# Weighted-Sum of Gaussian Process Latent Variable Models

arXiv: https://arxiv.org/abs/2402.09122 · HTML: https://mlsanity.com/paper/2402.09122/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 68 references that are in the map.
- First posted on arXiv 14 Feb 2024.

## Builds on (most cited first, 15 of 15)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- ["Double-DIP": Unsupervised Image Decomposition via Coupled Deep-Image-Priors](https://mlsanity.com/paper/1812.00467/) (2018)
- [A survey on high-dimensional Gaussian process modeling with application to Bayesian optimization](https://mlsanity.com/paper/2111.05040/) (2021)
- [Multi-Source Diffusion Models for Simultaneous Music Generation and Separation](https://mlsanity.com/paper/2302.02257/) (2023)
- [Spectral Variability in Hyperspectral Data Unmixing: A Comprehensive Review](https://mlsanity.com/paper/2001.07307/) (2020)
- [Source Separation with Deep Generative Priors](https://mlsanity.com/paper/2002.07942/) (2020)
- [Endmember-Guided Unmixing Network (EGU-Net): A General Deep Learning Framework for Self-Supervised Hyperspectral Unmixing](https://mlsanity.com/paper/2105.10194/) (2021)
- [Visual Scene Graphs for Audio Source Separation](https://mlsanity.com/paper/2109.11955/) (2021)
- [Deep Generative Endmember Modeling: An Application to Unsupervised Spectral Unmixing](https://mlsanity.com/paper/1902.05528/) (2019)
- [Efficient Modeling of Latent Information in Supervised Learning using Gaussian Processes](https://mlsanity.com/paper/1705.09862/) (2017)
- [Contextually Supervised Source Separation with Application to Energy Disaggregation](https://mlsanity.com/paper/1312.5023/) (2013)

## Built on by (most cited first, 1 of 1)

- [Amortized Structured Stochastic Variational Inference for Gaussian Process Latent Variable Models](https://mlsanity.com/paper/2610.03647/) (2026)

## Abstract (arXiv)

This work develops a Bayesian non-parametric approach to signal separation where the signals may vary according to latent variables. Our key contribution is to augment Gaussian Process Latent Variable Models (GPLVMs) for the case where each data point comprises the weighted sum of a known number of pure component signals, observed across several input locations. Our framework allows arbitrary non-linear variations in the signals while being able to incorporate useful priors for the linear weights, such as summing-to-one. Our contributions are particularly relevant to spectroscopy, where changing conditions may cause the underlying pure component signals to vary from sample to sample. To demonstrate the applicability to both spectroscopy and other domains, we consider several applications: a near-infrared spectroscopy dataset with varying temperatures, a simulated dataset for identifying flow configuration through a pipe, and a dataset for determining the type of rock from its reflectance.