arXiv:2604.02887v1 Announce Type: cross
Abstract: Feature maps associated with positive definite kernels play a central role in kernel methods and learning theory, where regularity properties such as Lipschitz continuity are closely related to robustn…
arXiv:2604.02849v1 Announce Type: cross
Abstract: We show that the error-gated Hebbian rule for PCA (EGHR-PCA), a three-factor learning rule equivalent to Oja’s subspace rule under Gaussian inputs, can be systematically derived from Oja’s subspace rul…
arXiv:2604.02969v1 Announce Type: cross
Abstract: The natural gradient method is widely used in statistical optimization, but its standard formulation assumes a Euclidean parameter space. This paper proposes an inversion-free stochastic natural gradie…
arXiv:2604.02886v1 Announce Type: cross
Abstract: We study high-dimensional mediation analysis in which exposures, mediators, and outcomes are all multivariate, and both exposures and mediators may be high-dimensional. We formalize this as a many (exp…
arXiv:2504.01938v2 Announce Type: replace
Abstract: Probabilistic generative models based on measure transport, such as diffusion and flow-based models, are often formulated in the language of Markovian stochastic dynamics, where the choice of the und…
arXiv:2604.03068v1 Announce Type: cross
Abstract: We analyze the one-pass stochastic gradient descent dynamics of a two-layer neural network with quadratic activations in a teacher–student framework. In the high-dimensional regime, where the input di…
arXiv:2604.03015v1 Announce Type: new
Abstract: Given $n$ independent samples from a $d$-dimensional probability distribution, our aim is to generate diffusion-based samples from a distribution obtained by tilting the original, where the degree of til…
arXiv:2604.03218v1 Announce Type: cross
Abstract: Suppose we observe data from a distribution $P$ and we wish to test the composite null hypothesis that $P\in\mathscr P$ against a composite alternative $P\in \mathscr Q\subseteq \mathscr P^c$. Herbert …
arXiv:2511.13394v2 Announce Type: replace
Abstract: Bayesian parameter inference for complex stochastic simulators is challenging due to intractable likelihood functions. Existing simulation-based inference methods often require large number of simula…
arXiv:2603.29889v2 Announce Type: replace-cross
Abstract: This paper develops a penalized GMM (PGMM) framework for automatic debiased inference on functionals of nonparametric instrumental variable estimators. We derive convergence rates for the PGMM …