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We compare alternative computing strategies for solving the constrained lasso problem. As its name suggests, the constrained lasso extends the widely-used lasso to handle linear constraints, which allow the user to incorporate prior information into the model. In addition to quadratic programming, we employ the alternating direction method of multipliers (ADMM) and also derive an efficient solution path algorithm. Through both simulations and benchmark data examples, we compare the different algorithms and provide practical recommendations in terms of efficiency and accuracy for various sizes of data. We also show that, for an arbitrary penalty matrix, the generalized lasso can be transformed to a constrained lasso, while the converse is not true. Thus, our methods can also be used for estimating a generalized lasso, which has wide-ranging applications. Code for implementing the algorithms is freely available in both the Matlab toolbox SparseReg and the Julia package ConstrainedLasso. Supplementary materials for this article are available online.

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Knowledge acquisition research supports the generation of knowledge-based systems through the development of principles, techniques, methodologies and tools. What differentiates knowledge-based system development from conventional system development is the emphasis on in-depth understanding and formalization of the relations between the conceptual structures underlying expert performance and the computational structures capable of emulating that performance.Personal construct psychology is a theory of individual and group psychological and social processes that has been used extensively in knowledge acquisition research to model the cognitive processes of human experts. The psychology takes a constructivist position appropriate to the modelling of human knowledge processes, but develops this through the characterization of human conceptual structures in axiomatic terms that translate directly to computational form. In particular, there is a close correspondence between the intensional logics of knowledge, belief and action developed in personal construct psychology, and the intensional logics for formal knowledge representation developed in artificial intelligence research as term subsumption, or KL-ONE-like, systems.This paper gives an overview of personal construct psychology and its expression as an intensional logic describing the cognitive processes of anticipatory agents, and uses this to survey knowledge acquisition tools deriving from personal construct psychology.