Publications

You can also find my articles on my Google Scholar profile.

An Elementary Proof of the Near Optimality of LogSumExp Smoothing

Published in ArXiv Preprint, 2025

The paper proves a sharp limitation on smoothing the max-of-coordinates function in \(d\) dimensions. Any convex surrogate with the desired smoothness must incur a worst-case error that grows like \(\log d\), so the standard LogSumExp smoothing is essentially optimal up to constants. This result is proved using elementary inequalities about smooth, convex functions. The paper also proves that in small dimensions (\(d = 2, 3\)) LogSumExp fails to be optimal.

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The Optimal Smoothings of Sublinear Functions and Convex Cones

Published in ArXiv Preprint, 2025

This paper provides smooth, convex functions (or sets) of fixed curvature that minimize the distance to the original function (or set).

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Scalable Projection-Free Optimization Methods via MultiRadial Duality Theory

Published in ArXiv Preprint, 2024

This paper presents the multiradial method for solving constrained convex optimization problems. This method assumes minimal structure on the objective function and does not rely on projections to the feasible region.

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On the consistency of graph-based Bayesian semi-supervised learning and the scalability of sampling algorithms

Published in Journal of Machine Learning Research, 2020

This paper presents interesting theoretical properties of a Bayesian approach to semi-supervised learning on graphs.

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Thabo Samakhoana

Publications

An Elementary Proof of the Near Optimality of LogSumExp Smoothing

The Optimal Smoothings of Sublinear Functions and Convex Cones

Scalable Projection-Free Optimization Methods via MultiRadial Duality Theory

On the consistency of graph-based Bayesian semi-supervised learning and the scalability of sampling algorithms