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Sufficient dimension reduction for high-dimensional regression and low-dimensional embedding: tutorial and survey

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arXiv 2021年

This is a tutorial and survey paper on various methods for Sufficient Dimension Reduction (SDR). We cover these methods with both statistical high-dimensional regression perspective and machine learning approach for dimensionality reduction. We start with introducing inverse regression methods including Sliced Inverse Regression (SIR), Sliced Average Variance Estimation (SAVE), contour regression, directional regression, Principal Fitted Components (PFC), Likelihood Acquired Direction (LAD), and graphical regression. Then, we introduce forward regression methods including Principal Hessian Directions (pHd), Minimum Average Variance Estimation (MAVE), Conditional Variance Estimation (CVE), and deep SDR methods. Finally, we explain Kernel Dimension Reduction (KDR) both for supervised and unsupervised learning. We also show that supervised KDR and supervised PCA are equivalent. Copyright © 2021, The Authors. All rights reserved.

关键词： Regression analysis

Uncertainty Quantification of the Virial Black Hole Mass with Conformal Prediction

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arXiv 2023年

作者： Yong, Suk Yee Ong, Cheng Soon Australia Astrophysics and Space Technologies Research Centre Macquarie University SydneyNSW2109 Australia School of Mathematical and Physical Sciences Macquarie University SydneyNSW2109 Australia Faculty of Science and Engineering Macquarie University SydneyNSW2109 Australia Machine Learning and Artificial Intelligence Future Science Platform CSIRO Australia Data61 CSIRO CanberraACT2601 Australia School of Computing The Australian National University CanberraACT2601 Australia

Precise measurements of the black hole mass are essential to gain insight on the black hole and host galaxy co-evolution. A direct measure of the black hole mass is often restricted to nearest galaxies and instead, an indirect method using the single-epoch virial black hole mass estimation is used for objects at high redshifts. However, this method is subjected to biases and uncertainties as it is reliant on the scaling relation from a small sample of local active galactic nuclei. In this study, we propose the application of conformalised quantile regression (CQR) to quantify the uncertainties of the black hole predictions in a machine learning setting. We compare CQR with various prediction interval techniques and demonstrated that CQR can provide a more useful prediction interval indicator. In contrast to baseline approaches for prediction interval estimation, we show that the CQR method provides prediction intervals that adjust to the black hole mass and its related properties. That is it yields a tighter constraint on the prediction interval (hence more certain) for a larger black hole mass, and accordingly, bright and broad spectral line width source. Using a combination of neural network model and CQR framework, the recovered virial black hole mass predictions and uncertainties are comparable to those measured from the Sloan Digital Sky Survey. The code is publicly available at https://***/yongsukyee/uncertain_blackholemass. Copyright © 2023, The Authors. All rights reserved.

关键词： Forecasting

DSGD-CECA: Decentralized SGD with Communication-Optimal Exact Consensus Algorithm

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arXiv 2023年

作者： Ding, Lisang Jin, Kexin Ying, Bicheng Yuan, Kun Yin, Wotao Department of Mathematics University of California Los AngelesCA United States Department of Mathematics Princeton University PrincetonNJ United States Google Inc. Los AngelesCA United States Center for Machine Learning Research Peking University Beijing China AI for Science Institute Beijing China National Engineering Labratory for Big Data Analytics and Applications Beijing China Decision Intelligence Lab. Alibaba US BellevueWA United States

Decentralized Stochastic Gradient Descent (SGD) is an emerging neural network training approach that enables multiple agents to train a model collaboratively and simultaneously. Rather than using a central parameter server to collect gradients from all the agents, each agent keeps a copy of the model parameters and communicates with a small number of other agents to exchange model updates. Their communication, governed by the communication topology and gossip weight matrices, facilitates the exchange of model updates. The state-of-the-art approach uses the dynamic one-peer exponential-2 topology, achieving faster training times and improved scalability than the ring, grid, torus, and hypercube topologies. However, this approach requires a power-of-2 number of agents, which is impractical at scale. In this paper, we remove this restriction and propose Decentralized SGD with Communication-optimal Exact Consensus Algorithm (DSGD-CECA), which works for any number of agents while still achieving state-of-the-art properties. In particular, DSGD-CECA incurs a unit per-iteration communication overhead and an Õ(n3) transient iteration complexity. Our proof is based on newly discovered properties of gossip weight matrices and a novel approach to combine them with DSGD’s convergence analysis. Numerical experiments show the efficiency of DSGD-CECA. Copyright © 2023, The Authors. All rights reserved.

关键词： Stochastic systems

Unified Framework for Spectral Dimensionality Reduction, Maximum Variance Unfolding, and Kernel learning By Semidefinite Programming: Tutorial and Survey

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arXiv 2021年

作者： Ghojogh, Benyamin Ghodsi, Ali Karray, Fakhri Crowley, Mark Department of Electrical and Computer Engineering Machine Learning Laboratory University of Waterloo WaterlooON Canada Department of Statistics and Actuarial Science David R. Cheriton School of Computer Science Data Analytics Laboratory University of Waterloo WaterlooON Canada Department of Electrical and Computer Engineering Centre for Pattern Analysis and Machine Intelligence University of Waterloo WaterlooON Canada

This is a tutorial and survey paper on unification of spectral dimensionality reduction methods, kernel learning by Semidefinite Programming (SDP), Maximum Variance Unfolding (MVU) or Semidefinite Embedding (SDE), and its variants. We first explain how the spectral dimensionality reduction methods can be unified as kernel Principal Component Analysis (PCA) with different kernels. This unification can be interpreted as eigenfunction learning or representation of kernel in terms of distance matrix. Then, since the spectral methods are unified as kernel PCA, we say let us learn the best kernel for unfolding the manifold of data to its maximum variance. We first briefly introduce kernel learning by SDP for the transduction task. Then, we explain MVU in detail. Various versions of supervised MVU using nearest neighbors graph, by class-wise unfolding, by Fisher criterion, and by colored MVU are explained. We also explain out-of-sample extension of MVU using eigenfunctions and kernel mapping. Finally, we introduce other variants of MVU including action respecting embedding, relaxed MVU, and landmark MVU for big data. Copyright © 2021, The Authors. All rights reserved.

关键词： Surveys

Parameter estimation for cellular automata

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arXiv 2023年

作者： Kazarnikov, Alexey Ray, Nadja Haario, Heikki Lappalainen, Joona Rupp, Andreas Heidelberg University Mathematikon Im Neuenheimer Feld 205 Heidelberg69120 Germany Mathematical Institute for Machine Learning and Data Science Catholic University of Eichstätt-Ingolstadt Hohe-Schul-Str. 5 Ingolstadt85049 Germany School of Engineering Science Lappeenranta–Lahti University of Technology P.O. Box 20 Lappeenranta53851 Finland Department of Mathematics Faculty of Mathematics and Computer Science Saarland University SaarbrückenDE-66123 Germany

Self-organizing complex systems can be modeled using cellular automaton models. However, the parametrization of these models is crucial and significantly determines the resulting structural pattern. In this research, we introduce and successfully apply a sound statistical method to estimate these parameters. The decisive difference to earlier applications of such approaches is that, in our case, both the CA rules and the resulting patterns are discrete. The method is based on constructing Gaussian likelihoods using characteristics of the structures, such as the mean particle size. We show that our approach is robust for the method parameters, domain size of patterns, or CA iterations. Copyright © 2023, The Authors. All rights reserved.

关键词： Statistical methods

Factor Analysis, Probabilistic Principal Component Analysis, Variational Inference, and Variational Autoencoder: Tutorial and Survey

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arXiv 2021年

作者： Ghojogh, Benyamin Ghodsi, Ali Karray, Fakhri Crowley, Mark Department of Electrical and Computer Engineering Machine Learning Laboratory University of Waterloo WaterlooON Canada Department of Statistics and Actuarial Science David R. Cheriton School of Computer Science Data Analytics Laboratory University of Waterloo WaterlooON Canada Department of Electrical and Computer Engineering Centre for Pattern Analysis and Machine Intelligence University of Waterloo WaterlooON Canada

This is a tutorial and survey paper on factor analysis, probabilistic Principal Component Analysis (PCA), variational inference, and Variational Autoencoder (VAE). These methods, which are tightly related, are dimensionality reduction and generative models. They assume that every data point is generated from or caused by a lowdimensional latent factor. By learning the parameters of distribution of latent space, the corresponding low-dimensional factors are found for the sake of dimensionality reduction. For their stochastic and generative behaviour, these models can also be used for generation of new data points in the data space. In this paper, we first start with variational inference where we derive the Evidence Lower Bound (ELBO) and Expectation Maximization (EM) for learning the parameters. Then, we introduce factor analysis, derive its joint and marginal distributions, and work out its EM steps. Probabilistic PCA is then explained, as a special case of factor analysis, and its closed-form solutions are derived. Finally, VAE is explained where the encoder, decoder and sampling from the latent space are introduced. Training VAE using both EM and backpropagation are explained. Copyright © 2021, The Authors. All rights reserved.

关键词： Maximum principle

An Investigation of Smart Detection for Small Lung Tumor with Tumor Pattern Recognition Algorithm

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An Investigation of Smart Detection for Small Lung Tumor wit...

Artificial Intelligence and Knowledge Discovery in Concurrent engineering (ICECONF), International Conference on

作者： G. Hariharan P. Prasanth P. Arthi Devarani T. Sajana Indhumathi C Ashok Kumar Deportment of Artificial Intelligence and Machine Learning Malla Reddy University Hyderabad Telangana India Department of Information Technology Vel Tech Multi Tech Dr. Rangarajan Dr.Sakunthala Engineering College Chennai Tamil Nadu India Department of Electronics and Communication Engineering R. M K College of Engineering and Technology Thiruvallur Tamil Nadu India Department of Artificial Intelligence and Data Science KoneruLakshmaiah Education Foundation Vaddeswaram Andhra Pradesh India Department of Computer Science and Business Systems R.M. K. Engineering College Kavaraipettai Tamil Nadu Department of Computer Science BanasthaliVidyapith Rajasthan India

The Small-cell lung tumor is the prime public concern, resulting in increased mortality. Various therapeutic approaches have made progress in the handling of small-cell lung tumor. It's considered the backbone of cytotoxic chemotherapy treatment. However, clinical research shows that because small-cell lung tumor is chemically approachable, high response rates among small-cell lung tumorinfecters are generally not translated into cure. Therefore, it is high time to make progress in small-cell lung tumor research because every success in clinical trials is fought, and every failure is a lesson. A recent study of small-cell lung tumor has improved the prognosis of patients. Some notable research areas have provided new options for patients by conducting multiple clinical trials. In this paper smart edge detection based small lung tumor identification method was proposed. This model operates with the pattern recognition algorithm model. This algorithm smartly finds the edges of the tumor cells and provides the edge results. This will helpful for the doctors to identify the tumor part exactly.

关键词： Chemotherapy Image edge detection Lung cancer Medical services Clinical trials Knowledge discovery Concurrent engineering

Advanced Process Control in Manufacturing Using IoT Devices and Artificial Neural Networks

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Advanced Process Control in Manufacturing Using IoT Devices ...

Sustainable Expert Systems (ICSES), International Conference on

作者： V. Sumathi Ramesh S Chethan Chandra S Basavaraddi Visumathi J Ishwarya M.V S. Srinivasan Department of Mathematics Sri Sairam Engineering College Chennai Tamil Nadu India Department of Computing Technologies School of Computing College of Engineering and Technology SRM Institute of Science and Technology Kattankulathur Chennai Tamil Nadu India Department of Artificial Intelligence and Machine Learning R&D Don Bosco Institute of Technology VTU Belagavi Karnataka India Department of Information Technology Veltech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology Chennai Tamil Nadu India Artificial intelligence and Data science Department Agni College of Technology Chennai Tamil Nadu India Department of Biomedical Engineering Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences Saveetha University Chennai Tamil Nadu India

ISBN: (数字)9798331540364

ISBN: (纸本)9798331540371

Optimization of industrial activities is significantly helped by Advanced Process Control (APC), which increases efficiency, decreases costs, and improves product quality. Artificial Neural Networks (ANNs) and the Internet of Things (IoT) have greatly improved APC in manufacturing. It examines how APC systems may include ANNs and IoT devices in industrial processes. By connecting to a wide range of sensors placed strategically throughout a production facility, IoT devices may gather data in real time, allowing for managing and monitoring crucial parameters. To APC systems, ANNs are invaluable for predictive modeling and control due to their adaptability to changing process conditions and capacity to represent complicated nonlinear interactions. Manufacturers may gain better control over their operations, improving productivity and product quality, by using data from the IoT to train and update ANN models. Recent advances in APC using IoT devices and ANNs are reviewed in this study. Their applications in various industrial industries are discussed, and case examples are shown to demonstrate their usefulness. Further improvements in APC for manufacturing using IoT devices and ANNs may be guided by highlighting the field's problems and future research goals. Challenges with data security, integration challenges, and reliability impact the accuracy of predictive modeling, scalability, and performance of IoT systems.

关键词： Performance evaluation Adaptation models Process control Artificial neural networks Predictive models Real-time systems Manufacturing Sensors Internet of Things Monitoring

Robust and Fast Measure of Information via Low-rank Representation

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arXiv 2022年

作者： Dong, Yuxin Gong, Tieliang Yu, Shujian Chen, Hong Li, Chen School of Computer Science and Technology Xi’an Jiaotong University Xi’an710049 China Shaanxi Provincial Key Laboratory of Big Data Knowledge Engineering Ministry of Education Xi’an710049 China Machine Learning Group UiT - The Arctic University of Norway Norway College of Science Huazhong Agriculture University Wuhan430070 China Engineering Research Center of Intelligent Technology for Agriculture Ministry of Education Wuhan430070 China

The matrix-based Rényi’s entropy allows us to directly quantify information measures from given data, without explicit estimation of the underlying probability distribution. This intriguing property makes it widely applied in statistical inference and machine learning tasks. However, this information theoretical quantity is not robust against noise in the data, and is computationally prohibitive in large-scale applications. To address these issues, we propose a novel measure of information, termed low-rank matrix-based Rényi’s entropy, based on low-rank representations of infinitely divisible kernel matrices. The proposed entropy functional inherits the specialty of of the original definition to directly quantify information from data, but enjoys additional advantages including robustness and effective calculation. Specifically, our low-rank variant is more sensitive to informative perturbations induced by changes in underlying distributions, while being insensitive to uninformative ones caused by noises. Moreover, low-rank Rényi’s entropy can be efficiently approximated by random projection and Lanczos iteration techniques, reducing the overall complexity from O(n3) to O(n2s) or even O(ns2), where n is the number of data samples and s n. We conduct large-scale experiments to evaluate the effectiveness of this new information measure, demonstrating superior results compared to matrix-based Rényi’s entropy in terms of both performance and computational efficiency. Copyright © 2022, The Authors. All rights reserved.

关键词： Entropy