The paper critiques the optimally‑transported generalized method of moments (OTGMM) estimator introduced by Schennach & Starck (2026a), presenting counterexamples that invalidate Theorems 2–6 under their stated assumptions. It shows that the small‑error assumptions fail to guarantee consistency and asymptotic normality, and that the large‑error analysis leads to a modified‑moment GMM estimator that can diverge from the true OTGMM minimizer, even in simple scalar and overidentified models. The authors further provide a sufficient condition ensuring that solutions of the modified moment equations also solve the original constrained problem, and replace a problematic Assumption 16 with a matrix condition that restores the required bound.
arXiv:2604. 03146v2 Announce Type: replace-cross Abstract: We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs.
arXiv:2608. 13201v1 Announce Type: cross Abstract: We develop the statistical and algorithmic theory of inverse optimal transport (IOT) under the feature-parameterized cost C_theta(i,j) = -theta^T phi(i,j).
arXiv:2609. 30105v1 Announce Type: new Abstract: For an arbitrary isotropic log-concave distribution $P$ on $\mathbb{R}^d$, we prove that the polynomial $(Cm)^m\|v\|_2^m - \mathbb{E}_{X\sim P}\langle X,v\rangle^m$ is a sum of squares for every even $m\ge2$, where $C>0$ is a universal constant.
arXiv:2608.30382v1 Announce Type: new Abstract: Popular adaptive stochastic gradient descent (SGD) methods to train artificial intelligence (AI) systems include the RMSprop, the Adam, and the AdamW o...
arXiv:2607. 21975v1 Announce Type: new Abstract: Low-rank adaptation (LoRA) optimizes $J(B,A)=\mathcal L(W_\mathrm{base}+sBA)$ over two adapters $B \in \mathbb{R}^{m \times r}$ and $A \in \mathbb{R}^{r \times n}$ that form a low-rank update to a frozen pretrained weight matrix $W_\mathrm{base} \in \mathbb{R}^{m \times n}$.
arXiv:2605.07107v4 Announce Type: replace-cross Abstract: It is well known that, under standard regularity conditions, the maximum likelihood estimator (MLE) satisfies a central limit theorem and con...
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.
arXiv:2606. 07931v1 Announce Type: cross Abstract: We prove a variance-aware pointwise majorizing-measure theorem for centered Gaussian processes.
arXiv:2607.04743v3 Announce Type: replace-cross Abstract: Higher-order influence functions, introduced in a series of articles (Robins et al., 2008, 2009a; van der Vaart, 2014; Robins et al., 2016, 2...
For an arbitrary isotropic log-concave distribution $P$ on $\mathbb{R}^d$, we prove that the polynomial $(Cm)^m\|v\|_2^m - \mathbb{E}_{X\sim P}\langle X,v\rangle^m$ is a sum of squares for every even $m\ge2$, where $C>0$ is a universal constant. This removes the dependence on the Poincaré constant in the theorem of Kothari and Steinhardt (arXiv:1711.
arXiv:2607. 10618v1 Announce Type: cross Abstract: We consider the recovery of a pair of sparse vectors from a limited number of nonlinear observations of their superposition: $y_i=g(\inner{\ba_i}{\bPhi\bw^\ast+\bPsi\bz^\ast})+e_i$, $i=1,\dots,m$, with $m\ll n$, incoherent orthonormal bases $\bPhi,\bPsi$, a scalar link $g$, and noise $e_i$ that may be heavy-tailed or contaminated.
The paper introduces a new convergence framework for solving distributionally robust optimization problems formulated as nonconvex, nonconcave minimax problems over a Euclidean space and a Riemannian manifold. It defines a "basin saddle point"—a locally defined Nash equilibrium—and proves that a Riemannian gradient ascent–descent algorithm converges to such points under a local Łojasiewicz growth condition. The authors apply this theory to a statistical risk DRO problem over Gaussian measures, deriving explicit convergence rates and constants in terms of data dimension, loss moments, and reference covariance.