# Estimating Joint Probability Distribution With Low-Rank Tensor Decomposition, Radon Transforms and Dictionaries

arXiv: https://arxiv.org/abs/2304.08740 · HTML: https://mlsanity.com/paper/2304.08740/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 11 references that are in the map.
- First posted on arXiv 18 Apr 2023.

## Builds on (most cited first, 7 of 7)

- [On Identifiability of Nonnegative Matrix Factorization](https://mlsanity.com/paper/1709.00614/) (2017)
- [Tensors, Learning, and 'Kolmogorov Extension' for Finite-alphabet Random Vectors](https://mlsanity.com/paper/1712.00205/) (2017)
- [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)
- [Recovering Joint Probability of Discrete Random Variables from Pairwise Marginals](https://mlsanity.com/paper/2006.16912/) (2020)
- [Recovery of Joint Probability Distribution from one-way marginals: Low rank Tensors and Random Projections](https://mlsanity.com/paper/2103.11864/) (2021)
- [Joint Probability Estimation Using Tensor Decomposition and Dictionaries](https://mlsanity.com/paper/2203.01667/) (2022)

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

- [A Nested Matrix-Tensor Model for Noisy Multi-view Clustering](https://mlsanity.com/paper/2305.19992/) (2023)

## Abstract (arXiv)

In this paper, we describe a method for estimating the joint probability density from data samples by assuming that the underlying distribution can be decomposed as a mixture of product densities with few mixture components. Prior works have used such a decomposition to estimate the joint density from lower-dimensional marginals, which can be estimated more reliably with the same number of samples. We combine two key ideas: dictionaries to represent 1-D densities, and random projections to estimate the joint distribution from 1-D marginals, explored separately in prior work. Our algorithm benefits from improved sample complexity over the previous dictionary-based approach by using 1-D marginals for reconstruction. We evaluate the performance of our method on estimating synthetic probability densities and compare it with the previous dictionary-based approach and Gaussian Mixture Models (GMMs). Our algorithm outperforms these other approaches in all the experimental settings.