Update 7d-OOD-detection-distance.md

episodes/7d-OOD-detection-distance.md

@@ -33,10 +33,12 @@ $$
 D_M(x) = \sqrt{(x - \mu)^T \Sigma^{-1} (x - \mu)}
 $$
 where:
+
 - x: The input data point.
 - \(mu\): The mean vector of the distribution.
 - Sigma: The covariance matrix of the distribution. The inverse of the covariance matrix is used to "whiten" the feature space, ensuring that features with larger variances do not dominate the distance computation. This adjustment also accounts for correlations between features, transforming the data into a space where all features are uncorrelated and standardized.
 This approach is robust for high-dimensional data as it accounts for correlations between features.
+
 ```python
 import numpy as np
 import matplotlib.pyplot as plt
@@ -403,4 +405,4 @@ This results in a *feature space with semantic clusters*, where data points with
 
 While contrastive learning provides an exciting opportunity to improve OOD detection, it represents a shift from the traditional threshold- or distance-based approaches we have discussed so far. By learning a feature space that is inherently more generalizable and robust, contrastive learning offers a promising solution to the challenges posed by overlapping Mahalanobis distance distributions.
 
-If you're interested, we can explore specific contrastive learning methods like **SimCLR** or **MoCo** in future sessions, diving into how their objectives help create robust feature spaces!
+If you're interested, we can explore specific contrastive learning methods like **SimCLR** or **MoCo** in future sessions, diving into how their objectives help create robust feature spaces!