We investigate the connection between Gaussian processes and Gaussian random elements in reproducing kernel Banach spaces. We show that the covariance operator of a weak second-order Radon probability measure on such a space is uniquely determined by a positive definite function. In the Gaussian case, we characterize those positive definite functions that arise from covariance operators in terms of $γ$-radonifying operators. Building on these results, we extend the classical Driscoll theorem to the Banach space setting.

We note that the interchange of the integral and infinite summation is justified by Section 3.7 in [5], since the coefficients Z Now,define action sequence (a)n such thata1 = a and an = a1 for alln > 1. Then we can use subadditivity of measure to bound the maximum difference across all entries of [kZ]. Therefore, the induced infinity norm error ofbZ isless thanεifthe element wise error isless than ε/k. Therefore,bα>Fφ(s) is ρ-Lipschitz if the absolute value of its derivativeisboundedbyρ,i.e. SincebF has all zeros beyond thek-th column and row, each infinite-matrix bF can be treated as ak k matrix.

In privacy-preserving machine learning, differentially private stochastic gradient descent (DP-SGD) performs worse than SGD due to per-sample gradient clipping and noise addition.A recent focus in private learning research is improving the performance of DP-SGD on private data by incorporating priors that are learned on real-world public data.In this work, we explore how we can improve the privacy-utility tradeoff of DP-SGD by learning priors from images generated by random processes and transferring these priors to private data. We propose DP-RandP, a three-phase approach. We attain new state-of-the-art accuracy when training from scratch on CIFAR10, CIFAR100, MedMNIST and ImageNet for a range of privacy budgets $\\varepsilon \\in [1, 8]$. In particular, we improve the previous best reported accuracy on CIFAR10 from $60.6 \\%$ to $72.3 \\%$ for $\\varepsilon=1$.

Discretizing continuous-time linear systems typically requires numerical integration. This document presents a convenient method for discretizing the dynamics, input, and process noise state-space matrices of a continuous-time linear system using a single matrix exponential.

In privacy-preserving machine learning, differentially private stochastic gradient descent (DP-SGD) performs worse than SGD due to per-sample gradient clipping and noise addition.A recent focus in private learning research is improving the performance of DP-SGD on private data by incorporating priors that are learned on real-world public data.In this work, we explore how we can improve the privacy-utility tradeoff of DP-SGD by learning priors from images generated by random processes and transferring these priors to private data. We propose DP-RandP, a three-phase approach. We attain new state-of-the-art accuracy when training from scratch on CIFAR10, CIFAR100, MedMNIST and ImageNet for a range of privacy budgets \\varepsilon \\in [1, 8] . In particular, we improve the previous best reported accuracy on CIFAR10 from 60.6 \\% to 72.3 \\% for \\varepsilon 1 .

The radio spectrum is characterized by a noticeable variability, which impairs performance and determinism of every wireless communication technology. To counteract this aspect, mechanisms like Minstrel are customarily employed in real Wi-Fi devices, and the adoption of machine learning for optimization is envisaged in next-generation Wi-Fi 8. All these approaches require communication quality to be monitored at runtime. In this paper, the effectiveness of simple techniques based on moving averages to estimate wireless link quality is analyzed, to assess their advantages and weaknesses. Results can be used, e.g., as a baseline when studying how artificial intelligence can be employed to mitigate unpredictability of wireless networks by providing reliable estimates about current spectrum conditions.

Purpose This article presents a case for a next-generation grid monitoring and control system, leveraging recent advances in generative artificial intelligence (AI), machine learning, and statistical inference. Advancing beyond earlier generations of wide-area monitoring systems built upon supervisory control and data acquisition (SCADA) and synchrophasor technologies, we argue for a monitoring and control framework based on the streaming of continuous point-on-wave (CPOW) measurements with AI-powered data compression and fault detection. Methods and Results: The architecture of the proposed design originates from the Wiener-Kallianpur innovation representation of a random process that transforms causally a stationary random process into an innovation sequence with independent and identically distributed random variables. This work presents a generative AI approach that (i) learns an innovation autoencoder that extracts innovation sequence from CPOW time series, (ii) compresses the CPOW streaming data with innovation autoencoder and subband coding, and (iii) detects unknown faults and novel trends via nonparametric sequential hypothesis testing. Conclusion: This work argues that conventional monitoring using SCADA and phasor measurement unit (PMU) technologies is ill-suited for a future grid with deep penetration of inverter-based renewable generations and distributed energy resources. A monitoring system based on CPOW data streaming and AI data analytics should be the basic building blocks for situational awareness of a highly dynamic future grid.

We propose a new class of models for variable clustering called Asymptotic Independent block (AI-block) models, which defines population-level clusters based on the independence of the maxima of a multivariate stationary mixing random process among clusters. This class of models is identifiable, meaning that there exists a maximal element with a partial order between partitions, allowing for statistical inference. We also present an algorithm for recovering the clusters of variables without specifying the number of clusters \emph{a priori}. Our work provides some theoretical insights into the consistency of our algorithm, demonstrating that under certain conditions it can effectively identify clusters in the data with a computational complexity that is polynomial in the dimension. This implies that groups can be learned nonparametrically in which block maxima of a dependent process are only sub-asymptotic. To further illustrate the significance of our work, we applied our method to neuroscience and environmental real-datasets. These applications highlight the potential and versatility of the proposed approach.

Sequences of repeated gambles provide an experimental tool to characterize the risk preferences of humans or artificial decision-making agents. The difficulty of this inference depends on factors including the details of the gambles offered and the number of iterations of the game played. In this paper we explore in detail the practical challenges of inferring risk preferences from the observed choices of artificial agents who are presented with finite sequences of repeated gambles. We are motivated by the fact that the strategy to maximize long-run wealth for sequences of repeated additive gambles (where gains and losses are independent of current wealth) is different to the strategy for repeated multiplicative gambles (where gains and losses are proportional to current wealth.) Accurate measurement of risk preferences would be needed to tell whether an agent is employing the optimal strategy or not. To generalize the types of gambles our agents face we use the Yeo-Johnson transformation, a tool borrowed from feature engineering for time series analysis, to construct a family of gambles that interpolates smoothly between the additive and multiplicative cases. We then analyze the optimal strategy for this family, both analytically and numerically. We find that it becomes increasingly difficult to distinguish the risk preferences of agents as their wealth increases. This is because agents with different risk preferences eventually make the same decisions for sufficiently high wealth. We believe that these findings are informative for the effective design of experiments to measure risk preferences in humans.