# The Deep Generative Decoder: MAP estimation of representations improves modeling of single-cell RNA data

arXiv: https://arxiv.org/abs/2110.06672 · HTML: https://mlsanity.com/paper/2110.06672/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 68 references that are in the map.
- First posted on arXiv 13 Oct 2021.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Designing Network Design Spaces](https://mlsanity.com/paper/2003.13678/) (2020)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [From Louvain to Leiden: guaranteeing well-connected communities](https://mlsanity.com/paper/1810.08473/) (2018)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [Optimizing the Latent Space of Generative Networks](https://mlsanity.com/paper/1707.05776/) (2017)
- [Inference Suboptimality in Variational Autoencoders](https://mlsanity.com/paper/1801.03558/) (2018)
- [Failure Modes of Variational Autoencoders and Their Effects on Downstream Tasks](https://mlsanity.com/paper/2007.07124/) (2020)
- [Gradient Origin Networks](https://mlsanity.com/paper/2007.02798/) (2020)
- [DuelGAN: A Duel Between Two Discriminators Stabilizes the GAN Training](https://mlsanity.com/paper/2101.07524/) (2021)
- [A manifold learning perspective on representation learning: Learning decoder and representations without an encoder](https://mlsanity.com/paper/2108.13910/) (2021)

## Built on by (most cited first, 2 of 2)

- [Riemannian Generative Decoder](https://mlsanity.com/paper/2506.19133/) (2025)
- [Improved Variational Inference in Discrete VAEs using Error Correcting Codes](https://mlsanity.com/paper/2410.07840/) (2024)

## Abstract (arXiv)

Learning low-dimensional representations of single-cell transcriptomics has become instrumental to its downstream analysis. The state of the art is currently represented by neural network models such as variational autoencoders (VAEs) which use a variational approximation of the likelihood for inference. We here present the Deep Generative Decoder (DGD), a simple generative model that computes model parameters and representations directly via maximum a posteriori (MAP) estimation. The DGD handles complex parameterized latent distributions naturally unlike VAEs which typically use a fixed Gaussian distribution, because of the complexity of adding other types. We first show its general functionality on a commonly used benchmark set, Fashion-MNIST. Secondly, we apply the model to multiple single-cell data sets. Here the DGD learns low-dimensional, meaningful and well-structured latent representations with sub-clustering beyond the provided labels. The advantages of this approach are its simplicity and its capability to provide representations of much smaller dimensionality than a comparable VAE.