Einige der zuletzt hier besonders häufig geteilten #News:
Zum Tod von Margaret Hamilton: Ihre Software half Apollo 11 bei der Mondlandung
"Climate change created conditions for Canada fires, scientists say, as Trump blames mismanagement"
#Canada #Climate #ClimateChange
"mit jeder Entscheidung, die wir an eine Maschine übertragen, übertragen wir auch Macht"
https://zackzack.at/2026/10/08/wer-kontrolliert-die-ki
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城市人生 II 🔃
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🎞️ LUCKY SHD 400 (6x7)
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Wise
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.
toXiv_bot_toot
Pionierin Margaret Hamilton, Informatikerin und Mathematikerin ist im Alter von 90 Jahren gestorben
https://www.t-online.de/digital/aktuelles/id_101471468/apollo-programmiererin-margaret-hamilton-ist-tot.html
Beim #csdbraunschweig sei die Polizei mit Maschinenpistolen zugegen, wie mir gerade zugetragen wird.
Was die Politik halt so tut, um bloß die Freiheit für Autofahrer nicht zu hinterfragen.
I'll be participating in #monsterdon tonight both in honor of Sam Neill and because Mouth of Madness is such a good movie
These are human children, damn you, not units of production for your grey and soulless mills and offices. They should be playing, not being assessed, psychologically profiled and assigned to the optimal task to extract the maximum profit from them for your #kleptocrat masters.
This is a monstrous, abhorrent, inhuman proposal.
Unbounded Characteristic and Universal Kernels
Jose Cribeiro-Ramallo, Florian Kalinke, Zolt\'an Szab\'o
https://arxiv.org/abs/2610.09731 https://arxiv.org/pdf/2610.09731 https://arxiv.org/html/2610.09731
arXiv:2610.09731v1 Announce Type: new
Abstract: Kernel methods are among the most powerful tools in machine learning and statistics, with a large number of successful applications. Their immense success stems from the flexible function class associated to each kernel---its reproducing kernel Hilbert space (RKHS)---which facilitates statistical analysis, as well as from their computational tractability and applicability to many domains. Multiple notions (such as characteristic, $L_p$-universal, and integrally strictly positive definite) capture the expressivity of kernels and their RKHSs and play a key role in understanding the statistical properties of kernel methods; these concepts and their relations are well-understood for bounded kernels. Even though unbounded kernels have received significant attention over the past decade (for instance, in the construction of kernel-based discrepancy and dependence measures such as the maximum mean discrepancy, the Hilbert-Schmidt independence criterion, and the kernel Stein discrepancy), surprisingly little is known about the relations of these notions in the unbounded case. In the present paper we tackle this severe bottleneck, establishing their relations under mild assumptions.
toXiv_bot_toot