每日简报

Wahkon：具有统计原则的深度RKHS叠加网络AI 解读

Deep learning excels at prediction but often lacks finite-sample guarantees and calibrated uncertainty; RKHS (Reproducing Kernel Hilbert Space)-based methods provide those guarantees but struggle to adapt in high dimensions. We propose Wahkon, a deep RKHS superposition network that unifies Kolmogorov's superposition principle with RKHS regularization in the smoothing-spline tradition of Wahba. This yields a finite-dimensional deep representer theorem that makes training…

遗憾与协方差：随机优化的闭式刻画AI 解读

Quantifying regret typically involves repeatedly re-solving a stochastic optimization problem across simulated scenarios. Such an approach is costly: the cost scales with the number of scenarios and the cost of each solve. We propose that regret can instead be measured using the joint moments of the cost vector $c$ and the optimal decision $π^*(c)$. Working with the optimal concave and Lipschitz under only a feasible region value function $v(c) = \min_{z\in Z} c^\top z$, we…

We consider the joint estimation of change-point locations and the sparsity pattern of the variance-covariance matrix, which is assumed to evolve in a piecewise constant manner. By applying Group Fused LASSO and LASSO penalties to the squared Frobenius norm, we estimate both the covariance structure and the change points. Adaptive weights are incorporated into the penalty terms to enhance change-point detection and covariance estimation accuracy. We establish the conditions…

拜占庭鲁棒分布式稀疏学习再审视AI 解读

We revisit Byzantine robust distributed estimation for high-dimensional sparse linear models. By combining local $\ell_1$-regularized robust estimation with robust aggregation at the server, the framework applies to pseudo-Huber regression, quantile regression, and sparse SVM. We show that the resulting estimators yield non-asymptotic guarantees and attain near-optimal statistical rates under mild conditions, while remaining communication-efficient. Simulations confirm…

永远不晚：潜在结果框架的完全随机化更新AI 解读

In the classic potential outcome framework, the local average treatment effect (LATE) and its identification via an instrumental variable are stated in a deterministic setting at the individual level: each individual has settled potential outcomes such as ``cured if treated''. Several authors have proposed working instead with \emph{stochastic} potential outcomes -- counterfactual probabilities of the form ``the chance of being cured if treated'' -- but the integration of…

电价波动率的精细结构AI 解读

We conduct the first rigorous study of electricity price volatility for the full panel of electricity prices across three European generation zones. By interpreting the observed day-ahead prices as local averages of a latent price process governed by a stochastic partial differential equation, we develop estimators of the weekly integrated variance. The inherently infinite dimensional setting introduce several complications that are not relevant in the conventional finite…

非随机研究中二元结局因果推断方法的选择手册：模拟研究AI 解读

Applied researchers in biomedicine and related fields are often interested in estimating the causal effect of a treatment or intervention. Although randomized clinical trials are considered the gold standard for establishing causal effects, they are not always feasible, and real-world data may represent the only available source of evidence. In such settings, causal effects must be estimated using statistical methods applied to observational data. Over the last few decades,…

通过统计功效进行因果发现AI 解读

Causal discovery methods aim to infer causal direction from observational data. Functional causal discovery approaches use structural asymmetries to identify causal directionality but rely on strong modeling assumptions and provide limited tools for uncertainty quantification. We introduce Causal Discovery via Statistical Power (CDSP), a statistical inference framework that connects causal direction estimation with statistical power and enables uncertainty quantification.…

基于 MCMC 的功能磁共振有效连接动态因果建模AI 解读

Effective connectivity analysis in functional magnetic resonance imaging (fMRI) studies directional interactions among brain regions and experimental stimuli. Dynamic causal modeling (DCM) is a widely used method to estimate effective connectivity, based on a state-space representation consisting of a latent neural signal model and an observation model transforming the neural signal into the observed blood-oxygen-level-dependent (BOLD) response. A standard DCM combines…

算法计量学：算法反馈下的预测AI 解读

In algorithmic markets, predictive models become part of the data-generating process they aim to forecast. Once their outputs are converted into trades, allocations, execution schedules, or risk controls, they change the future data on which they are evaluated. I introduce algometrics, a framework for time series whose evolution depends on the predictive algorithms forecasting them. The framework distinguishes historical risk, measured under passive forecasting, from…

递归似然模型加速推断的稳定化加权子抽样AI 解读

Inference for models with recursively defined likelihoods is computationally demanding, limiting scalability to large datasets. We propose a stabilised weighted subsampling methodology for accelerated inference based on an unbiased estimator of the log-likelihood. By assigning higher sampling probabilities to early observations, the method reduces the effective depth of recursive likelihood evaluations and hence computational cost. However, sampling probabilities that decay…

因果效应识别中的选择偏差：走向整体理解AI 解读

Selection bias is pervasive in observational studies. For example, large scale biobanks data can exhibit ``healthy volunteer bias'' when respondents are healthier and of higher socio-economic status than the population they are meant to represent. Recovering causal effects from such sub-population is an important problem in causal inference, as estimating average treatment effects (ATE) from selected populations can result in a severely biased estimate of the ATE from the…

非受控概率测度族下能否恢复 L¹–L∞ 对偶性？AI 解读

The duality $L^{\infty}\simeq (L^{1})'$ frequently breaks down in the presence of model uncertainty, where a single reference measure $P$ is replaced by a non-dominated family of probability measures $\mathcal{P}$. The unavailability of classical measure-theoretic and functional-analytic tools in this regime poses a significant obstacle to developing robust probabilistic frameworks. We show that this duality can be restored for a broad class of robust statistical models by…

稀疏性的脆弱性AI 解读

We show, using three empirical applications, that linear regression estimates predicated on the assumption of sparsity are fragile in two ways. First, we document that different choices of the regressor matrix which do not impact ordinary least squares (OLS) estimates, such as the choice of baseline category with categorical controls, can move sparsity-based estimates by two standard errors or more. Second, we develop two tests of the sparsity assumption by comparing…

线性过程尾部依赖的度量：理论与实证AI 解读

The quantitative analysis of financial time series often reveals two distinct features that standard Gaussian frameworks fail to capture: heavy-tailed marginal distributions and the phenomenon of extreme co-movements.While extreme value theory characterizes marginal behavior, Copulas provide a functional bridge to describe the dependence structure independently of the marginals. We are proposing a different way of looking at the joint extremes on the basis of a dependence…

效应异质性下个体化治疗规则的惩罚回归审慎迁移学习AI 解读

Estimating individualized treatment rules (ITRs) is fundamental to precision medicine, where the goal is to tailor treatment decisions to individual patient characteristics. While numerous methods have been developed for ITR estimation, there is limited research on model updating that accounts for shifted treatment-covariate relationships in the ITR setting. In practice, models trained on source data must be updated for new (target) datasets that exhibit shifts in treatment…