# PMODE: Theoretically Grounded and Modular Mixture Modeling

arXiv: https://arxiv.org/abs/2508.21396 · HTML: https://mlsanity.com/paper/2508.21396/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 75 references that are in the map.
- First posted on arXiv 29 Aug 2025.

## Builds on (most cited first, 30 of 32)

- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Unsupervised Anomaly Detection with Generative Adversarial Networks to Guide Marker Discovery](https://mlsanity.com/paper/1703.05921/) (2017)
- [Using Self-Supervised Learning Can Improve Model Robustness and Uncertainty](https://mlsanity.com/paper/1906.12340/) (2019)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [CSI: Novelty Detection via Contrastive Learning on Distributionally Shifted Instances](https://mlsanity.com/paper/2007.08176/) (2020)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Deep Anomaly Detection Using Geometric Transformations](https://mlsanity.com/paper/1805.10917/) (2018)
- [FastFlow: Unsupervised Anomaly Detection and Localization via 2D Normalizing Flows](https://mlsanity.com/paper/2111.07677/) (2021)
- [Identifiability of deep generative models without auxiliary information](https://mlsanity.com/paper/2206.10044/) (2022)
- [Exposing Outlier Exposure: What Can Be Learned From Few, One, and Zero Outlier Images](https://mlsanity.com/paper/2205.11474/) (2022)
- [Deep Gaussian Mixture Models](https://mlsanity.com/paper/1711.06929/) (2017)
- [DASVDD: Deep Autoencoding Support Vector Data Descriptor for Anomaly Detection](https://mlsanity.com/paper/2106.05410/) (2021)
- [The More, the Merrier: the Blessing of Dimensionality for Learning Large Gaussian Mixtures](https://mlsanity.com/paper/1311.2891/) (2013)
- [Identifiability of Nonparametric Mixture Models and Bayes Optimal Clustering](https://mlsanity.com/paper/1802.04397/) (2018)
- [Low-rank Characteristic Tensor Density Estimation Part I: Foundations](https://mlsanity.com/paper/2008.12315/) (2020)
- [Learning Mixtures of Smooth Product Distributions: Identifiability and Algorithm](https://mlsanity.com/paper/1904.01156/) (2019)
- [An Equal-Size Hard EM Algorithm for Diverse Dialogue Generation](https://mlsanity.com/paper/2209.14627/) (2022)
- [Sample-Efficient Learning of Mixtures](https://mlsanity.com/paper/1706.01596/) (2017)
- [Consistent Estimation of Identifiable Nonparametric Mixture Models from Grouped Observations](https://mlsanity.com/paper/2006.07459/) (2020)
- [Low-rank Characteristic Tensor Density Estimation Part II: Compression and Latent Density Estimation](https://mlsanity.com/paper/2106.10591/) (2021)
- [Beyond Smoothness: Incorporating Low-Rank Analysis into Nonparametric Density Estimation](https://mlsanity.com/paper/2204.00930/) (2022)
- [Nonparametric Estimation of Multi-View Latent Variable Models](https://mlsanity.com/paper/1311.3287/) (2013)
- [Recovery Guarantees for Kernel-based Clustering under Non-parametric Mixture Models](https://mlsanity.com/paper/2110.09476/) (2021)
- [Uniform Consistency in Nonparametric Mixture Models](https://mlsanity.com/paper/2108.14003/) (2021)
- [Dimension-independent rates for structured neural density estimation](https://mlsanity.com/paper/2411.15095/) (2024)
- [Sample Complexity Using Infinite Multiview Models](https://mlsanity.com/paper/2302.04292/) (2023)
- [Breaking the curse of dimensionality in structured density estimation](https://mlsanity.com/paper/2410.07685/) (2024)
- [On w-mixtures: Finite convex combinations of prescribed component distributions](https://mlsanity.com/paper/1708.00568/) (2017)

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

- [The Silhouette Operator: Identifiability of Low-Rank Measures from One-Dimensional Projections](https://mlsanity.com/paper/2610.09687/) (2026)

## Abstract (arXiv)

We introduce PMODE (Partitioned Mixture Of Density Estimators), a general and modular framework for mixture modeling with both parametric and nonparametric components. PMODE builds mixtures by partitioning the data and fitting separate estimators to each subset. It attains near-optimal rates for this estimator class and remains valid even when the mixture components come from different distribution families. As an application, we develop MV-PMODE, which scales a previously theoretical approach to high-dimensional density estimation to settings with thousands of dimensions. Despite its simplicity, it performs competitively against deep baselines on CIFAR-10 anomaly detection.