Tootfinder

Anthropic says Fable 5.1 sets new standards on coding, knowledge work, and long-running problem-solving tasks, and can fix the root causes of software issues (Carl Franzen/VentureBeat)
https://venturebeat.com/technology/ant

Sharp Asymptotic Theory of Maximum Likelihood Estimation for Gaussian Processes with an RBF Kernel
Ameer Qaqish, Didong Li
https://arxiv.org/abs/2610.10080 https://arxiv.org/pdf/2610.10080 https://arxiv.org/html/2610.10080
arXiv:2610.10080v1 Announce Type: new
Abstract: Gaussian processes (GPs) are widely used across machine learning, spatial statistics, time-series analysis, optimization, Bayesian statistics, and scientific applications. A central component of a GP model is its kernel, which is typically specified through a parametric family. Among the most widely used choices is the radial basis function (RBF), also known as the squared exponential or Gaussian kernel, owing to its simple form, smoothness, and flexibility. In practice, the kernel parameters are routinely estimated by the maximum likelihood estimators (MLEs), as implemented by standard GP software. Despite this widespread use, the asymptotic behavior of the MLEs remains poorly understood under fixed-domain asymptotics, even for the RBF kernel. The main difficulty arises from the increasingly strong dependence among densely sampled observations and the nonlinear dependence of the covariance matrix on the kernel parameters. In this paper, we address this gap by providing, to the best of our knowledge, the first complete asymptotic characterization of the joint MLE of the spatial variance, lengthscale, and nugget variance under fixed-domain asymptotics. We establish consistency, derive convergence rates for all three parameters, prove joint asymptotic normality, and
show that these rates are minimax optimal.
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Routle - SF Muni
08/02/2026
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https://www.routle.city/muni

Adaptive minimax multivariate \(L^1\)-deconvolution: harmonic-mean rates under noise filtering, and a \(1\)-Wasserstein equivalence
Catia Scricciolo
https://arxiv.org/abs/2610.11760 https://arxiv.org/pdf/2610.11760 https://arxiv.org/html/2610.11760
arXiv:2610.11760v1 Announce Type: new
Abstract: We study the multivariate convolution model with additive independent noise, multidimensional signal and noise, aiming to recover the signal's cumulative distribution function from contaminated observations. The noise is ordinary smooth with anisotropic regularity, and the signal belongs to an anisotropic Nikol'skii density class. We extend to the multivariate setting an approximate minimum \(L^1\)-distance estimator based on integrated kernel density estimation, and establish matching upper and lower bounds for the \(L^1\)-risk over anisotropic Nikol'skii classes. To our knowledge, this is the first minimax rate, not a sharpening of existing bounds. Although the lower-bound scheme is classical, the test-function construction is novel: it distinguishes no active component from at least one active component. The rate is governed by a censoring mechanism through the positive part, a noise filter in a harmonic-mean representation of the exponent. We further propose a fully data-driven, rate-adaptive procedure selecting an optimal bandwidth vector over the full Nikol'skii scale. On Nikol'skii product density classes, the \(L^1\)-distance between cumulative distribution functions and the \(1\)-Wasserstein distance share the same minimax rate, though not equivalent in general, via coordinate-wise decoupling of the \(1\)-Wasserstein cost on product measures. These findings reveal a link between the two distances, whose full understanding remains an open question.
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Routle - SF Muni
09/22/2026
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https://www.routle.city/muni

Routle - SF Muni
07/22/2026
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https://www.routle.city/muni
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