updating readme

README.Rmd

@@ -27,7 +27,11 @@ $$W_p(\mu,\nu) = \left(\inf_{\pi \in \Pi(\mu,\nu)} \int_{\mathbb{R}^d \times \ma
 where $\Pi(\mu,\nu)$ is the set of all joint distributions with marginals $\mu$ and $\nu$.
 
 In the our package, if $\mu$ is the original prediction from the original model, such as from a Bayesian linear regression or a neural network, then we seek to find a new prediction $\nu$ that minimizes the Wasserstein distance between the two:
-$$ \text{argmin}_\nu W_p(\mu,\nu)$$
+$$\text{argmin}_\nu W_p(\mu,\nu)^p.$$
+subject to the constraint that $\nu$ is a linear model. To reduce the complexity of the number of parameters, we add an L1 penalty to the coefficients of the linear model to reduce the complexity of the model space:
+$$\text{argmin}_\nu W_p(\mu,\nu)^p + P_\lambda(\nu),$$
+where $P_\lambda(\nu)$ is the L1 penalty on the coefficients of the linear model.
+
 
 ## Installation
 

README.md

@@ -23,7 +23,13 @@ In the our package, if $\mu$ is the original prediction from the
 original model, such as from a Bayesian linear regression or a neural
 network, then we seek to find a new prediction $\nu$ that minimizes the
 Wasserstein distance between the two:
-$$ \text{argmin}_\nu W_p(\mu,\nu)$$
+$$\text{argmin}_\nu W_p(\mu,\nu)^p.$$ subject to the constraint that
+$\nu$ is a linear model. To reduce the complexity of the number of
+parameters, we add an L1 penalty to the coefficients of the linear model
+to reduce the complexity of the model space:
+$$\text{argmin}_\nu W_p(\mu,\nu)^p + P_\lambda(\nu),$$ where
+$P_\lambda(\nu)$ is the L1 penalty on the coefficients of the linear
+model.
 
 ## Installation