This is the simulation code for the article:
M. Baur, B. Fesl, and W. Utschick, "Leveraging Variational Autoencoders for Parameterized MMSE Estimation," arXiv preprint arXiv:2307.05352, 2023.
In this manuscript, we propose to use a variational autoencoder-based framework for parameterizing a conditional linear minimum mean squared error estimator. The variational autoencoder models the underlying unknown data distribution as conditionally Gaussian, yielding the conditional first and second moments of the estimand, given a noisy observation. The derived estimator is shown to approximate the minimum mean squared error estimator by utilizing the variational autoencoder as a generative prior for the estimation problem. We propose three estimator variants that differ in their access to ground-truth data during the training and estimation phases. The proposed estimator variant trained solely on noisy observations is particularly noteworthy as it does not require access to ground-truth data during training or estimation. We conduct a rigorous analysis by bounding the difference between the proposed and the minimum mean squared error estimator, connecting the training objective and the resulting estimation performance. Furthermore, the resulting bound reveals that the proposed estimator entails a bias-variance tradeoff, which is well-known in the estimation literature. As an example application, we portray channel estimation, allowing for a structured covariance matrix parameterization and low-complexity implementation. Nevertheless, the proposed framework is not limited to channel estimation but can be applied to a broad class of estimation problems. Extensive numerical simulations first validate the theoretical analysis of the proposed variational autoencoder-based estimators and then demonstrate excellent estimation performance compared to related classical and machine learning-based state-of-the-art estimators.
Please download the data under this link by clicking on the Download button. The password is VAE-est-2023!. Afterward, place the data folder in the same directory as the datasets and models folders.
The scripts for reproducing the paper results are eval_baselines.py, eval_baselines_mimo.py, and eval_baselines_samples.py. The remaining files contain auxiliary functions and classes. The folder models contains the pre-trained model weights with corresponding config files.
This code is written in Python version 3.8. It uses the deep learning library PyTorch and the numpy, scipy, matplotlib, and json packages. The code was tested with the versions visible in the requirements file.
Alternatively, a conda environment that meets the requirements can be created by executing the following lines:
conda create -n vae_est python=3.8 numpy=1.23.5 matplotlib=3.6.2 scipy=1.10.0 simplejson
conda activate vae_est
conda install pytorch cpuonly -c pytorch
Run eval_baselines.py to reproduce the SIMO results from the paper. To this end, adapt the simulation parameters at the beginning of the file to select the desired scenario. Models are only available for the scenarios from the paper. Other scenario parameters will result in an error message.
Proceed analogously with eval_baselines_mimo.py, where the results for the MIMO signal model can be reproduced.
In eval_baselines_samples.py, the results for drawing different amounts of samples in the latent space can be investigated. Here, selecting any SIMO simulation scenario from the paper and an SNR value between -10 and 30 dB is possible to produce estimation results.
This code is licensed under 3-clause BSD License:
Copyright (c) 2023 M. Baur and B.Fesl.
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
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Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
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