Partitioned Least Squares
Roberto Esposito, Mattia Cerrato, Marco Locatelli

TL;DR
This paper introduces a novel partitioned least squares model that allows grouping features for similar contribution, providing methods for exact and approximate solutions, and analyzing their efficiency and correctness.
Contribution
It presents a new non-convex formulation of least squares with feature partitioning and offers both an exact reformulation and an approximate alternating least squares method.
Findings
The exact method guarantees optimal solutions.
The approximate method is faster and nearly as accurate.
The problem is NP-complete, indicating computational difficulty.
Abstract
In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows practitioners to assess the importance of each group and of each variable in the group. We formally show that the new formulation is not convex and provide two alternative methods to deal with the problem: one non-exact method based on an alternating least squares approach; and one exact method based on a reformulation of the problem using an exponential number of sub-problems whose minimum is guaranteed to be the optimal solution. We formally show the correctness of the exact method and also compare the two solutions showing that the exact solution provides better results in a fraction of the time required by the alternating least squares solution (assuming…
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Taxonomy
TopicsSpectroscopy and Chemometric Analyses · Bayesian Modeling and Causal Inference · Advanced Statistical Methods and Models
