last fix

README.Rmd

@@ -23,16 +23,16 @@ knitr::opts_chunk$set(
 The goal of `WpProj` is to perform Wasserstein projections from the predictive distributions of any model into the   space of predictive distributions of linear models. We utilize L1 penalties to also reduce the complexity of the model space. This package employs the methods as described in [Eric Dunipace and Lorenzo Trippa (2020).](https://arxiv.org/abs/2012.09999) <arXiv:2012.09999>.
 
 The Wasserstein distance is a measure of distance between two probability distributions. It is defined as:  
-$$ W_p(\mu,\nu) = \left(\inf_{\pi \in \Pi(\mu,\nu)} \int_{\mathbb{R}^d \times \mathbb{R}^d} \|x-y\|^p d\pi(x,y)\right)^{1/p} $$  
+$$W_p(\mu,\nu) = \left(\inf_{\pi \in \Pi(\mu,\nu)} \int_{\mathbb{R}^d \times \mathbb{R}^d} \|x-y\|^p d\pi(x,y)\right)^{1/p}$$  
 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:  
-$$ \text{argmin}_{\nu} W_{p}(\mu,\nu)^{p}, $$  
+$$\mathop{\text{argmin}} _ {\nu} W _ {p}(\mu,\nu) ^ {p},$$  
 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:  
-$$ \text{argmin}_{\nu} W_{p}(\mu,\nu)^{p} + P_{\lambda}(\nu), $$  
+$$\mathop{\text{argmin}} _ {\nu}  W _ {p}(\mu,\nu) ^ {p} + P_{\lambda}(\nu),$$    
 where $P_\lambda(\nu)$ is the L1 penalty on the coefficients of the linear model.
 
 

README.md

@@ -15,21 +15,21 @@ described in [Eric Dunipace and Lorenzo Trippa
 
 The Wasserstein distance is a measure of distance between two
 probability distributions. It is defined as:  
-$$ W_p(\mu,\nu) = \left(\inf_{\pi \in \Pi(\mu,\nu)} \int_{\mathbb{R}^d \times \mathbb{R}^d} \|x-y\|^p d\pi(x,y)\right)^{1/p} $$  
+$$W_p(\mu,\nu) = \left(\inf_{\pi \in \Pi(\mu,\nu)} \int_{\mathbb{R}^d \times \mathbb{R}^d} \|x-y\|^p d\pi(x,y)\right)^{1/p}$$  
 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:  
-$$ \text{argmin}_{\nu} W_{p}(\mu,\nu)^{p}, $$  
+$$\mathop{\text{argmin}} _ {\nu} W _ {p}(\mu,\nu) ^ {p},$$  
 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:  
-$$ \text{argmin}_{\nu} W_{p}(\mu,\nu)^{p} + P_{\lambda}(\nu), $$  
+$$\mathop{\text{argmin}} _ {\nu}  W _ {p}(\mu,\nu) ^ {p} + P_{\lambda}(\nu),$$  
 where $P_\lambda(\nu)$ is the L1 penalty on the coefficients of the
 linear model.