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1. Improved Pathwise Coordinate Descent for Power Penalties

   https://doi.org/10.1080/10618600.2023.2256807  

   Griffin, Maryclare (January 2024, Journal of Computational and Graphical Statistics)

   Pathwise coordinate descent algorithms have been used to compute entire solution paths for lasso and other penalized regression problems quickly with great success. They improve upon cold start algorithms by solving the problems that make up the solution path sequentially for an ordered set of tuning parameter values, instead of solving each problem separately. However, extending pathwise coordinate descent algorithms to more the general bridge or power family of penalties is challenging. Faster algorithms for computing solution paths for these penalties are needed because these penalized regression problems can be nonconvex and especially burdensome to solve. In this article, we show that a reparameterization of these penalized regression problems is more amenable to pathwise coordinate descent algorithms. This allows us to improve computation of the mode-thresholding function for penalized regression problems in practice and introduce two separate pathwise algorithms. We show that either pathwise algorithm is faster than the corresponding cold start alternative, and demonstrate that different pathwise algorithms may be more likely to reach better solutions. Supplemental materials for this article are available online. 

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2. Optimization using pathwise algorithmic derivatives of electromagnetic shower simulations

   Aehle, Max; Novák, Mihály; Vassilev, Vassil; Gauger, Nicolas R; Heinrich, Lucas; Kagan, Michael; Lange, David (April 2025, Computer physics communications)

   Among the well-known methods to approximate derivatives of expectancies computed by Monte-Carlo simulations, averages of pathwise derivatives are often the easiest one to apply. Computing them via algorithmic differentiation typically does not require major manual analysis and rewriting of the code, even for very complex programs like simulations of particle-detector interactions in high-energy physics. However, the pathwise derivative estimator can be biased if there are discontinuities in the program, which may diminish its value for applications. This work integrates algorithmic differentiation into the electromagnetic shower simulation code HepEmShow based on G4HepEm, allowing us to study how well pathwise derivatives approximate derivatives of energy depositions in a sampling calorimeter with respect to parameters of the beam and geometry. We found that when multiple scattering is disabled in the simulation, means of pathwise derivatives converge quickly to their expected values, and these are close to the actual derivatives of the energy deposition. Additionally, we demonstrate the applicability of this novel gradient estimator for stochastic gradient-based optimization in a model example. 

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3. PATHWiSE: An AI-Assisted Teacher Authoring Tool for Creating Custom Robot-Assisted Learning Activities

   https://doi.org/10.1145/3610978.3641086  

   Rahman, Md Anisur; Felix, Isaac Aurelio; Shahid, Usman; Michaelis, Joseph E (March 2024, ACM)

   Social robots can enhance deeper learning through social processes by providing companionship during typically isolated learning activities. Yet, there is limited exploration into the use of authoring tools for teachers to create and customize social robot-assisted lessons. To address this need, we present PATHWiSE, an authoring tool that utilizes teacher-in-the-loop AI-assisted verbal and non-verbal robot interaction design to customize RAL lessons to the needs and strengths of individual students and classrooms. We demonstrate the operation, AI-assist functions, and practical applications of the PATHWiSE UI. Our work underscores the need for developing tools for computing novices utilizing AI and RAL technologies 

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4. On Fast Convergence of Proximal Algorithms for SQRT-Lasso Optimization: Don't Worry About Its Nonsmooth Loss Function

   Li, Xingguo; Jiang, Haoming; Haupt, Jarvis; Arora, Raman; Liu, Han; Hong, Mingyi; Zhao, Tuo (July 2019, Conference on Uncertainty and Artificial Intelligence)

   Many machine learning techniques sacrifice convenient computational structures to gain estimation robustness and modeling flexibility. However, by exploring the modeling structures, we find these ``sacrifices'' do not always require more computational efforts. To shed light on such a ``free-lunch'' phenomenon, we study the square-root-Lasso (SQRT-Lasso) type regression problem. Specifically, we show that the nonsmooth loss functions of SQRT-Lasso type regression ease tuning effort and gain adaptivity to inhomogeneous noise, but is not necessarily more challenging than Lasso in computation. We can directly apply proximal algorithms (e.g. proximal gradient descent, proximal Newton, and proximal quasi-Newton algorithms) without worrying about the nonsmoothness of the loss function. Theoretically, we prove that the proximal algorithms combined with the pathwise optimization scheme enjoy fast convergence guarantees with high probability. Numerical results are provided to support our theory. 

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5. Circulation and Energy Theorem Preserving Stochastic Fluids

   https://doi.org/10.1017/prm.2019.43  

   Drivas, Theodore D.; Holm, Darryl D. (December 2020, Proceedings of the Royal Society of Edinburgh: Section A Mathematics)

   null (Ed.)

   Abstract Smooth solutions of the incompressible Euler equations are characterized by the property that circulation around material loops is conserved. This is the Kelvin theorem. Likewise, smooth solutions of Navier–Stokes are characterized by a generalized Kelvin's theorem, introduced by Constantin–Iyer (2008). In this note, we introduce a class of stochastic fluid equations, whose smooth solutions are characterized by natural extensions of the Kelvin theorems of their deterministic counterparts, which hold along certain noisy flows. These equations are called the stochastic Euler–Poincaré and stochastic Navier–Stokes–Poincaré equations respectively. The stochastic Euler–Poincaré equations were previously derived from a stochastic variational principle by Holm (2015), which we briefly review. Solutions of these equations do not obey pathwise energy conservation/dissipation in general. In contrast, we also discuss a class of stochastic fluid models, solutions of which possess energy theorems but do not, in general, preserve circulation theorems. 

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