Tensor Methods in High Dimensional Data Analysis: Opportunities and Challenges

• URL: http://arxiv.org/abs/2405.18412v1
• Date: Tue, 28 May 2024 17:54:03 GMT
• Title: Tensor Methods in High Dimensional Data Analysis: Opportunities and Challenges
• Authors: Arnab Auddy, Dong Xia, Ming Yuan,
• Abstract summary: Multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. Addressing these challenges requires an interdisciplinary approach that brings together tools and insights from statistics, optimization and numerical linear algebra among other fields. This review seeks to examine some of the key advancements and identify common threads among them, under eight different statistical settings.
• Score: 16.544309363025324
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity of such data provides vast new opportunities for modeling and analysis, but efficiently extracting information content from them, both statistically and computationally, presents unique and fundamental challenges. Addressing these challenges requires an interdisciplinary approach that brings together tools and insights from statistics, optimization and numerical linear algebra among other fields. Despite these hurdles, significant progress has been made in the last decade. This review seeks to examine some of the key advancements and identify common threads among them, under eight different statistical settings.

Related papers

• Simultaneous Dimensionality Reduction for Extracting Useful Representations of Large Empirical Multimodal Datasets [0.0]
  We focus on the sciences of dimensionality reduction as a means to obtain low-dimensional descriptions from high-dimensional data. We address the challenges posed by real-world data that defy conventional assumptions, such as complex interactions within systems or high-dimensional dynamical systems.
  arXiv  Detail & Related papers  (2024-10-23T21:27:40Z)
• Transforming Multidimensional Time Series into Interpretable Event Sequences for Advanced Data Mining [5.2863523790908955]
  This paper introduces a novel proposed representation model designed to address the limitations of traditional methods in multidimensional time series (MTS) analysis. The proposed framework has significant potential for applications across various fields, including services for monitoring and optimizing IT infrastructure, medical diagnosis through continuous patient monitoring, trend analysis, and internet businesses for tracking user behavior and forecasting.
  arXiv  Detail & Related papers  (2024-09-22T06:27:07Z)
• High-dimensional learning of narrow neural networks [1.7094064195431147]
  This manuscript reviews the tools and ideas underlying recent progress in machine learning. We introduce a generic model -- the sequence multi-index model -- which encompasses numerous previously studied models as special instances. We explicate in full detail the analysis of the learning of sequence multi-index models, using statistical physics techniques such as the replica method and approximate message-passing algorithms.
  arXiv  Detail & Related papers  (2024-09-20T21:20:04Z)
• SIaM: Self-Improving Code-Assisted Mathematical Reasoning of Large Language Models [54.78329741186446]
  We propose a novel paradigm that uses a code-based critic model to guide steps including question-code data construction, quality control, and complementary evaluation. Experiments across both in-domain and out-of-domain benchmarks in English and Chinese demonstrate the effectiveness of the proposed paradigm.
  arXiv  Detail & Related papers  (2024-08-28T06:33:03Z)
• HEMM: Holistic Evaluation of Multimodal Foundation Models [91.60364024897653]
  Multimodal foundation models can holistically process text alongside images, video, audio, and other sensory modalities. It is challenging to characterize and study progress in multimodal foundation models, given the range of possible modeling decisions, tasks, and domains.
  arXiv  Detail & Related papers  (2024-07-03T18:00:48Z)
• Bayesian Nonparametrics: An Alternative to Deep Learning [0.5801621787540265]
  This survey aims to delve into the significance of Bayesian nonparametrics, particularly in addressing complex challenges across various domains such as statistics, computer science, and electrical engineering. We uncover the versatility and efficacy of Bayesian nonparametric methodologies, paving the way for innovative solutions to intricate challenges across diverse disciplines.
  arXiv  Detail & Related papers  (2024-03-29T17:32:42Z)
• Enhancing Deep Learning Models through Tensorization: A Comprehensive Survey and Framework [0.0]
  This paper explores the steps involved in multidimensional data sources, various multiway analysis methods employed, and the benefits of these approaches. A small example of Blind Source Separation (BSS) is presented comparing 2-dimensional algorithms and a multiway algorithm in Python. Results indicate that multiway analysis is more expressive.
  arXiv  Detail & Related papers  (2023-09-05T17:56:22Z)
• Enhancing Human-like Multi-Modal Reasoning: A New Challenging Dataset and Comprehensive Framework [51.44863255495668]
  Multimodal reasoning is a critical component in the pursuit of artificial intelligence systems that exhibit human-like intelligence. We present Multi-Modal Reasoning(COCO-MMR) dataset, a novel dataset that encompasses an extensive collection of open-ended questions. We propose innovative techniques, including multi-hop cross-modal attention and sentence-level contrastive learning, to enhance the image and text encoders.
  arXiv  Detail & Related papers  (2023-07-24T08:58:25Z)
• Quantifying & Modeling Multimodal Interactions: An Information Decomposition Framework [89.8609061423685]
  We propose an information-theoretic approach to quantify the degree of redundancy, uniqueness, and synergy relating input modalities with an output task. To validate PID estimation, we conduct extensive experiments on both synthetic datasets where the PID is known and on large-scale multimodal benchmarks. We demonstrate their usefulness in (1) quantifying interactions within multimodal datasets, (2) quantifying interactions captured by multimodal models, (3) principled approaches for model selection, and (4) three real-world case studies.
  arXiv  Detail & Related papers  (2023-02-23T18:59:05Z)
• Graph signal processing for machine learning: A review and new perspectives [57.285378618394624]
  We review a few important contributions made by GSP concepts and tools, such as graph filters and transforms, to the development of novel machine learning algorithms. We discuss exploiting data structure and relational priors, improving data and computational efficiency, and enhancing model interpretability. We provide new perspectives on future development of GSP techniques that may serve as a bridge between applied mathematics and signal processing on one side, and machine learning and network science on the other.
  arXiv  Detail & Related papers  (2020-07-31T13:21:33Z)
• Bayesian Sparse Factor Analysis with Kernelized Observations [67.60224656603823]
  Multi-view problems can be faced with latent variable models. High-dimensionality and non-linear issues are traditionally handled by kernel methods. We propose merging both approaches into single model.
  arXiv  Detail & Related papers  (2020-06-01T14:25:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.