# Deep Nonparametric Estimation of Discrete Conditional Distributions via Smoothed Dyadic Partitioning

## TL;DR

This paper introduces a deep nonparametric method for estimating discrete conditional distributions using dyadic partitioning and graph smoothing, improving sample efficiency and accuracy in modeling complex data.

## Contribution

It combines dyadic partitioning with graph-based smoothing to create a structured, efficient model for discrete distribution estimation, outperforming existing methods.

## Key findings

- Nearly halved error on benchmarks
- Higher sample efficiency in synthetic and real data
- Effective modeling of complex discrete distributions

## Abstract

We present an approach to deep estimation of discrete conditional probability distributions. Such models have several applications, including generative modeling of audio, image, and video data. Our approach combines two main techniques: dyadic partitioning and graph-based smoothing of the discrete space. By recursively decomposing each dimension into a series of binary splits and smoothing over the resulting distribution using graph-based trend filtering, we impose a strict structure to the model and achieve much higher sample efficiency. We demonstrate the advantages of our model through a series of benchmarks on both synthetic and real-world datasets, in some cases reducing the error by nearly half in comparison to other popular methods in the literature. All of our models are implemented in Tensorflow and publicly available at https://github.com/tansey/sdp .