fix typo

_posts/2024-03-03-post1.md

@@ -225,7 +225,7 @@ for $$\mathcal{N}(\vec{0}^{\,}, {I}) = (2\pi)^{-k/2} \text{exp}(-\frac{1}{2}x^Tx
 
 $$min_{\mu, \Sigma} \;  \sum_i [\frac{\mu_i^2}{\sigma_i^2} + \log\sigma_i - \frac{1}{2}] - \frac{1}{K} \sum_i \sum_k \log(p(Y_i \mid X_i, \theta_k)) + C$$ where $$\theta_k \sim \mathcal{N}(\mu, \text{diag}(\sigma^2))$$ 
 
-Now, our equations are not still not Neural Network friendly - because we have to try to minimize a function that is not directly dependent on $$\mu$$ and $$\Sigma$$. We have to represent $$\theta$$  to include both $$\mu$$ and $$\Sigma$$. We can use the reparameterization here.
+Now, our equations are still not Neural Network friendly - because we have to try to minimize a function that is not directly dependent on $$\mu$$ and $$\Sigma$$. We have to represent $$\theta$$  to include both $$\mu$$ and $$\Sigma$$. We can use the reparameterization here.
 
 
 If $$X \sim \mathcal{N}(\mu, \sigma^2)$$, then $$Z = \frac{X - \mu}{\sigma} \sim \mathcal{N}(0, 1)$$

_posts/2024-06-12-post5.md

@@ -0,0 +1,18 @@
+---
+layout: page
+permalink: /blog/20240612
+title: The Art of Approximation
+date: 2024-06-12 11:12:00           # NAME OF THE FILE MUST BE IN THIS FORMAT: date-xxx.md
+tags: machine-learning
+categories: computer-science
+nav: true
+---
+
+### Table of Contents
+- [Introduction](#introduction)
+- [Taylor Approximation](#taylor-approximation)
+- [Newton's Method](#newtons-method)
+- [Laplace Approximation](#laplace-approximation)
+- [Approximate Inference](#approximate-inference)
+    - [Monte Carlo Methods](#monte-carlo-methods)
+- [Conclusion](#conclusion)