change subject data verbiage

joss/paper.md

@@ -73,10 +73,10 @@ However, prior methods only permit model variation across a few continuous covar
 Recently, contextual explanation networks (CENs) reframed the sample-specific parameter estimation problem as a more flexible and generalizable latent variable inference problem that can naturally leverage any additional contextual data pertinent to the study subjects [@al-shedivat_contextual_2020]. 
 Contextualized Machine Learning is a generalization of the CEN method, which provides a unified mathematical framework for inferring and estimating personalized models of heterogeneous and context-dependent systems [@lengerich_contextualized_2023].
 
-Formally, given subject data $X = \{X_i\}_{i=1}^N$ and context data $C = \{C_i\}_{i=1}^N$ where $i$ indexes subjects, each observed only once, we can express the likelihood of all data in the form of 
+Formally, given subject data $X = \{X_i\}_{i=1}^N$ and context data $C = \{C_i\}_{i=1}^N$ where $i$ indexes samples, we can express the likelihood of all data in the form of 
 $$P(X,C) \propto \int_{\theta} d\theta P_M (X \mid \theta) P ( \theta \mid C)\,$$
 where we call $P ( \theta \mid C)$ the context encoder, and $P_M (X \mid \theta)$ the sample-specific model, where $M$ denotes model class or type.
-So long as the choice for both the context encoder and sample-specific model are differentiable, we can learn to estimate parameters $\theta_i$ for each subject $i$ via end-to-end backpropagation with gradient-based algorithms 
+So long as the choice for both the context encoder and sample-specific model are differentiable, we can learn to estimate parameters $\theta_i$ for each sample $i$ via end-to-end backpropagation with gradient-based algorithms 
 such that $P(X \mid C)$ is maximized.
 Conveniently, $C$ can contain any multivariate or real features that are relevant to the study, such as clinical, genetic, textual, or image data, and the context encoder can be any differentiable function, such as a neural network, that maps $C_i$ to $\theta_i$.