Fitting Jump Models
This work provides a flexible approach for modeling sequential data with jumps, potentially benefiting researchers in fields like signal processing and time-series analysis, though it appears incremental as it builds on existing model classes.
The authors introduced a general framework for fitting jump models to sequential data by alternating between minimizing a loss function for model parameters and a discrete loss function for determining active parameters at each data point, encompassing models like hidden Markov models and piecewise affine models.
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.