Fused Lasso Nearly Isotonic Signal Approximation in General Dimensions

TL;DR

This paper introduces a fused lasso nearly-isotonic signal approximation method that combines fused lasso and nearly-isotonic regression, providing a computationally feasible solution with a trade-off between monotonicity, sparsity, and fit.

Contribution

It develops a new combined estimator, analyzes its properties, and derives an unbiased degrees of freedom estimator for general dimensions.

Findings

The method effectively balances monotonicity, sparsity, and fit.

The solution is computationally feasible for general dimensions.

An unbiased estimator of degrees of freedom is derived.

Abstract

In this paper we introduce and study fused lasso nearly-isotonic signal approximation, which is a combination of fused lasso and generalized nearly-isotonic regression. We show how these three estimators relate to each other, derive solution to the general problem, show that it is computationally feasible and provides a trade-off between piecewise monotonicity, sparsity and goodness-of-fit. Also, we derive an unbiased estimator of the degrees of freedom of the approximator.