Fitting Jump Models

TL;DR

This paper introduces a versatile framework for fitting jump models to sequential data by alternating between continuous parameter optimization and discrete model selection, unifying various model classes.

Contribution

It presents a general approach that encompasses hidden Markov models and piecewise affine models, allowing flexible loss function choices to shape the jump model.

Findings

Framework effectively fits jump models to data sequences.

Unifies multiple model classes under a common approach.

Flexible loss functions enable tailored model shapes.

Abstract

We describe a new framework for fitting jump models to a sequence of data. The key idea is to alternate between minimizing a loss function to fit multiple model parameters, and minimizing a discrete loss function to determine which set of model parameters is active at each data point. The framework is quite general and encompasses popular classes of models, such as hidden Markov models and piecewise affine models. The shape of the chosen loss functions to minimize determine the shape of the resulting jump model.