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The Mathematics of Dots and Pixels: On the Theoretical Foundations of Image Halftoning

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arXiv 2024年

作者： Krahmer, Felix Veselovska, Anna Technical University of Munich Department of Mathematics and Munich Data Science Institute Munich Center for Machine Learning Germany

The evolution of image halftoning, from its analog roots to contemporary digital methodologies, encapsulates a fascinating journey marked by technological advancements and creative innovations. Yet the theoretical understanding of halftoning is much more recent. In this article, we explore various approaches towards shedding light on the design of halftoning approaches and why they work. We discuss both halftoning in a continuous domain and on a pixel grid. We start by reviewing the mathematical foundation of the so-called electrostatic halftoning method, which departed from the heuristic of considering the back dots of the halftoned image as charged particles attracted by the grey values of the image in combination with mutual repulsion. Such an attraction-repulsion model can be mathematically represented via an energy functional in a reproducing kernel Hilbert space allowing for a rigorous analysis of the resulting optimization problem as well as a convergence analysis in a suitable topology. A second class of methods that we discuss in detail is the class of error diffusion schemes, arguably among the most popular halftoning techniques due to their ability to work directly on a pixel grid and their ease of application. The main idea of these schemes is to choose the locations of the black pixels via a recurrence relation designed to agree with the image in terms of the local averages. We discuss some recent mathematical understanding of these methods that is based on a connection to ΣΔ quantizers, a popular class of algorithms for analog-to-digital *** Codes 94A08, 62H35 © 2024, CC BY-NC-SA.

关键词： Pixels

Optimization and Benchmarking of Convolutional Networks with Quantization and OpenVINO in Baggage Image Recognition 8

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Optimization and Benchmarking of Convolutional Networks with...

8th International Conference on Information Technology and Nanotechnology, ITNT 2022

作者： Andriyanov, Nikita Papakostas, George Financial University under the Government of the Russian Federation Department of Data Analysis and Machine Learning Moscow Russia International Hellenic University Department of Computer Science Thessaloniki Greece

ISBN: (数字)9781665485715

ISBN: (纸本)9781665485715

The paper is devoted to the study of the neural networks inference acceleration using the weights quantization and Intel OpenVINO Toolkit. At the same time, the study considers block architecture convolutional networks trained from scratch. In addition, it is shown that transfer learning makes it possible to obtain higher model accuracy. And their implementation on OpenVINO can significantly increase the processing performance. It is also shown that the use of OpenVINO provides significant acceleration without loss of performance for such networks, while quantization leads to significant loss of quality. © 2022 IEEE.

关键词： Computer vision

Smart Telemedicine Using IoT by Integrating 5G and Block-Chain Techniques 6

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Smart Telemedicine Using IoT by Integrating 5G and Block-Cha...

6th International Conference on Contemporary Computing and Informatics, IC3I 2023

作者： Choudhary, Shailee Lohmor Dixit, Rinku Sharma Das, Deepak Ranjith Singh, K. Dinesh Babu, V. New Delhi Institute of Management Department of Artificial Intelligence & Machine Learning - Data Science New Delhi India Karunya Institute of Science and Technology Agricultural Engineering Coimbatore India Karpagam Academy of Higher Education Department of Computer Science Coimbatore India Karpagam Institute of Technology Department of Information Technology Coimbatore India

ISBN: (纸本)9798350304480

There are many medical applications for the Internet of Health Things (IoHT). In order to offer patients with more intelligent and effective health diagnoses, contemporary IoHT incorporates wellness items such sensors with continuously monitored medical equipment for the evaluation and handling of a medical chart. Using the combination of 5G networks and ethereum technology, we presented the IoT using a fog medical decision assistance system in this study for the forecast and monitoring of illness along with its severities. Due to its visibility, a frame provides a method for keeping and exchanging knowledge which is safe. Ethereum has various uses in the medical industry and therefore can enhance monitoring equipment, clinical study storage systems, mobile medical software, exchanging and keeping of digital media files, and insurer details stockpiling. The suggested structure will assemble a cloud provider will hold client information from the health equipment that's going to be connected to the individual, along with any pertinent health records. The use of 5G with cryptocurrency technologies allows the reliable transfer of patient information at high transmission rates with short reaction times. In addition, a Deep Neural (NN) classification is employed to forecast illnesses as well as the degree of underlying severity. The suggested model is tested using a variety of classifiers. In order to determine which classification is appropriate for the information, the effectiveness of various classifier is compared by contrasting the results. The NN improved a 98.98 average accuracy. This NN is additionally trained on the information such so this can forecast the outcome of the information category that carries no labels. A taught Naive Bayes is more accurate than conventional classifications at making predictions and effectively displaying the findings. © 2023 IEEE.

关键词： 5G Blockchain CDSS DNN IoHT IoT

Exploring Neural Network Landscapes: Star-Shaped and Geodesic Connectivity

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arXiv 2024年

作者： Lin, Zhanran Li, Puheng Wu, Lei Department of Statistics and Data Science Wharton School University of Pennsylvania United States Department of Statistics Stanford University United States School of Mathematical Sciences Peking University China Center for Machine Learning Research Peking University China

One of the most intriguing findings in the structure of neural network landscape is the phenomenon of mode connectivity [FB17, DVSH18]: For two typical global minima, there exists a path connecting them without barrier. This concept of mode connectivity has played a crucial role in understanding important phenomena in deep learning. In this paper, we conduct a fine-grained analysis of this connectivity phenomenon. First, we demonstrate that in the overparameterized case, the connecting path can be as simple as a two-piece linear path, and the path length can be nearly equal to the Euclidean distance. This finding suggests that the landscape should be nearly convex in a certain sense. Second, we uncover a surprising star-shaped connectivity: For a finite number of typical minima, there exists a center on minima manifold that connects all of them simultaneously via linear paths. These results are provably valid for linear networks and two-layer ReLU networks under a teacher-student setup, and are empirically supported by models trained on MNIST and CIFAR-10. Copyright © 2024, The Authors. All rights reserved.

关键词： Deep learning

Feature Importance: A Closer Look at Shapley Values and LOCO

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arXiv 2023年

作者： Verdinelli, Isabella Wasserman, Larry Department of Statistics and Data Science Carnegie Mellon University PittsburghPA United States Machine Learning Department Carnegie Mellon University PA United States

There is much interest lately in explainability in statistics and machine learning. One aspect of explainability is to quantify the importance of various features (or covariates). Two popular methods for defining variable importance are LOCO (Leave Out COvariates) and Shapley Values. We take a look at the properties of these methods and their advantages and disadvantages. We are particularly interested in the effect of correlation between features which can obscure interpretability. Contrary to some claims, Shapley values do not eliminate feature correlation. We critique the game theoretic axioms for Shapley values and suggest some new axioms. We propose new, more statistically oriented axioms for feature importance and some measures that satisfy these axioms. However, correcting for correlation is a Faustian bargain: removing the effect of correlation creates other forms of bias. Ultimately, we recommend a slightly modified version of LOCO. We briefly consider how to modify Shapley values to better address feature correlation. © 2023, CC BY.

关键词： Game theory

An Improved Finite-time Analysis of Temporal Difference learning with Deep Neural Networks 41

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An Improved Finite-time Analysis of Temporal Difference Lear...

41st International Conference on machine learning, ICML 2024

作者： Ke, Zhifa Wen, Zaiwen Zhang, Junyu Center for Data Science Peking University China Beijing International Center for Mathematical Research Center for Machine Learning Research Changsha Institute for Computing and Digital Economy Beijing China Department of Industrial Systems Engineering and Management National University of Singapore Singapore

Temporal difference (TD) learning algorithms with neural network function parameterization have well-established empirical success in many practical large-scale reinforcement learning tasks. However, theoretical understanding of these algorithms remains challenging due to the nonlinearity of the action-value approximation. In this paper, we develop an improved non-asymptotic analysis of the neural TD method with a general L-layer neural network. New proof techniques are developed and an improved new Õ(ϵ-1) sample complexity is derived. To our best knowledge, this is the first finite-time analysis of neural TD that achieves an Õ(ϵ-1) complexity under the Markovian sampling, as opposed to the best known Õ(ϵ-2) complexity in the existing literature. Copyright 2024 by the author(s)

关键词： Adversarial machine learning

Low-Rank Optimal Transport through Factor Relaxation with Latent Coupling

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arXiv 2024年

作者： Halmos, Peter Liu, Xinhao Gold, Julian Raphael, Benjamin J. Department of Computer Science Princeton University United States Center for Statistics and Machine Learning Princeton University United States

Optimal transport (OT) is a general framework for finding a minimum-cost transport plan, or coupling, between probability distributions, and has many applications in machine learning. A key challenge in applying OT to massive datasets is the quadratic scaling of the coupling matrix with the size of the dataset. Forrow et al. (2019) introduced a factored coupling for the k-Wasserstein barycenter problem, which Scetbon et al. (2021) adapted to solve the primal low-rank OT problem. We derive an alternative parameterization of the low-rank problem based on the latent coupling (LC) factorization previously introduced by Lin et al. (2021) generalizing Forrow et al. (2019). The LC factorization has multiple advantages for low-rank OT including decoupling the problem into three OT problems and greater flexibility and interpretability. We leverage these advantages to derive a new algorithm Factor Relaxation with Latent Coupling (FRLC), which uses coordinate mirror descent to compute the LC factorization. FRLC handles multiple OT objectives (Wasserstein, Gromov-Wasserstein, Fused Gromov-Wasserstein), and marginal constraints (balanced, unbalanced, and semi-relaxed) with linear space complexity. We provide theoretical results on FRLC, and demonstrate superior performance on diverse applications – including graph clustering and spatial transcriptomics – while demonstrating its interpretability. Copyright © 2024, The Authors. All rights reserved.

关键词： Matrix factorization

Model and Feature Diversity for Bayesian Neural Networks in Mutual learning 37

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Model and Feature Diversity for Bayesian Neural Networks in ...

37th Conference on Neural Information Processing Systems, NeurIPS 2023

作者： Pham, Cuong Nguyen, Cuong C. Le, Trung Phung, Dinh Carneiro, Gustavo Do, Thanh-Toan Department of Data Science and AI Monash University Australia Australian Institute for Machine Learning University of Adelaide Australia Centre for Vision Speech and Signal Processing University of Surrey United Kingdom VinAI Viet Nam

ISBN: (纸本)9781713899921

Bayesian Neural Networks (BNNs) offer probability distributions for model parameters, enabling uncertainty quantification in predictions. However, they often underperform compared to deterministic neural networks. Utilizing mutual learning can effectively enhance the performance of peer BNNs. In this paper, we propose a novel approach to improve BNNs performance through deep mutual learning. The proposed approaches aim to increase diversity in both network parameter distributions and feature distributions, promoting peer networks to acquire distinct features that capture different characteristics of the input, which enhances the effectiveness of mutual learning. Experimental results demonstrate significant improvements in the classification accuracy, negative log-likelihood, and expected calibration error when compared to traditional mutual learning for BNNs. © 2023 Neural information processing systems foundation. All rights reserved.

关键词： Probability distributions

ON THE EXISTENCE OF POWERFUL P-VALUES AND E-VALUES FOR COMPOSITE HYPOTHESES

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arXiv 2023年

作者： Zhang, Zhenyuan Ramdas, Aaditya Wang, Ruodu Department of Mathematics Stanford University United States Depts. of Statistics & Data Science and Machine Learning Carnegie Mellon Univ. United States Department of Statistics and Actuarial Science University of Waterloo Canada

Given a composite null P and composite alternative Q, when and how can we construct a p-value whose distribution is exactly uniform under the null, and stochastically smaller than uniform under the alternative? Similarly, when and how can we construct an e-value whose expectation exactly equals one under the null, but its expected logarithm under the alternative is positive? We answer these basic questions, and other related ones, when P and Q are convex polytopes (in the space of probability measures). We prove that such constructions are possible if and only if Q does not intersect the span of P. If the p-value is allowed to be stochastically larger than uniform under P ∈ P, and the e-value can have expectation at most one under P ∈ P, then it is achievable whenever P and Q are disjoint. More generally, even when P and Q are not polytopes, we characterize the existence of a bounded nontrivial e-variable whose expectation exactly equals one under any P ∈ P. The proofs utilize recently developed techniques in simultaneous optimal transport. A key role is played by coarsening the filtration: sometimes, no such p-value or e-value exists in the richest data filtration, but it does exist in some reduced filtration, and our work provides the first general characterization of this phenomenon. We also provide an iterative construction that explicitly constructs such processes, and under certain conditions it finds the one that grows fastest under a specific alternative Q. We discuss implications for the construction of composite nonnegative (super)martingales, and end with some conjectures and open problems. Copyright © 2023, The Authors. All rights reserved.

关键词： Stochastic systems