop a new Bayesian modelling framework for the class of higher-order, variable-memory Markov chains, and introduce an associated collection of methodological tools for exact inference with discrete time series. We show that a version of the context tree weighting alg-orithm can compute the prior predictive likelihood exa-ctly (averaged over both models and parameters), and two related algorithms are introduced, which identify the a posteriori most likely…

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…

扩散模型贝叶斯推断的流形马尔可夫链蒙特卡洛方法AI 解读

Abstract Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction, and accompanying methodology—borrowing ideas from statistical physics and computational chemistry—for inferring the posterior distribution of latent diffusion paths and model parameters, given observations of the process. Joint…

近似贝叶斯高斯过程回归的快速高保真采样AI 解读

Abstract Gaussian processes (GPs) are common components in Bayesian non-parametric models having a rich methodological literature and strong theoretical grounding. The use of exact GPs in Bayesian models is limited to problems containing several thousand observations due to their prohibitive computational demands. We develop a posterior sampling algorithm using H-matrix approximations that scales at O(nlog2n). We show that this approximation's Kullback–Leibler divergence to…

重复事件数据的半参数潜类别分析AI 解读

Abstract Recurrent event data frequently arise in chronic disease studies, providing rich information on disease progression. The concept of latent class offers a sensible perspective to characterize complex population heterogeneity in recurrent event trajectories that may not be adequately captured by a single regression model. However, the development of latent class methods for recurrent event data has been sparse, typically requiring strong parametric assumptions and…

复杂抽样设计下有限总体均值的 Bootstrap 推断AI 解读

Abstract Bootstrap is a useful computational tool for statistical inference, but it may lead to erroneous analysis under complex survey sampling. In this paper, we propose a unified bootstrap method for stratified multi-stage cluster sampling, Poisson sampling, simple random sampling without replacement and probability proportional to size sampling with replacement. In the proposed bootstrap method, we first generate bootstrap finite populations, apply the same sampling…

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…

利用局部球面高效逼近流形AI 解读

Abstract In statistical dimensionality reduction, it is common to rely on the assumption that high dimensional data tend to concentrate near a lower dimensional manifold. There is a rich literature on approximating the unknown manifold, and on exploiting such approximations in clustering, data compression, and prediction. Most of the literature relies on linear or locally linear approximations. In this article, we propose a simple and general alternative, which instead uses…

多重检验问题的最优与最大最小程序AI 解读

Abstract Multiple testing problems (MTPs) are a staple of modern statistical analysis. The fundamental objective of MTPs is to reject as many false null hypotheses as possible (that is, maximize some notion of power), subject to controlling an overall measure of false discovery, like family-wise error rate (FWER) or false discovery rate (FDR). In this paper we provide generalizations to MTPs of the optimal Neyman-Pearson test for a single hypothesis. We show that for simple…

MCMC 输出的最优抽稀AI 解读

Abstract The use of heuristics to assess the convergence and compress the output of Markov chain Monte Carlo can be sub-optimal in terms of the empirical approximations that are produced. Typically a number of the initial states are attributed to ‘burn in’ and removed, while the remainder of the chain is ‘thinned’ if compression is also required. In this paper, we consider the problem of retrospectively selecting a subset of states, of fixed cardinality, from the sample path…

条件离散—连续分布的自适应贝叶斯估计及股票交易活动应用AI 解读

We consider Bayesian nonparametric estimation of conditional discrete-continuous distributions. Our model is based on a mixture of normal distributions with covariate dependent mixing probabilities. We use continuous latent variables for modeling the discrete part of the distribution. The marginal distribution of covariates is not modeled. Under anisotropic smoothness conditions on the data generating conditional distribution and a possibly increasing number of the support…

促进大规模状态空间模型简约性的先验AI 解读

State–space models are commonly used in the engineering, economic, and statistical literature. They are flexible and encompass many well-known statistical models, including random coefficient autoregressive models and dynamic factor models. Bayesian analysis of state–space models has attracted much interest in recent years. However, for large scale models, prior specification becomes a challenging issue in Bayesian inference. In this paper, we propose a flexible prior for…

仿射无套利收益率网络模型及欧债危机应用AI 解读

We develop a parsimonious class of affine arbitrage-free yield net models for consistent bond pricing across maturities and issuers of different risk levels. Containing a core curve and multiple peripheral curves, the yield net is spanned by three layers of factors: base factors spanning all curves, and common and individual spread factors. Under the arbitrage-free assumption, we prove a parsimonious solution to the risk-neutral process that guarantees joint identification…

基于后验分布的 Wald 型假设检验统计量AI 解读

A new Wald-type statistic is proposed for hypothesis testing based on Bayesian posterior distributions under the correct model specification. The new statistic can be explained as a posterior version of the Wald statistic and has several nice properties. First, it is well-defined under improper prior distributions. Second, it avoids Jeffreys–Lindley–Bartlett’s paradox. Third, under the null hypothesis and repeated sampling, it follows a χ2 distribution asymptotically,…

因子投资：贝叶斯层级方法AI 解读

This paper investigates the asset allocation problem when returns are predictable. We introduce a market-timing Bayesian hierarchical (BH) approach that adopts heterogeneous time-varying coefficients driven by lagged fundamental characteristics. Our approach estimates the conditional expected returns and residual covariance matrix jointly enables evaluating the estimation risk in the portfolio analysis. The hierarchical prior allows the modeling of different assets…

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…

共同基金行业技能分布的贝叶斯非参数学习AI 解读

In this paper, we use Bayesian nonparametric learning to estimate the skill of actively managed mutual funds and also to estimate the population distribution of skill. A nonparametric hierarchical prior, where the hyperprior distribution is unknown and modeled with a Dirichlet Process prior, is used to model the skill parameter, with its posterior predictive distribution being an estimate of the population distribution. Our nonparametric approach is equivalent to an…

实时贝叶斯学习与债券收益可预测性AI 解读

The paper examines statistical and economic evidence of out-of-sample bond return predictability for a real-time Bayesian investor who learns about parameters, hidden states, and predictive models over time. We find some statistical evidence using information contained in forward rates. However, such statistical predictability can hardly generate any economic value for investors. Furthermore, we find that strong statistical and economic evidence of bond return predictability…