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Detection and tracking of gas plumes in LWIR hyperspectral video sequence data

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arXiv 2024年

作者： Gerhart, Torin Sunu, Justin Lieu, Lauren Merkurjev, Ekaterina Chang, Jen-Mei Gilles, Jérome Bertozzi, Andrea L. Department of Mathematics and Statistics California State University Long Beach Long BeachCA United States Department of Mathematics University of California Los Angeles 520 Portola Plaza Los AngelesCA United States Department of Engineering Harvey Mudd College ClaremontCA United States

Automated detection of chemical plumes presents a segmentation challenge. The segmentation problem for gas plumes is difficult due to the diffusive nature of the cloud. The advantage of considering hyperspectral images in the gas plume detection problem over the conventional RGB imagery is the presence of non-visual data, allowing for a richer representation of information. In this paper we present an effective method of visualizing hyperspectral video sequences containing chemical plumes and investigate the effectiveness of segmentation techniques on these post-processed videos. Our approach uses a combination of dimension reduction and histogram equalization to prepare the hyperspectral videos for segmentation. First, Principal Components Analysis (PCA) is used to reduce the dimension of the entire video sequence. This is done by projecting each pixel onto the first few Principal Components resulting in a type of spectral filter. Next, a Midway method for histogram equalization is used. These methods redistribute the intensity values in order to reduce flicker between frames. This properly prepares these high-dimensional video sequences for more traditional segmentation techniques. We compare the ability of various clustering techniques to properly segment the chemical plume. These include K-means, spectral clustering, and the Ginzburg-Landau functional. © 2024, CC BY-NC-ND.

关键词： Video recording

Memory-based optimization methods for model-agnostic meta-learning and personalized federated learning

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2023年第1期24卷 6926-6971页

作者： Bokun Wang Zhuoning Yuan Yiming Ying Tianbao Yang Department of Computer Science and Engineering Texas A&M University College Station TX Department of Computer Science The University of Iowa Iowa City IA Department of Mathematics and Statistics University at Albany Albany NY

In recent years, model-agnostic meta-learning (MAML) has become a popular research area. However, the stochastic optimization of MAML is still underdeveloped. Existing MAML algorithms rely on the "episode" idea by sampling a few tasks and data points to update the meta-model at each iteration. Nonetheless, these algorithms either fail to guarantee convergence with a constant mini-batch size or require processing a large number of tasks at every iteration, which is unsuitable for continual learning or cross-device federated learning where only a small number of tasks are available per iteration or per round. To address these issues, this paper proposes memory-based stochastic algorithms for MAML that converge with vanishing error. The proposed algorithms require sampling a constant number of tasks and data samples per iteration, making them suitable for the continual learning scenario. Moreover, we introduce a communication-efficient memory-based MAML algorithm for personalized federated learning in cross-device (with client sampling) and cross-silo (without client sampling) settings. Our theoretical analysis improves the optimization theory for MAML, and our empirical results corroborate our theoretical findings. Interested readers can access our code at https://***/bokun-wang/moml.

关键词： meta-learning federated learning model-agnostic meta-learning personalized federated learning memory-based algorithms

Bayesian functional data analysis in astronomy

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arXiv 2024年

作者： Loredo, Thomas Budavári, Tamás Kent, David Ruppert, David Cornell Center for Astrophysics and Planetary Science Department of Statistics and Data Science Cornell University United States Department of Applied Mathematics and Statistics Johns Hopkins University United States Department of Statistics and Data Science Cornell University United States School of Operations Research and Information Engineering Department of Statistics and Data Science Cornell University United States

Cosmic demographics—the statistical study of populations of astrophysical objects—has long relied on multivariate statistics, providing methods for analyzing data comprising fixed-length vectors of properties of objects, as might be compiled in a tabular astronomical catalog (say, with sky coordinates, and brightness measurements in a fixed number of spectral passbands). But beginning with the emergence of automated digital sky surveys, ca. 2000, astronomers began producing large collections of data with more complex structure: light curves (brightness time series) and spectra (brightness vs. wavelength). These comprise what statisticians call functional data—measurements of populations of functions. Upcoming automated sky surveys will soon provide astronomers with a flood of functional data. New methods are needed to accurately and optimally analyze large ensembles of light curves and spectra, accumulating information both along and across measured functions. Functional data analysis (FDA) provides tools for statistical modeling of functional data. Astronomical data presents several challenges for FDA methodology, e.g., sparse, irregular, and asynchronous sampling, and heteroscedastic measurement error. Bayesian FDA uses hierarchical Bayesian models for function populations, and is well suited to addressing these challenges. We provide an overview of astronomical functional data, and of some key Bayesian FDA modeling approaches, including functional mixed effects models, and stochastic process models. We briefly describe a Bayesian FDA framework combining FDA and machine learning methods to build low-dimensional parametric models for galaxy spectra. © 2024, CC BY.

关键词： Cosmology

Inference with Deep Gaussian Process State Space Models

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Inference with Deep Gaussian Process State Space Models

European Signal Processing Conference (EUSIPCO)

作者： Yuhao Liu Marzieh Ajirak Petar M. Djurić Department of Applied Mathematics and Statistics Department of Electrical and Computer Engineering Stony Brook University NY

ISBN: (数字)9789082797091

ISBN: (纸本)9781665467995

In this paper, we address the problem of sequential processing of observations modeled by deep Gaussian process state space models. First, we introduce the model where the Gaus-sian processes are based on random features and where both the transition and observation functions of the models are unknown. Then we propose a method that can estimate the unknowns of the model. The method allows for incremental learning of the system without requiring all the historical information. We also propose an ensemble version of the method, where each member of the ensemble has its own set of features. We show with computer simulations that the method can track the latent states up to scale and rotation.

关键词： Computational modeling Computer simulation Europe Gaussian processes Signal processing

Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI 41

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Position: Bayesian Deep Learning is Needed in the Age of Lar...

41st International Conference on Machine Learning, ICML 2024

作者： Papamarkou, Theodore Skoularidou, Maria Palla, Konstantina Aitchison, Laurence Arbel, Julyan Dunson, David Filippone, Maurizio Fortuin, Vincent Hennig, Philipp Hernández-Lobato, José Miguel Hubin, Aliaksandr Immer, Alexander Karaletsos, Theofanis Khan, Mohammad Emtiyaz Kristiadi, Agustinus Li, Yingzhen Mandt, Stephan Nemeth, Christopher Osborne, Michael A. Rudner, Tim G.J. Rügamer, David Teh, Yee Whye Welling, Max Wilson, Andrew Gordon Zhang, Ruqi Department of Mathematics The University of Manchester Manchester United Kingdom Eric and Wendy Schmidt Center Broad Institute of MIT and Harvard Cambridge United States Spotify London United Kingdom Computational Neuroscience Unit University of Bristol Bristol United Kingdom Centre Inria de l'Université Grenoble Alpes Grenoble France Department of Statistical Science Duke University United States Statistics Program KAUST Saudi Arabia Helmholtz AI Munich Germany Department of Computer Science Technical University of Munich Munich Germany Munich Center for Machine Learning Munich Germany Tübingen AI Center University of Tübingen Tübingen Germany Department of Engineering University of Cambridge Cambridge United Kingdom Department of Mathematics University of Oslo Oslo Norway Bioinformatics and Applied Statistics Norwegian University of Life Sciences Ås Norway Department of Computer Science ETH Zurich Switzerland Chan Zuckerberg Initiative CA United States Center for Advanced Intelligence Project RIKEN Tokyo Japan Vector Institute Toronto Canada Department of Computing Imperial College London London United Kingdom Department of Computer Science UC Irvine Irvine United States Department of Mathematics and Statistics Lancaster University Lancaster United Kingdom Department of Engineering Science University of Oxford Oxford United Kingdom Center for Data Science New York University New York United States Department of Statistics LMU Munich Munich Germany DeepMind London United Kingdom Department of Statistics University of Oxford Oxford United Kingdom Informatics Institute University of Amsterdam Amsterdam Netherlands Courant Institute of Mathematical Sciences Center for Data Science Computer Science Department New York University New York United States Department of Computer Science Purdue University West Lafayette United States

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential. Copyright 2024 by the author(s)

关键词： Contrastive Learning

SCHREIER MULTISETS AND THE S-STEP FIBONACCI SEQUENCES

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arXiv 2023年

作者： Chu, Hùng Viêt Irmak, Nurettin Miller, Steven J. Szalay, László Zhang, Sindy Xin Department of Mathematics University of Illinois Urbana-Champaign UrbanaIL United States Department of Engineering Basic Sciences Konya Technical University Konya Turkey Department of Mathematics and Statistics Williams College WilliamstownMA United States Department of Mathematics J. Selye University Komárno Slovakia Institute of Informatics and Mathematics University of Sopron Sopron Hungary Department of Mathematics University at Buffalo BuffaloNY United States Department of Mathematics Tufts University MedfordMA United States

Inspired by the surprising relationship (due to A. Bird) between Schreier sets and the Fibonacci sequence, we introduce Schreier multisets and connect these multisets with the s-step Fibonacci sequences, defined, for each s > 2, as: F2(s) -s = · · · = F0(s) = 0, F1(s) = 1, and Fn(s) = Fn(s)−1 + · · · + Fn(s) -s, for n > 2. Next, we use Schreier-type conditions on multisets to retrieve a family of sequences which satisfy a recurrence of the form a(n) = a(n − 1) + a(n − u), with a(n) = 1 for n = 1, . . ., u. Finally, we study nonlinear Schreier conditions and show that these conditions are related to integer decompositions, each part of which is greater than the number of parts raised to some *** Codes 11B39, 11B37, 11Y55 © 2023, CC BY.

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Robust Clustering with Adaptive Order Graph Learning

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SSRN

SSRN 2023年

作者： Tang, Jiayi Gao, Yan Jia, Suqi Feng, Hui School of Mathematics and Statistics Wuhan University Wuhan430061 China Department of Information Engineering Wuhan Business University Wuhan430056 China

Non-negative matrix factorization and spectral clustering are widely recognized techniques in data analysis due to their unique geometric significance, and have been successful in achieving accurate results in a variety of *** their popularity, these methods often suffer from certain shortcomings. For instance, they may be susceptible to noise (outliers), which can negatively impact their clustering performance. Additionally, the spatial learning ability of these methods is highly dependent on the initial adjacency matrix and the selection of the nearest neighbor parameter *** address the aforementioned shortcomings, this paper presents a novel approach to clustering that combines non-negative matrix factorization and spectral clustering. The proposed method employs a new robust loss function to measure the reconstruction error of samples, which enhances the model's ability to handle noise (outliers) and improve clustering ***, our proposed method incorporates an adaptive-order graph learning strategy that improves the model's independence from the initial adjacency matrix. To solve the corresponding model, we have developed an efficient optimization algorithm and analyzed its convergence properties. Experimental results on diverse datasets demonstrate the effectiveness of our method in robust clustering and spatial learning tasks. © 2023, The Authors. All rights reserved.

关键词： Non-negative matrix factorization

Narrative Analysis of True Crime Podcasts With Knowledge Graph-Augmented Large Language Models

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arXiv 2024年

作者： Leng, Xinyi Liang, Jason Mauro, Jack Wang, Xu Chapman, James Bertozzi, Andrea L. Lin, Junyuan Chen, Bohan Ye, Chenchen Daniel, Temple Brantingham, P. Jeffrey Carleton College Department of Mathematics and Statistics United States Claremont McKenna College Department of Mathematical Sciences United States University of California Los Angeles Department of Mathematics United States Loyola Marymount University Department of Mathematics Statistics and Data Science United States California Institute of Technology Computing + Mathematical Sciences Division of Engineering and Applied Science United States University of California Los Angeles Department of Computer Science United States University of California Los Angeles Department of Anthropology United States

Narrative data spans all disciplines and provides a coherent model of the world to the reader or viewer. Recent advancement in machine learning and Large Language Models (LLMs) have enable great strides in analyzing natural language. However, Large language models (LLMs) still struggle with complex narrative arcs as well as narratives containing conflicting information. Recent work indicates LLMs augmented with external knowledge bases can improve the accuracy and interpretability of the resulting models. In this work, we analyze the effectiveness of applying knowledge graphs (KGs) in understanding true-crime podcast data from both classical Natural Language Processing (NLP) and LLM approaches. We directly compare KG-augmented LLMs (KGLLMs) with classical methods for KG construction, topic modeling, and sentiment analysis. Additionally, the KGLLM allows us to query the knowledge base in natural language and test its ability to factually answer questions. We examine the robustness of the model to adversarial prompting in order to test the model's ability to deal with conflicting information. Finally, we apply classical methods to understand more subtle aspects of the text such as the use of hearsay and sentiment in narrative construction and propose future directions. Our results indicate that KGLLMs outperform LLMs on a variety of metrics, are more robust to adversarial prompts, and are more capable of summarizing the text into topics. © 2024, CC BY.

关键词： Knowledge graph

Improvement for heat transfer applications through a ternary alloy on flow over a melted sheet

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International Journal of Thermofluids 2023年 20卷

作者： Archana, M. Kumar, K. Ganesh Prakasha, D.G. Vasanth, K.R. Khan, M. Ijaz Department of Mathematics K.L.E Society's S.K Arts College and H.S.K Science Institute Karnataka Hubballi India Department of Mathematics NMAM Institute of Technology Nitte Karnataka Karkala574110 India Department of Mathematics Davangere University Karnataka Davangere India Department of Mechanical Engineering Lebanese American University Beirut Lebanon Department of Mathematics and Statistics Riphah International University I-14 Islamabad44000 Pakistan

A material is considered an alloy if it contains at least two different metals or one metal and one nonmetal. It might be a single phase, a mixture of metallic phases, or an intermetallic compound with no clear boundary between the steps. Alternatively, it could be none of these things. Aircraft construction, the military, industry, medicine, and manufacturing are some of the many alloy applications. Aluminium, copper, nickel, stainless steel, and titanium alloys are used in various tools, machines, vehicles, and buildings across multiple fields. As a consequence of these applications, we look at the role that radiative heat transfer plays in the movement of ternary alloys over a melting surface. Furthermore, Nimonic 80A and aluminium alloys (AA7072-AA7075) are combined to make ternary alloys, with Ethylene Glycol as the solvent. The PDEs were obtained by approximating the Navier–Stokes equation using the boundary layer approach under the flow assumptions. This system is translated into ODEs using similarity transformations. A dimensionless system is explained using the bvp4c method. The impacts of the relevant physical parameters are elucidated quantitatively and visually. It is found that, the higher R value indicates a more robust heat transmission to the liquid, resulting in a thicker temperature field. Furthermore, the mixing of more nanoparticles may need more energy, which will result in an increase in the temperature profile. © 2023 The Author(s)

关键词： Ternary alloys