Accelerated Bayesian Additive Regression Trees
Although less widely known than random forests or boosted regression trees, Bayesian additive regression trees (BART) \citep{chipman2010bart} is a powerful predictive model that often outperforms those better-known alternatives at out-of-sample prediction. BART is especially well-suited to settings with unstructured predictor variables and substantial sources of unmeasured variation as is typical in the social, behavioral and health sciences. This paper develops a modified version of BART that is amenable to fast posterior estimation. We present a stochastic hill climbing algorithm that matches the remarkable predictive accuracy of previous BART implementations, but is orders of magnitude faster and uses a fraction of the memory. Simulation studies show that the new method is comparable in computation time and more accurate at function estimation than both random forests and gradient boosting. …

Tropical Linear Programming
On Tropical Linear and Integer Programs …

Adapted Increasingly Rarely Markov Chain Monte Carlo (AirMCMC)
We introduce a class of Adapted Increasingly Rarely Markov Chain Monte Carlo (AirMCMC) algorithms where the underlying Markov kernel is allowed to be changed based on the whole available chain output but only at specific time points separated by an increasing number of iterations. The main motivation is the ease of analysis of such algorithms. Under the assumption of either simultaneous or (weaker) local simultaneous geometric drift condition, or simultaneous polynomial drift we prove the $L_2-$convergence, Weak and Strong Laws of Large Numbers (WLLN, SLLN), Central Limit Theorem (CLT), and discuss how our approach extends the existing results. We argue that many of the known Adaptive MCMC algorithms may be transformed into the corresponding Air versions, and provide an empirical evidence that performance of the Air version stays virtually the same. …