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@Article{vargasshro2021,
AUTHOR = {Vargas, Francisco and Thodoroff, Pierre and Lamacraft, Austen and Lawrence, Neil},
TITLE = {Solving {S}chr{\"o}dinger Bridges via Maximum Likelihood},
JOURNAL = {Entropy},
VOLUME = {23},
YEAR = {2021},
NUMBER = {9},
ARTICLE-NUMBER = {1134},
URL = {https://www.mdpi.com/1099-4300/23/9/1134},
ISSN = {1099-4300},
ABSTRACT = {The Schrödinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have important applications in machine learning such as dataset alignment and hypothesis testing. Whilst the theory behind this problem is relatively mature, scalable numerical recipes to estimate the Schrödinger bridge remain an active area of research. Our main contribution is the proof of equivalence between solving the SBP and an autoregressive maximum likelihood estimation objective. This formulation circumvents many of the challenges of density estimation and enables direct application of successful machine learning techniques. We propose a numerical procedure to estimate SBPs using Gaussian process and demonstrate the practical usage of our approach in numerical simulations and experiments.},
DOI = {10.3390/e23091134}
}



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@article{sharma2017markov,
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@article{simonyan2014very,
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@article{chen2021likelihood,
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@inproceedings{Hsieh2018,
    author = {Hsieh, Ya-Ping and Kavis, Ali and Rolland, Paul and Cevher, Volkan},
    booktitle = {Advances in Neural Information Processing Systems},
    editor = {S. Bengio and H. Wallach and H. Larochelle and K. Grauman and N. Cesa-Bianchi and R. Garnett},
    pages = {},
    publisher = {Curran Associates, Inc.},
    title = {Mirrored Langevin Dynamics},
    url = {https://proceedings.neurips.cc/paper/2018/file/6490791e7abf6b29a381288cc23a8223-Paper.pdf},
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    year = {2018}
}

@article{Eches2010,
    abstract = {This paper studies a new Bayesian unmixing algorithm for hyperspectral images. Each pixel of the image is modeled as a linear combination of so-called endmembers. These endmembers are supposed to be random in order to model uncertainties regarding their knowledge. More precisely, we model endmembers as Gaussian vectors whose means have been determined using an endmember extraction algorithm such as the famous N-finder (N-FINDR) or Vertex Component Analysis (VCA) algorithms. This paper proposes to estimate the mixture coefficients (referred to as abundances) using a Bayesian algorithm. Suitable priors are assigned to the abundances in order to satisfy positivity and additivity constraints whereas conjugate priors are chosen for the remaining parameters. A hybrid Gibbs sampler is then constructed to generate abundance and variance samples distributed according to the joint posterior of the abundances and noise variances. The performance of the proposed methodology is evaluated by comparison with other unmixing algorithms on synthetic and real images. {\textcopyright} 2010 IEEE.},
    author = {Eches, Olivier and Dobigeon, Nicolas and Mailhes, Corinne and Tourneret, Jean Yves},
    doi = {10.1109/TIP.2010.2042993},
    file = {:home/andrius/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Eches et al. - 2010 - Bayesian Estimation of Linear Mixtures Using the Normal Compositional Model. Application to Hyperspectral Image(2).pdf:pdf},
    issn = {10577149},
    journal = {IEEE Transactions on Image Processing},
    keywords = {Bayesian inference,Hyperspectral images,Monte Carlo methods,Normal compositional model,Spectral unmixing},
    mendeley-groups = {Probabilistic unmixing,Nonlinear unmixing/Normal Compositional Model},
    number = {6},
    pages = {1403--1413},
    pmid = {20215083},
    title = {{Bayesian Estimation of Linear Mixtures Using the Normal Compositional Model. Application to Hyperspectral Imagery}},
    volume = {19},
    year = {2010}
}

@article{altschuler2019massively,
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  volume={32},
  year={2019}
}

@article{ye2022first,
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}

@article{bunne2022recovering,
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  year={2022}
}

@article{haussmann1986time,
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}

@article{Bioucas-Dias2012,
    abstract = {Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally. {\textcopyright} 2012 IEEE.},
    archivePrefix = {arXiv},
    arxivId = {1202.6294},
    author = {Bioucas-Dias, Jos{\'{e}} M. and Plaza, Antonio and Dobigeon, Nicolas and Parente, Mario and Du, Qian and Gader, Paul and Chanussot, Jocelyn},
    doi = {10.1109/JSTARS.2012.2194696},
    eprint = {1202.6294},
    file = {:home/andrius/Downloads/papers/Dias_unmixing_review.pdf:pdf},
    issn = {19391404},
    journal = {IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing},
    keywords = {Hyperspectral imaging,hyperspectral remote sensing,image analysis,image processing,imaging spectroscopy,inverse problems,linear mixture,machine learning algorithms,nonlinear mixtures,pattern recognition,remote sensing,sparsity,spectroscopy,unmixing},
    mendeley-groups = {Nonlinear unmixing},
    number = {2},
    pages = {354--379},
    title = {{Hyperspectral unmixing overview: Geometrical, statistical, and sparse regression-based approaches}},
    volume = {5},
    year = {2012}
}

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  year={2018}
}

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 pages = {},
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 title = {Using the Nystr\"{o}m Method to Speed Up Kernel Machines},
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  organization={PMLR}
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@inproceedings{
anonymous2023denoising,
title={Denoising Diffusion Samplers},
author={Francisco Vargas and Will Sussman Grathwohl and Arnaud Doucet},
booktitle={The Eleventh International Conference on Learning Representations },
year={2023},
url={https://openreview.net/forum?id=8pvnfTAbu1f}
}


@InProceedings{pmlr-v99-tzen19a,
  title = 	 {Theoretical guarantees for sampling and inference in generative models with latent diffusions},
  author =       {Tzen, Belinda and Raginsky, Maxim},
  booktitle = 	 {Proceedings of the Thirty-Second Conference on Learning Theory},
  pages = 	 {3084--3114},
  year = 	 {2019},
  editor = 	 {Beygelzimer, Alina and Hsu, Daniel},
  volume = 	 {99},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {25--28 Jun},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v99/tzen19a/tzen19a.pdf},
  url = 	 {https://proceedings.mlr.press/v99/tzen19a.html},
  abstract = 	 {We introduce and study a class of probabilistic generative models, where the latent object is a finite-dimensional diffusion process on a finite time interval and the observed variable is drawn conditionally on the terminal point of the diffusion. We make the following contributions: We provide a unified viewpoint on both sampling and variational inference in such generative models through the lens of stochastic control. We quantify the expressiveness of diffusion-based generative models. Specifically, we show that one can efficiently sample from a wide class of terminal target distributions by choosing the drift of the.}
}


@inproceedings{
vargas2023denoising,
title={Denoising Diffusion Samplers},
author={Francisco Vargas and Will Sussman Grathwohl and Arnaud Doucet},
booktitle={The Eleventh International Conference on Learning Representations },
year={2023},
url={https://openreview.net/forum?id=8pvnfTAbu1f}
}

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  pages={6840--6851},
  year={2020}
}

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