Simultaneous Dimensionality Reduction for Extracting Useful Representations of Large Empirical Multimodal Datasets

• URL: http://arxiv.org/abs/2410.19867v1
• Date: Wed, 23 Oct 2024 21:27:40 GMT
• Title: Simultaneous Dimensionality Reduction for Extracting Useful Representations of Large Empirical Multimodal Datasets
• Authors: Eslam Abdelaleem,
• Abstract summary: 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.
• Score: 0.0
• License:
• Abstract: The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional descriptions from high-dimensional data, facilitating comprehension and analysis. We address the challenges posed by real-world data that defy conventional assumptions, such as complex interactions within neural systems or high-dimensional dynamical systems. Leveraging insights from both theoretical physics and machine learning, this work unifies diverse reduction methods under a comprehensive framework, the Deep Variational Multivariate Information Bottleneck. This framework enables the design of tailored reduction algorithms based on specific research questions. We explore and assert the efficacy of simultaneous reduction approaches over their independent reduction counterparts, demonstrating their superiority in capturing covariation between multiple modalities, while requiring less data. We also introduced novel techniques, such as the Deep Variational Symmetric Information Bottleneck, for general nonlinear simultaneous reduction. We show that the same principle of simultaneous reduction is the key to efficient estimation of mutual information. We show that our new method is able to discover the coordinates of high-dimensional observations of dynamical systems. Through analytical investigations and empirical validations, we shed light on the intricacies of dimensionality reduction methods, paving the way for enhanced data analysis across various domains. We underscore the potential of these methodologies to extract meaningful insights from complex datasets, driving advancements in fundamental research and applied sciences. As these methods evolve, they promise to deepen our understanding of complex systems and inform more effective data analysis strategies.

Related papers

• You are out of context! [0.0]
  New data can act as forces stretching, compressing, or twisting the geometric relationships learned by a model. We propose a novel drift detection methodology for machine learning (ML) models based on the concept of ''deformation'' in the vector space representation of data.
  arXiv  Detail & Related papers  (2024-11-04T10:17:43Z)
• Automated Global Analysis of Experimental Dynamics through Low-Dimensional Linear Embeddings [3.825457221275617]
  We introduce a data-driven computational framework to derive low-dimensional linear models for nonlinear dynamical systems. This framework enables global stability analysis through interpretable linear models that capture the underlying system structure. Our method offers a promising pathway to analyze complex dynamical behaviors across fields such as physics, climate science, and engineering.
  arXiv  Detail & Related papers  (2024-11-01T19:27:47Z)
• Deep Learning Through A Telescoping Lens: A Simple Model Provides Empirical Insights On Grokking, Gradient Boosting & Beyond [61.18736646013446]
  In pursuit of a deeper understanding of its surprising behaviors, we investigate the utility of a simple yet accurate model of a trained neural network. Across three case studies, we illustrate how it can be applied to derive new empirical insights on a diverse range of prominent phenomena.
  arXiv  Detail & Related papers  (2024-10-31T22:54:34Z)
• A Novel Paradigm in Solving Multiscale Problems [14.84863023066158]
  In this paper, a novel decoupling solving paradigm is proposed through modelling large-scale dynamics independently and treating small-scale dynamics as a slaved system. A Spectral Physics-informed Neural Network (PINN) is developed to characterize the small-scale system in an efficient and accurate way.
  arXiv  Detail & Related papers  (2024-02-07T18:19:51Z)
• Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein [56.62376364594194]
  Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. In this work, we revisit these approaches under the lens of optimal transport and exhibit relationships with the Gromov-Wasserstein problem. This unveils a new general framework, called distributional reduction, that recovers DR and clustering as special cases and allows addressing them jointly within a single optimization problem.
  arXiv  Detail & Related papers  (2024-02-03T19:00:19Z)
• Learning Latent Dynamics via Invariant Decomposition and (Spatio-)Temporal Transformers [0.6767885381740952]
  We propose a method for learning dynamical systems from high-dimensional empirical data. We focus on the setting in which data are available from multiple different instances of a system. We study behaviour through simple theoretical analyses and extensive experiments on synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2023-06-21T07:52:07Z)
• On Robust Numerical Solver for ODE via Self-Attention Mechanism [82.95493796476767]
  We explore training efficient and robust AI-enhanced numerical solvers with a small data size by mitigating intrinsic noise disturbances. We first analyze the ability of the self-attention mechanism to regulate noise in supervised learning and then propose a simple-yet-effective numerical solver, Attr, which introduces an additive self-attention mechanism to the numerical solution of differential equations.
  arXiv  Detail & Related papers  (2023-02-05T01:39:21Z)
• Dynamic Latent Separation for Deep Learning [67.62190501599176]
  A core problem in machine learning is to learn expressive latent variables for model prediction on complex data. Here, we develop an approach that improves expressiveness, provides partial interpretation, and is not restricted to specific applications.
  arXiv  Detail & Related papers  (2022-10-07T17:56:53Z)
• Variational Distillation for Multi-View Learning [104.17551354374821]
  We design several variational information bottlenecks to exploit two key characteristics for multi-view representation learning. Under rigorously theoretical guarantee, our approach enables IB to grasp the intrinsic correlation between observations and semantic labels.
  arXiv  Detail & Related papers  (2022-06-20T03:09:46Z)
• Learning Neural Causal Models with Active Interventions [83.44636110899742]
  We introduce an active intervention-targeting mechanism which enables a quick identification of the underlying causal structure of the data-generating process. Our method significantly reduces the required number of interactions compared with random intervention targeting. We demonstrate superior performance on multiple benchmarks from simulated to real-world data.
  arXiv  Detail & Related papers  (2021-09-06T13:10:37Z)
• Information Theory Measures via Multidimensional Gaussianization [7.788961560607993]
  Information theory is an outstanding framework to measure uncertainty, dependence and relevance in data and systems. It has several desirable properties for real world applications. However, obtaining information from multidimensional data is a challenging problem due to the curse of dimensionality.
  arXiv  Detail & Related papers  (2020-10-08T07:22:16Z)

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.