NICE: Non-linear Independent Components Estimation

Abstract

We propose a deep learning framework for modeling complex high-dimensional densities called Non-linear Independent Component Estimation (NICE). It is based on the idea that a good representation is one in which the data has a distribution that is easy to model. For this purpose, a non-linear deterministic transformation of the data is learned that maps it to a latent space so as to make the transformed data conform to a factorized distribution, i.e., resulting in independent latent variables. We parametrize this transformation so that computing the Jacobian determinant and inverse transform is trivial, yet we maintain the ability to learn complex non-linear transformations, via a composition of simple building blocks, each based on a deep neural network. The training criterion is simply the exact log-likelihood, which is tractable. Unbiased ancestral sampling is also easy. We show that this approach yields good generative models on four image datasets and can be used for inpainting.

11 pages and 2 pages Appendix, workshop paper at ICLR 2015

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• TzK: Flow-Based Conditional Generative Model
• PointLIE: Locally Invertible Embedding for Point Cloud Sampling and Recovery
• Exploiting Invertible Decoders for Unsupervised Sentence Representation Learning
• Iterative Alignment Flows
• Prior Flow Variational Autoencoder: A density estimation model for Non-Intrusive Load Monitoring
• Out-of-Distribution Detection of Melanoma using Normalizing Flows
• Imitation with Neural Density Models
• Training End-to-end Single Image Generators without GANs
• Generative Model with Dynamic Linear Flow
• Generative Parameter Sampler For Scalable Uncertainty Quantification
• Backpropagating through Fréchet Inception Distance
• Black-box Adversarial Example Generation with Normalizing Flows
• Time Series Source Separation with Slow Flows
• X2CT-FLOW: Maximum a posteriori reconstruction using a progressive flow-based deep generative model for ultra sparse-view computed tomography in ultra low-dose protocols
• Continuous normalizing flows on manifolds
• GFlowNet Foundations
• Lossless Compression with Probabilistic Circuits
• Disentangling Physical Parameters for Anomalous Sound Detection Under Domain Shifts