Joint matrix triangularization is often used for estimating the joint eigenstructure of a set M of matrices, with applications in signal processing and machine learning. We consider the problem of approximate joint matrix triangularization when the matrices in M are jointly diagonalizable and real, but we only observe a set M' of noise perturbed versions of the matrices in M. Our main result is a first-order upper bound on the distance between any approximate joint triangularizer of the matrices in M' and any exact joint triangularizer of the matrices in M. The bound depends only on the observable matrices in M' and the noise level. In particular, it does not depend on optimization specific properties of the triangularizer, such as its proximity to critical points, that are typical of existing bounds in the literature. To our knowledge, this is the first a posteriori bound for joint matrix decomposition. We demonstrate the bound on synthetic data for which the ground truth is known.

Joint matrix triangularization is often used for estimating the joint eigenstructure of a set M of matrices, with applications in signal processing and machine learning. We consider the problem of approximate joint matrix triangularization when the matrices in M are jointly diagonalizable and real, but we only observe a set M' of noise perturbed versions of the matrices in M. Our main result is a first-order upper bound on the distance between any approximate joint triangularizer of the matrices in M' and any exact joint triangularizer of the matrices in M. The bound depends only on the observable matrices in M' and the noise level. In particular, it does not depend on optimization specific properties of the triangularizer, such as its proximity to critical points, that are typical of existing bounds in the literature. To our knowledge, this is the first a posteriori bound for joint matrix decomposition. We demonstrate the bound on synthetic data for which the ground truth is known.

The advent of Industry 4.0 has precipitated the incorporation of Artificial Intelligence (AI) methods within industrial contexts, aiming to realize intelligent manufacturing, operation as well as maintenance, also known as industrial intelligence. However, intricate industrial milieus, particularly those relating to energy exploration and production, frequently encompass data characterized by long-tailed class distribution, sample imbalance, and domain shift. These attributes pose noteworthy challenges to data-centric Deep Learning (DL) techniques, crucial for the realization of industrial intelligence. The present study centers on the intricate and distinctive industrial scenarios of Nuclear Power Generation (NPG), meticulously scrutinizing the application of DL techniques under the constraints of finite data samples. Initially, the paper expounds on potential employment scenarios for AI across the full life-cycle of NPG. Subsequently, we delve into an evaluative exposition of DL's advancement, grounded in the finite sample perspective. This encompasses aspects such as small-sample learning, few-shot learning, zero-shot learning, and open-set recognition, also referring to the unique data characteristics of NPG. The paper then proceeds to present two specific case studies. The first revolves around the automatic recognition of zirconium alloy metallography, while the second pertains to open-set recognition for signal diagnosis of machinery sensors. These cases, spanning the entirety of NPG's life-cycle, are accompanied by constructive outcomes and insightful deliberations. By exploring and applying DL methodologies within the constraints of finite sample availability, this paper not only furnishes a robust technical foundation but also introduces a fresh perspective toward the secure and efficient advancement and exploitation of this advanced energy source.

Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies such as neuroimaging, computer vision, climatology and social networks, has brought challenges to traditional data representation methods. Tensors, as high dimensional extensions of vectors, are considered as natural representations of high dimensional data. In this book, the authors provide a systematic study and analysis of tensor-based regression models and their applications in recent years. It groups and illustrates the existing tensor-based regression methods and covers the basics, core ideas, and theoretical characteristics of most tensor-based regression methods. In addition, readers can learn how to use existing tensor-based regression methods to solve specific regression tasks with multiway data, what datasets can be selected, and what software packages are available to start related work as soon as possible. Tensor Regression is the first thorough overview of the fundamentals, motivations, popular algorithms, strategies for efficient implementation, related applications, available datasets, and software resources for tensor-based regression analysis. It is essential reading for all students, researchers and practitioners of working on high dimensional data.

Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for representing a matrix from a set of selected rows and columns-is an efficient method for constructing a tensor train decomposition of a tensor from few of its entries. While tensor train cross approximation has achieved remarkable performance in practical applications, its theoretical analysis, in particular regarding the error of the approximation, is so far lacking. To our knowledge, existing results only provide element-wise approximation accuracy guarantees, which lead to a very loose bound when extended to the entire tensor. In this paper, we bridge this gap by providing accuracy guarantees in terms of the entire tensor for both exact and noisy measurements. Our results illustrate how the choice of selected subtensors affects the quality of the cross approximation and that the approximation error caused by model error and/or measurement error may not grow exponentially with the order of the tensor. These results are verified by numerical experiments, and may have important implications for the usefulness of cross approximations for high-order tensors, such as those encountered in the description of quantum many-body states.

Adversarial training is one of the most effective approaches to improve model robustness against adversarial examples. However, previous works mainly focus on the overall robustness of the model, and the in-depth analysis on the role of each class involved in adversarial training is still missing. In this paper, we propose to analyze the class-wise robustness in adversarial training. First, we provide a detailed diagnosis of adversarial training on six benchmark datasets, i.e., MNIST, CIFAR-10, CIFAR-100, SVHN, STL-10 and ImageNet. Surprisingly, we find that there are remarkable robustness discrepancies among classes, leading to unbalance/unfair class-wise robustness in the robust models. Furthermore, we keep investigating the relations between classes and find that the unbalanced class-wise robustness is pretty consistent among different attack and defense methods. Moreover, we observe that the stronger attack methods in adversarial learning achieve performance improvement mainly from a more successful attack on the vulnerable classes (i.e., classes with less robustness). Inspired by these interesting findings, we design a simple but effective attack method based on the traditional PGD attack, named Temperature-PGD attack, which proposes to enlarge the robustness disparity among classes with a temperature factor on the confidence distribution of each image. Experiments demonstrate our method can achieve a higher attack rate than the PGD attack. Furthermore, from the defense perspective, we also make some modifications in the training and inference phases to improve the robustness of the most vulnerable class, so as to mitigate the large difference in class-wise robustness. We believe our work can contribute to a more comprehensive understanding of adversarial training as well as rethinking the class-wise properties in robust models.

Sentiment analysis is contextual mining of text which identifies and extracts subjective information in source material, and helping a business to understand the social sentiment of the brand, product or service while monitoring online conversations. However, analysis of social media streams is usually restricted to just basic sentiment analysis and count based metrics. This is akin to just scratching the surface and missing out on those high value insights that are waiting to be discovered. So what should a brand do to capture that low hanging fruit? With the recent advances in deep learning, the ability of algorithms to analyse text has improved considerably.

Joint matrix triangularization is often used for estimating the joint eigenstructure of a set M of matrices, with applications in signal processing and machine learning. We consider the problem of approximate joint matrix triangularization when the matrices in M are jointly diagonalizable and real, but we only observe a set M' of noise perturbed versions of the matrices in M. Our main result is a first-order upper bound on the distance between any approximate joint triangularizer of the matrices in M' and any exact joint triangularizer of the matrices in M. The bound depends only on the observable matrices in M' and the noise level. In particular, it does not depend on optimization specific properties of the triangularizer, such as its proximity to critical points, that are typical of existing bounds in the literature. To our knowledge, this is the first a posteriori bound for joint matrix decomposition. We demonstrate the bound on synthetic data for which the ground truth is known.