Variational inference (VI) is widely used as an efficient alternative to Markov chain Monte Carlo. It posits a family of approximating distributions $q$ and finds the closest member to the exact posterior $p$. Closeness is usually measured via a divergence $D(q || p)$ from $q$ to $p$. While successful, this approach also has problems. Notably, it typically leads to underestimation of the posterior variance.

Variational inference (VI) is widely used as an efficient alternative to Markov chain Monte Carlo. It posits a family of approximating distributions $q$ and finds the closest member to the exact posterior $p$. Closeness is usually measured via a divergence $D(q || p)$ from $q$ to $p$. While successful, this approach also has problems. Notably, it typically leads to underestimation of the posterior variance.

Notably, it typically leads to underestimation of the posterior variance.

Advancements in Earth system science have seen a surge in diverse datasets. Earth System Data Cubes (ESDCs) have been introduced to efficiently handle this influx of high-dimensional data. ESDCs offer a structured, intuitive framework for data analysis, organising information within spatio-temporal grids. The structured nature of ESDCs unlocks significant opportunities for Artificial Intelligence (AI) applications. By providing well-organised data, ESDCs are ideally suited for a wide range of sophisticated AI-driven tasks. An automated framework for creating AI-focused ESDCs with minimal user input could significantly accelerate the generation of task-specific training data. Here we introduce cubo, an open-source Python tool designed for easy generation of AI-focused ESDCs. Utilising collections in SpatioTemporal Asset Catalogs (STAC) that are stored as Cloud Optimised GeoTIFFs (COGs), cubo efficiently creates ESDCs, requiring only central coordinates, spatial resolution, edge size, and time range.

Variational inference (VI) is widely used as an efficient alternative to Markov chain Monte Carlo. It posits a family of approximating distributions $q$ and finds the closest member to the exact posterior $p$. Closeness is usually measured via a divergence $D(q p)$ from $q$ to $p$. While successful, this approach also has problems. Notably, it typically leads to underestimation of the posterior variance.

Variational inference (VI) is widely used as an efficient alternative to Markov chain Monte Carlo. It posits a family of approximating distributions $q$ and finds the closest member to the exact posterior $p$. Closeness is usually measured via a divergence $D(q || p)$ from $q$ to $p$. While successful, this approach also has problems. Notably, it typically leads to underestimation of the posterior variance. In this paper we propose CHIVI, a black-box variational inference algorithm that minimizes $D_{\chi}(p || q)$, the $\chi$-divergence from $p$ to $q$. CHIVI minimizes an upper bound of the model evidence, which we term the $\chi$ upper bound (CUBO). Minimizing the CUBO leads to improved posterior uncertainty, and it can also be used with the classical VI lower bound (ELBO) to provide a sandwich estimate of the model evidence. We study CHIVI on three models: probit regression, Gaussian process classification, and a Cox process model of basketball plays. When compared to expectation propagation and classical VI, CHIVI produces better error rates and more accurate estimates of posterior variance.