  Many studies have proposed a relationship between COVID-19 transmissibility
and ambient pollution levels. However, a major limitation in establishing such
associations is to adequately account for complex disease dynamics, influenced
by e.g. significant differences in control measures and testing policies.
Another difficulty is appropriately controlling the effects of other
potentially important factors, due to both their mutual correlations and a
limited dataset. To overcome these difficulties, we will here use the basic
reproduction number ($R_0$) that we estimate for USA states using non-linear
dynamics methods. To account for a large number of predictors (many of which
are mutually strongly correlated), combined with a limited dataset, we employ
machine-learning methods. Specifically, to reduce dimensionality without
complicating the variable interpretation, we employ Principal Component
Analysis on subsets of mutually related (and correlated) predictors. Methods
that allow feature (predictor) selection, and ranking their importance, are
then used, including both linear regressions with regularization and feature
selection (Lasso and Elastic Net) and non-parametric methods based on ensembles
of weak-learners (Random Forest and Gradient Boost). Through these
substantially different approaches, we robustly obtain that PM$_{2.5}$ levels
are the main predictor of $R_0$ in USA states, with corrections from factors
such as other pollutants, prosperity measures, population density, chronic
disease levels, and possibly racial composition. As a rough magnitude estimate,
we obtain that a relative change in $R_0$, with variations in pollution levels
observed in the USA, is typically ~30%, going up to 70%, which further
underscores the importance of pollution in COVID-19 transmissibility.
