update notations

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Trance-0
2025-11-04 12:43:23 -06:00
parent d24c0bdd9e
commit 614479e4d0
27 changed files with 333 additions and 100 deletions

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@@ -96,7 +96,7 @@ Example: Linear classification models
Find a linear function that separates the data.
$$
f(x) = w^T x + b
f(x) = w^\top x + b
$$
[Linear classification models](http://cs231n.github.io/linear-classify/)
@@ -144,13 +144,13 @@ This is a convex function, so we can find the global minimum.
The gradient is:
$$
\nabla_w||Xw-Y||^2 = 2X^T(Xw-Y)
\nabla_w||Xw-Y||^2 = 2X^\top(Xw-Y)
$$
Set the gradient to 0, we get:
$$
w = (X^T X)^{-1} X^T Y
w = (X^\top X)^{-1} X^\top Y
$$
From the maximum likelihood perspective, we can also derive the same result.