Granular-ball computing is an efficient, robust, and scalable learning method for granular computing. The basis of granular-ball computing is the granular-ball generation method. This paper proposes a method for accelerating the granular-ball generation using the division to replace $k$-means. It can greatly improve the efficiency of granular-ball generation while ensuring the accuracy similar to the existing method. Besides, a new adaptive method for the granular-ball generation is proposed by considering granular-ball's overlap eliminating and some other factors. This makes the granular-ball generation process of parameter-free and completely adaptive in the true sense. In addition, this paper first provides the mathematical models for the granular-ball covering. The experimental results on some real data sets demonstrate that the proposed two granular-ball generation methods have similar accuracies with the existing method while adaptiveness or acceleration is realized.

In this article we consider Bayesian inference associated to deep neural networks (DNNs) and in particular, trace-class neural network (TNN) priors which were proposed by Sell et al. [39]. Such priors were developed as more robust alternatives to classical architectures in the context of inference problems. For this work we develop multilevel Monte Carlo (MLMC) methods for such models. MLMC is a popular variance reduction technique, with particular applications in Bayesian statistics and uncertainty quantification. We show how a particular advanced MLMC method that was introduced in [4] can be applied to Bayesian inference from DNNs and establish mathematically, that the computational cost to achieve a particular mean square error, associated to posterior expectation computation, can be reduced by several orders, versus more conventional techniques. To verify such results we provide numerous numerical experiments on model problems arising in machine learning. These include Bayesian regression, as well as Bayesian classification and reinforcement learning.

This work in progress aims to provide a unified introduction to statistical learning, building up slowly from classical models like the GMM and HMM to modern neural networks like the VAE and diffusion models. There are today many internet resources that explain this or that new machine-learning algorithm in isolation, but they do not (and cannot, in so brief a space) connect these algorithms with each other or with the classical literature on statistical models, out of which the modern algorithms emerged. Also conspicuously lacking is a single notational system which, although unfazing to those already familiar with the material (like the authors of these posts), raises a significant barrier to the novice's entry. Likewise, I have aimed to assimilate the various models, wherever possible, to a single framework for inference and learning, showing how (and why) to change one model into another with minimal alteration (some of them novel, others from the literature). Some background is of course necessary. I have assumed the reader is familiar with basic multivariable calculus, probability and statistics, and linear algebra. The goal of this book is certainly not completeness, but rather to draw a more or less straight-line path from the basics to the extremely powerful new models of the last decade. The goal then is to complement, not replace, such comprehensive texts as Bishop's \emph{Pattern Recognition and Machine Learning}, which is now 15 years old.

Trustworthy and reliable data delivery is a challenging task in Wireless Sensor Networks (WSNs) due to unique characteristics and constraints. To acquire secured data delivery and address the conflict between security and energy, in this paper we present an evolutionary game based secure clustering protocol with fuzzy trust evaluation and outlier detection for WSNs. Firstly, a fuzzy trust evaluation method is presented to transform the transmission evidences into trust values while effectively alleviating the trust uncertainty. And then, a K-Means based outlier detection scheme is proposed to further analyze plenty of trust values obtained via fuzzy trust evaluation or trust recommendation. It can discover the commonalities and differences among sensor nodes while improving the accuracy of outlier detection. Finally, we present an evolutionary game based secure clustering protocol to achieve a trade-off between security assurance and energy saving for sensor nodes when electing for the cluster heads. A sensor node which failed to be the cluster head can securely choose its own head by isolating the suspicious nodes. Simulation results verify that our secure clustering protocol can effectively defend the network against the attacks from internal selfish or compromised nodes. Correspondingly, the timely data transfer rate can be improved significantly.

Physical modeling is critical for many modern science and engineering applications. From a data science or machine learning perspective, where more domain-agnostic, data-driven models are pervasive, physical knowledge -- often expressed as differential equations -- is valuable in that it is complementary to data, and it can potentially help overcome issues such as data sparsity, noise, and inaccuracy. In this work, we propose a simple, yet powerful and general framework -- AutoIP, for Automatically Incorporating Physics -- that can integrate all kinds of differential equations into Gaussian Processes (GPs) to enhance prediction accuracy and uncertainty quantification. These equations can be linear or nonlinear, spatial, temporal, or spatio-temporal, complete or incomplete with unknown source terms, and so on. Based on kernel differentiation, we construct a GP prior to sample the values of the target function, equation-related derivatives, and latent source functions, which are all jointly from a multivariate Gaussian distribution. The sampled values are fed to two likelihoods: one to fit the observations, and the other to conform to the equation. We use the whitening method to evade the strong dependency between the sampled function values and kernel parameters, and we develop a stochastic variational learning algorithm. AutoIP shows improvement upon vanilla GPs in both simulation and several real-world applications, even using rough, incomplete equations.

Evaluating image generation models such as generative adversarial networks (GANs) is a challenging problem. A common approach is to compare the distributions of the set of ground truth images and the set of generated test images. The Frech\'et Inception distance is one of the most widely used metrics for evaluation of GANs, which assumes that the features from a trained Inception model for a set of images follow a normal distribution. In this paper, we argue that this is an over-simplified assumption, which may lead to unreliable evaluation results, and more accurate density estimation can be achieved using a truncated generalized normal distribution. Based on this, we propose a novel metric for accurate evaluation of GANs, named TREND (TRuncated gEneralized Normal Density estimation of inception embeddings). We demonstrate that our approach significantly reduces errors of density estimation, which consequently eliminates the risk of faulty evaluation results. Furthermore, we show that the proposed metric significantly improves robustness of evaluation results against variation of the number of image samples.

Naive Bayes is a probabilistic machine learning algorithm that is based on the Bayes Theorem and is used for a wide range of classification challenges. In this blog, we will learn about the Naive Bayes algorithm and all of its core concepts so that there are no gaps in the information. As we all know, machine learning is the technology that predicts goal B using characteristics A, i.e., computing the conditional probability P(B A). Then, for the discriminative model, we only take into account assessing the conditional probability. This establishes the classifier under the condition of a limited sample, without evaluating the sample's generative model, instead of learning the prediction model, like in the binary classification problem.

Bayesian optimization is a popular framework for the optimization of black box functions. Multifidelity methods allows to accelerate Bayesian optimization by exploiting low-fidelity representations of expensive objective functions. Popular multifidelity Bayesian strategies rely on sampling policies that account for the immediate reward obtained evaluating the objective function at a specific input, precluding greater informative gains that might be obtained looking ahead more steps. This paper proposes a non-myopic multifidelity Bayesian framework to grasp the long-term reward from future steps of the optimization. Our computational strategy comes with a two-step lookahead multifidelity acquisition function that maximizes the cumulative reward obtained measuring the improvement in the solution over two steps ahead. We demonstrate that the proposed algorithm outperforms a standard multifidelity Bayesian framework on popular benchmark optimization problems.

5G edge computing enabled Internet of Medical Things (IoMT) is an efficient technology to provide decentralized medical services while Device-to-device (D2D) communication is a promising paradigm for future 5G networks. To assure secure and reliable communication in 5G edge computing and D2D enabled IoMT systems, this paper presents an intelligent trust cloud management method. Firstly, an active training mechanism is proposed to construct the standard trust clouds. Secondly, individual trust clouds of the IoMT devices can be established through fuzzy trust inferring and recommending. Thirdly, a trust classification scheme is proposed to determine whether an IoMT device is malicious. Finally, a trust cloud update mechanism is presented to make the proposed trust management method adaptive and intelligent under an open wireless medium. Simulation results demonstrate that the proposed method can effectively address the trust uncertainty issue and improve the detection accuracy of malicious devices.

With the increasing abundance of pretrained models in recent years, the problem of selecting the best pretrained checkpoint for a particular downstream classification task has been gaining increased attention. Although several methods have recently been proposed to tackle the selection problem (e.g. LEEP, H-score), these methods resort to applying heuristics that are not well motivated by learning theory. In this paper we present PACTran, a theoretically grounded family of metrics for pretrained model selection and transferability measurement. We first show how to derive PACTran metrics from the optimal PAC-Bayesian bound under the transfer learning setting. We then empirically evaluate three metric instantiations of PACTran on a number of vision tasks (VTAB) as well as a language-and-vision (OKVQA) task. An analysis of the results shows PACTran is a more consistent and effective transferability measure compared to existing selection methods.