Fig. 2.

MAVE-NN quantitative modeling strategy. a Structure of latent phenotype models. A deterministic G-P map f(x) maps each sequence x to a latent phenotype ϕ, after which a probabilistic measurement process p(y| ϕ) generates a corresponding measurement y. b Example of an MPA measurement process inferred from the sort-seq MPRA data of Kinney et al. [12]. MPA measurement processes are used when y values are discrete. c Structure of a GE regression model, which is used when y is continuous. A GE measurement process assumes that the mode of p(y| ϕ), called the prediction $\widehat{y}$, is given by a nonlinear function g(ϕ), and the scatter about this mode is described by a noise model $p\left(y|,\widehat{y}\right)$. d Example of a GE measurement process inferred from the DMS data of Olson et al. [8]. Shown are the nonlinearity, the 68% PI, and the 95% PI. e Information-theoretic quantities used to assess model performance. Intrinsic information, I_int, is the mutual information between sequences x and measurements y. Predictive information, I_pre, is the mutual information between measurements y and the latent phenotype values ϕ assigned by a G-P map. Variational information, I_var, is a linear transformation of the log likelihood of a full latent phenotype model. The model performance inequality, I_int ≥ I_pre ≥ I_var, always holds on test data (modulo finite data uncertainties), with I_int = I_pre when the G-P map is correct, and I_pre = I_var when the measurement process correctly describes the distribution of y conditioned on ϕ. G-P: genotype-phenotype; MPA: measurement process agnostic; MPRA: massively parallel reporter assay; GE: global epistasis; DMS: deep mutational scanning; PI: prediction interval