The paper introduces generalized Riesz regression, a framework that minimizes a Bregman divergence made observable through the Riesz identity. By selecting squared or Kullback–Leibler-type divergences, it recovers existing Riesz regression, tailored loss minimization, and density‑ratio objectives. The authors derive first‑order conditions that enforce empirical Riesz equations in model‑dependent tangent directions, provide convergence rates for sparse, RKHS, and neural network models, and establish asymptotic normality under Donsker or cross‑fitting conditions, with applications to treatment effects, average marginal effects, and covariate shift.
arXiv:2406. 13944v2 Announce Type: replace-cross Abstract: This paper establishes the generalization error of pooled min-$\ell_2$-norm interpolation in transfer learning, where data from diverse distributions are available.
arXiv:2411.02771v3 Announce Type: replace-cross Abstract: Doubly robust estimators are widely used for estimating average treatment effects and other linear summaries of regression functions. While c...
arXiv:2609. 03129v1 Announce Type: cross Abstract: Several classical machine-learning methods, such as KRRs and SVRs, are both computationally and analytically tractable since their estimators either admit closed-form expressions or are obtained by minimizing convex training objectives; neither feature is generally available for deep neural networks.
arXiv:2501.18581v5 Announce Type: replace Abstract: Bias-variance decompositions are widely used to understand the generalization performance of machine learning models. While the squared error loss...
arXiv:2410. 02596v2 Announce Type: replace-cross Abstract: Generative Flow Networks (GFlowNets) are a novel class of generative models designed to sample from unnormalized distributions and have found applications in various important tasks, attracting great research interest in their training algorithms.
arXiv:2406. 14340v2 Announce Type: replace-cross Abstract: The standard stochastic gradient descent (SGD) optimization method, as well as adaptive methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (particularly, in the situation of constant learning rates).
arXiv:2608. 16340v1 Announce Type: cross Abstract: The combination of traditional statistical models and neural network (NN) components into semi-structured hybrid models is an intriguing approach to construct models that, ideally, combine traditional interpretability with the unprecedented flexibility of NNs.
arXiv:2605. 27991v2 Announce Type: replace-cross Abstract: Gradient-flow optimization is usually viewed as an algorithmic procedure for minimizing empirical loss, with training duration selected by validation or heuristic early-stopping rules.
arXiv:2603. 04895v2 Announce Type: replace-cross Abstract: Overparameterized ML models, including neural networks, typically induce underdetermined training objectives with multiple global minima.
arXiv:2505. 12430v2 Announce Type: replace Abstract: Recently, innovative adaptations of the Ritz method incorporating deep learning have been developed, known as the Deep Ritz Method.
arXiv:2607. 02681v1 Announce Type: cross Abstract: Integrating information across related tasks can improve estimation and prediction in transfer, multi-task, and federated learning, but contamination and heterogeneity make robust borrowing challenging.
The paper investigates Double Machine Learning (DML) estimators under structure‑agnostic (SA) models, which assume the data‑generating law lies within a neighborhood of fixed machine‑learning estimates. It shows that for two of three studied functionals—the quadratic functional in the Gaussian sequence model and the quadratic density integral functional—the DML estimators are asymptotically inadmissible, being dominated by second‑order empirical higher‑order influence function (HOIF) estimators. For the third functional, the expected conditional covariance, both DML and HOIF estimators remain minimax but neither dominates the other.