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基于抛物型Monge–Ampère偏微分方程的无遗憾生成建模AI 解读

We introduce a novel generative modeling framework based on a discretized parabolic Monge–Ampère PDE, which emerges as a continuous limit of the Sinkhorn algorithm commonly used in optimal transport. Our method performs iterative refinement in the space of Brenier maps using a mirror gradient descent step. We establish theoretical guarantees for generative modeling through the lens of no-regret analysis, demonstrating that the iterates converge to the optimal Brenier map…

随机实验中协变量平衡的高斯化设计优化AI 解读

Abstract Achieving covariate balance in randomized experiments enhances the precision of treatment effect estimation. However, existing methods often require heuristic adjustments based on domain knowledge and are primarily developed for binary treatments. This paper presents Gaussianized Design Optimization, a novel framework for optimally balancing covariates in experimental design. The core idea is to Gaussianize the treatment assignments: we model treatments as…

概念漂移下的学习：混杂、不变性与降维AI 解读

Practitioners often face the challenge of deploying prediction models in new environments with shifted distributions of covariates and responses. With observational data, such shifts are often driven by unobserved confounding, and can in fact alter the concept of which model is best. This paper studies distribution shifts in the domain adaptation problem with unobserved confounding. We postulate a linear structural causal model to account for endogeneity and unobserved…

样本单位数为一时的随机化推断AI 解读

Summary For decades, $ N $-of-1 experiments, where a unit serves as its own control and treatment in different time windows, have been used in certain medical contexts. However, due to effects that accumulate over long time windows and interventions that have complex evolution, a lack of robust inference tools has limited the widespread applicability of such $ N $-of-1 designs. This work combines techniques from experimental design in causal inference and system…

利用位移插值检测微弱分布变化AI 解读

Detecting weak, systematic distribution shifts and quantitatively modeling individual, heterogeneous responses to policies or incentives have found increasing empirical applications in social and economic sciences. Given two probability distributions P (null) and Q (alternative), we study the problem of detecting weak distribution shift deviating from the null P toward the alternative Q, where the level of deviation vanishes as a function of n, the sample size. We propose a…

利用半正定规划构造通用预测带AI 解读

Abstract We propose a computationally efficient method to construct nonparametric, heteroscedastic prediction bands for uncertainty quantification, with or without any user-specified predictive model. Our approach provides an alternative to the now-standard conformal prediction for uncertainty quantification, with novel theoretical insights and computational advantages. The data-adaptive prediction band is universally applicable with minimal distributional assumptions, has…

Boosting 与最小 ℓ1 范数插值分类器的精确高维渐近理论AI 解读

This paper establishes a precise high-dimensional asymptotic theory for boosting on separable data, taking statistical and computational perspectives. We consider a high-dimensional setting where the number of features (weak learners) p scales with the sample size n, in an overparametrized regime. Under a class of statistical models, we provide an exact analysis of the generalization error of boosting when the algorithm interpolates the training data and maximizes the…

神经网络训练作为数据自适应核学习：表示与逼近收益AI 解读

Consider the problem: given the data pair (x,y) drawn from a population with f*(x)=E[y|x=x], specify a neural network model and run gradient flow on the weights over time until reaching any stationarity. How does ft , the function computed by the neural network at time t, relate to f*, in terms of approximation and representation? What are the provable benefits of the adaptive representation by neural networks compared to the pre-specified fixed basis representation in the…

用于估计与推断的深度神经网络AI 解读

We study deep neural networks and their use in semiparametric inference. We establish novel nonasymptotic high probability bounds for deep feedforward neural nets. These deliver rates of convergence that are sufficiently fast (in some cases minimax optimal) to allow us to establish valid second‐step inference after first‐step estimation with deep learning, a result also new to the literature. Our nonasymptotic high probability bounds, and the subsequent semiparametric…

直接插值：无岭惩罚核回归也能泛化AI 解读

In the absence of explicit regularization, Kernel “Ridgeless” Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirically, however, that such interpolated solutions can still generalize well on test data. We isolate a phenomenon of implicit regularization for minimum-norm interpolated solutions which is due to a combination of high dimensionality of the input data, curvature of the kernel function and favorable…

通过矩调整随机梯度对总体目标景观进行统计推断AI 解读

Summary Modern statistical inference tasks often require iterative optimization methods to compute the solution. Convergence analysis from an optimization viewpoint informs us only how well the solution is approximated numerically but overlooks the sampling nature of the data. In contrast, recognizing the randomness in the data, statisticians are keen to provide uncertainty quantification, or confidence, for the solution obtained by using iterative optimization methods. The…

大型噪声矩阵中子矩阵定位的计算与统计边界AI 解读

We study in this paper computational and statistical boundaries for submatrix localization. Given one observation of (one or multiple nonoverlapping) signal submatrix (of magnitude $\lambda$ and size $k_{m}\times k_{n}$) embedded in a large noise matrix (of size $m\times n$), the goal is to optimal identify the support of the signal submatrix computationally and statistically. Two transition thresholds for the signal-to-noise ratio $\lambda/\sigma$ are established in terms…

一般高维线性逆问题的几何推断AI 解读

This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix estimation and noisy matrix completion. We propose computationally feasible convex programs for statistical inference including estimation, confidence intervals and hypothesis testing. A theoretical framework is developed to characterize…