Nonlinear Isometric Manifold Learning for Injective Normalizing Flows

• URL: http://arxiv.org/abs/2203.03934v2
• Date: Mon, 8 May 2023 17:22:42 GMT
• Title: Nonlinear Isometric Manifold Learning for Injective Normalizing Flows
• Authors: Eike Cramer, Felix Rauh, Alexander Mitsos, Ra\'ul Tempone, Manuel Dahmen
• Abstract summary: We use isometries to separate manifold learning and density estimation. We also employ autoencoders to design embeddings with explicit inverses that do not distort the probability distribution.
• Score: 58.720142291102135
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: To model manifold data using normalizing flows, we employ isometric autoencoders to design embeddings with explicit inverses that do not distort the probability distribution. Using isometries separates manifold learning and density estimation and enables training of both parts to high accuracy. Thus, model selection and tuning are simplified compared to existing injective normalizing flows. Applied to data sets on (approximately) flat manifolds, the combined approach generates high-quality data.

Related papers

• Canonical normalizing flows for manifold learning [14.377143992248222]
  We propose a canonical manifold learning flow method, where a novel objective enforces the transformation matrix to have few prominent and non-degenerate basis functions. Canonical manifold flow yields a more efficient use of the latent space, automatically generating fewer prominent and distinct dimensions to represent data.
  arXiv  Detail & Related papers  (2023-10-19T13:48:05Z)
• Out-of-distribution detection using normalizing flows on the data manifold [3.725042082196983]
  This study investigates the effect of manifold learning using normalizing flows on out-of-distribution detection. We show that manifold learning improves the out-of-distribution detection ability of a class of likelihood-based models known as normalizing flows.
  arXiv  Detail & Related papers  (2023-08-26T07:35:16Z)
• Convolutional Filtering on Sampled Manifolds [122.06927400759021]
  We show that convolutional filtering on a sampled manifold converges to continuous manifold filtering. Our findings are further demonstrated empirically on a problem of navigation control.
  arXiv  Detail & Related papers  (2022-11-20T19:09:50Z)
• VQ-Flows: Vector Quantized Local Normalizing Flows [2.7998963147546148]
  We introduce a novel statistical framework for learning a mixture of local normalizing flows as "chart maps" over a data manifold. Our framework augments the expressivity of recent approaches while preserving the signature property of normalizing flows, that they admit exact density evaluation.
  arXiv  Detail & Related papers  (2022-03-22T09:22:18Z)
• Discrete Denoising Flows [87.44537620217673]
  We introduce a new discrete flow-based model for categorical random variables: Discrete Denoising Flows (DDFs) In contrast with other discrete flow-based models, our model can be locally trained without introducing gradient bias. We show that DDFs outperform Discrete Flows on modeling a toy example, binary MNIST and Cityscapes segmentation maps, measured in log-likelihood.
  arXiv  Detail & Related papers  (2021-07-24T14:47:22Z)
• Tractable Density Estimation on Learned Manifolds with Conformal Embedding Flows [0.0]
  Normalizing flows provide tractable density estimation by transforming a simple base distribution into a complex target distribution. Recent attempts to remedy this have introduced geometric complications that defeat a central benefit of normalizing flows: exact density estimation. We argue that composing a standard flow with a trainable conformal embedding is the most natural way to model manifold-supported data.
  arXiv  Detail & Related papers  (2021-06-09T18:00:00Z)
• Rectangular Flows for Manifold Learning [38.63646804834534]
  Normalizing flows are invertible neural networks with tractable change-of-volume terms. Data of interest is typically assumed to live in some (often unknown) low-dimensional manifold embedded in high-dimensional ambient space. We propose two methods to tractably the gradient of this term with respect to the parameters of the model.
  arXiv  Detail & Related papers  (2021-06-02T18:30:39Z)
• Scalable Marginal Likelihood Estimation for Model Selection in Deep Learning [78.83598532168256]
  Marginal-likelihood based model-selection is rarely used in deep learning due to estimation difficulties. Our work shows that marginal likelihoods can improve generalization and be useful when validation data is unavailable.
  arXiv  Detail & Related papers  (2021-04-11T09:50:24Z)
• Graph Embedding with Data Uncertainty [113.39838145450007]
  spectral-based subspace learning is a common data preprocessing step in many machine learning pipelines. Most subspace learning methods do not take into consideration possible measurement inaccuracies or artifacts that can lead to data with high uncertainty.
  arXiv  Detail & Related papers  (2020-09-01T15:08:23Z)
• Semi-Supervised Learning with Normalizing Flows [54.376602201489995]
  FlowGMM is an end-to-end approach to generative semi supervised learning with normalizing flows. We show promising results on a wide range of applications, including AG-News and Yahoo Answers text data.
  arXiv  Detail & Related papers  (2019-12-30T17:36:33Z)

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.