# Generative structured normalizing flow Gaussian processes applied to spectroscopic data

arXiv: https://arxiv.org/abs/2212.07554 · HTML: https://mlsanity.com/paper/2212.07554/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 23 references that are in the map.
- First posted on arXiv 14 Dec 2022.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Gaussian Process Prior Variational Autoencoders](https://mlsanity.com/paper/1810.11738/) (2018)
- [Transforming Gaussian Processes With Normalizing Flows](https://mlsanity.com/paper/2011.01596/) (2020)
- [Rapid identification of pathogenic bacteria using Raman spectroscopy and deep learning](https://mlsanity.com/paper/1901.07666/) (2019)
- [Normalizing Flows Across Dimensions](https://mlsanity.com/paper/2006.13070/) (2020)
- [Deep Spectral CNN for Laser Induced Breakdown Spectroscopy](https://mlsanity.com/paper/2012.01653/) (2020)
- [Machine Learning Allows Calibration Models to Predict Trace Element Concentration in Soil with Generalized LIBS Spectra](https://mlsanity.com/paper/1906.08597/) (2019)
- [Neural density estimation and uncertainty quantification for laser induced breakdown spectroscopy spectra](https://mlsanity.com/paper/2108.08709/) (2021)

## Abstract (arXiv)

In this work, we propose a novel generative model for mapping inputs to structured, high-dimensional outputs using structured conditional normalizing flows and Gaussian process regression. The model is motivated by the need to characterize uncertainty in the input/output relationship when making inferences on new data. In particular, in the physical sciences, limited training data may not adequately characterize future observed data; it is critical that models adequately indicate uncertainty, particularly when they may be asked to extrapolate. In our proposed model, structured conditional normalizing flows provide parsimonious latent representations that relate to the inputs through a Gaussian process, providing exact likelihood calculations and uncertainty that naturally increases away from the training data inputs. We demonstrate the methodology on laser-induced breakdown spectroscopy data from the ChemCam instrument onboard the Mars rover Curiosity. ChemCam was designed to recover the chemical composition of rock and soil samples by measuring the spectral properties of plasma atomic emissions induced by a laser pulse. We show that our model can generate realistic spectra conditional on a given chemical composition and that we can use the model to perform uncertainty quantification of chemical compositions for new observed spectra. Based on our results, we anticipate that our proposed modeling approach may be useful in other scientific domains with high-dimensional, complex structure where it is important to quantify predictive uncertainty.