# First Paper Accepted Into NeurIPS 2020!

My first paper since I started my PhD, titled “Bayesian probabilistic numerical integral with tree based priors”, got accepted into NeurIPS 2020 🎉!

Short summary:

• We want to approximate $\Pi[f] = \int f d\Pi$ for some probability space $(\mathcal{X}, \mathcal{B}, \Pi)$ for some $f\in\mathcal{H}\subset L^2(\mathcal{X})$ using Bayesian methods.
• We propose a novel Bayesian probabilistic numerical integration method using Bayesian Additive Regression Trees (BART) that could complement existing Gaussian Process Bayesian Quadrature techniques.
• We give posterior contraction rates using different tree priors and under different smoothness and design point settings
• We give experiments on various test functions and a real dataset consisting of population surveys in the US, where we also propose a Bayesian Survey Design method. In particular, we find that BART, as expected theoretically, performs well on discontinuous or non-smooth functions $f$.

Furthermore, this methodology could motivate other tree-based algorithms in this field. One that I am especially excited about is using Mondrian Forests as a prior (well, a prior on a function means a stochastic process) along with active learning, which is a lot more scalable than BART or CART due to how Mondrian forests could be trained in an online setting.

Final revision (with lots of corrections!) in progress and so stay tuned for the final version!