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PerspeCtive M-estimation (PCM)

Authors: Patrick L. Combettes, North Carolina State University (, Christian L. Mueller, Simons Foundation (

This is the PCM MATLAB package for perspective M-estimation accompanying the paper Proximal Analysis for Perspective M-estimation. The package introduces an optimization model for maximum likelihood-type estimation (M-estimation) that generalizes a large class of known statistical models, including Huber’s concomitant M- estimation model, the scaled Lasso, Support Vector Machine Regression, and penalized estimation with structured sparsity. The model, termed perspective M-estimation, leverages the observation that convex M-estimators with concomitant scale as well as structured norms are instances of perspective functions.

The code developed here also builds on prior work: Perspective functions: Proximal calculus and applications in high-dimensional statistics


The package is self-contained. No external software needed. Run the addPCM

Basic Usage

In the /examples/ folder you find several examples about the different modes of usage.