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We investigate which physical properties are most predictive of the positionof local star forming galaxies on the BPT diagrams, by means of differentMachine Learning (ML) algorithms. Exploiting the large statistics from theSloan Digital Sky Survey (SDSS), we define a framework in which the deviationof star-forming galaxies from their median sequence can be described in termsof the relative variations in a variety of observational parameters. We trainartificial neural networks (ANN) and random forest (RF) trees to predictwhether galaxies are offset above or below the sequence (via classification),and to estimate the exact magnitude of the offset itself (via regression). Wefind, with high significance, that parameters primarily associated tovariations in the nitrogen-over-oxygen abundance ratio (N/O) are the mostpredictive for the [N II]-BPT diagram, whereas properties related to starformation (like variations in SFR or EW[H$\alpha$]) perform better in the [SII]-BPT diagram. We interpret the former as a reflection of the N/O-O/Hrelationship for local galaxies, while the latter as primarily tracing thevariation in the effective size of the S$^{+}$ emitting region, which directlyimpacts the [S II]emission lines. This analysis paves the way to assess to whatextent the physics shaping local BPT diagrams is also responsible for theoffsets seen in high redshift galaxies or, instead, whether a differentframework or even different mechanisms need to be invoked.

What drives the scatter of local star-forming galaxies in the BPT diagrams? A Machine Learning based analysis