Omer Ronen

Omer Ronen, Theo Saarinen, Yan Shuo Tan et al.

Bayesian Additive Regression Trees (BART) is a popular Bayesian non-parametric regression algorithm. The posterior is a distribution over sums of decision trees, and predictions are made by averaging approximate samples from the posterior. The combination of strong predictive performance and the ability to provide uncertainty measures has led BART to be commonly used in the social sciences, biostatistics, and causal inference. BART uses Markov Chain Monte Carlo (MCMC) to obtain approximate posterior samples over a parameterized space of sums of trees, but it has often been observed that the chains are slow to mix. In this paper, we provide the first lower bound on the mixing time for a simplified version of BART in which we reduce the sum to a single tree and use a subset of the possible moves for the MCMC proposal distribution. Our lower bound for the mixing time grows exponentially with the number of data points. Inspired by this new connection between the mixing time and the number of data points, we perform rigorous simulations on BART. We show qualitatively that BART's mixing time increases with the number of data points. The slow mixing time of the simplified BART suggests a large variation between different runs of the simplified BART algorithm and a similar large variation is known for BART in the literature. This large variation could result in a lack of stability in the models, predictions, and posterior intervals obtained from the BART MCMC samples. Our lower bound and simulations suggest increasing the number of chains with the number of data points.

Omer Ronen, Ahmed Imtiaz Humayun, Richard Baraniuk et al.

We develop Latent Exploration Score (LES) to mitigate over-exploration in Latent Space Optimization (LSO), a popular method for solving black-box discrete optimization problems. LSO utilizes continuous optimization within the latent space of a Variational Autoencoder (VAE) and is known to be susceptible to over-exploration, which manifests in unrealistic solutions that reduce its practicality. LES leverages the trained decoder's approximation of the data distribution, and can be employed with any VAE decoder - including pretrained ones - without additional training, architectural changes or access to the training data. Our evaluation across five LSO benchmark tasks and twenty-two VAE models demonstrates that LES always enhances the quality of the solutions while maintaining high objective values, leading to improvements over existing solutions in most cases. We believe that new avenues to LSO will be opened by LES' ability to identify out of distribution areas, differentiability, and computational tractability. Open source code for LES is available at https://github.com/OmerRonen/les.

Abhineet Agarwal, Yan Shuo Tan, Omer Ronen et al.

Tree-based models such as decision trees and random forests (RF) are a cornerstone of modern machine-learning practice. To mitigate overfitting, trees are typically regularized by a variety of techniques that modify their structure (e.g. pruning). We introduce Hierarchical Shrinkage (HS), a post-hoc algorithm that does not modify the tree structure, and instead regularizes the tree by shrinking the prediction over each node towards the sample means of its ancestors. The amount of shrinkage is controlled by a single regularization parameter and the number of data points in each ancestor. Since HS is a post-hoc method, it is extremely fast, compatible with any tree growing algorithm, and can be used synergistically with other regularization techniques. Extensive experiments over a wide variety of real-world datasets show that HS substantially increases the predictive performance of decision trees, even when used in conjunction with other regularization techniques. Moreover, we find that applying HS to each tree in an RF often improves accuracy, as well as its interpretability by simplifying and stabilizing its decision boundaries and SHAP values. We further explain the success of HS in improving prediction performance by showing its equivalence to ridge regression on a (supervised) basis constructed of decision stumps associated with the internal nodes of a tree. All code and models are released in a full-fledged package available on Github (github.com/csinva/imodels)

Yan Shuo Tan, Omer Ronen, Theo Saarinen et al.

Bayesian Additive Regression Trees (BART) is a popular Bayesian non-parametric regression model that is commonly used in causal inference and beyond. Its strong predictive performance is supported by well-developed estimation theory, comprising guarantees that its posterior distribution concentrates around the true regression function at optimal rates under various data generative settings and for appropriate prior choices. However, the computational properties of the widely-used BART sampler proposed by Chipman et al. (2010) are yet to be well-understood. In this paper, we perform an asymptotic analysis of a slightly modified version of the default BART sampler when fitted to data-generating processes with discrete covariates. We show that the sampler's time to convergence, evaluated in terms of the hitting time of a high posterior density set, increases with the number of training samples, due to the multi-modal nature of the target posterior. On the other hand, we show that this trend can be dampened by simple changes, such as increasing the number of trees in the ensemble or raising the temperature of the sampler. These results provide a nuanced picture on the computational efficiency of the BART sampler in the presence of large amounts of training data while suggesting strategies to improve the sampler. We complement our theoretical analysis with a simulation study focusing on the default BART sampler. We observe that the increasing trend of convergence time against number training samples holds for the default BART sampler and is robust to changes in sampler initialization, number of burn-in iterations, feature selection prior, and discretization strategy. On the other hand, increasing the number of trees or raising the temperature sharply dampens this trend, as indicated by our theory.