# Probabilistic Regressor Chains with Monte Carlo Methods

## TL;DR

This paper introduces a probabilistic approach to regressor chains using Monte Carlo methods, improving multi-output regression by addressing previous limitations and enhancing flexibility and effectiveness.

## Contribution

It develops a sequential Monte Carlo scheme for probabilistic regressor chains, overcoming prior greedy inference limitations and expanding applicability in multi-output regression tasks.

## Key findings

- Monte Carlo methods improve regression chain performance
- Probabilistic regressor chains are flexible across data types
- Enhanced understanding of classifier and regressor chains

## Abstract

A large number and diversity of techniques have been offered in the literature in recent years for solving multi-label classification tasks, including classifier chains where predictions are cascaded to other models as additional features. The idea of extending this chaining methodology to multi-output regression has already been suggested and trialed: regressor chains. However, this has so-far been limited to greedy inference and has provided relatively poor results compared to individual models, and of limited applicability. In this paper we identify and discuss the main limitations, including an analysis of different base models, loss functions, explainability, and other desiderata of real-world applications. To overcome the identified limitations we study and develop methods for regressor chains. In particular we present a sequential Monte Carlo scheme in the framework of a probabilistic regressor chain, and we show it can be effective, flexible and useful in several types of data. We place regressor chains in context in general terms of multi-output learning with continuous outputs, and in doing this shed additional light on classifier chains.