: Single and multivariate calculus, including limits, derivatives (chain rule), and optimization. Probability & Statistics
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Given ( z = w_1 \cdot x + b ), ( a = \sigma(z) ) (sigmoid), loss ( L = \frac12(y - a)^2 ). Derive ( \frac\partial L\partial w_1 ). Given ( z = w_1 \cdot x +
: Discrete and continuous distributions, Bayes' Theorem, mean, variance, and standard deviation. Optimization : Gradients, Jacobians, and Hessians. Optimization : Gradients, Jacobians, and Hessians
Consider the loss function ( L(w) = \frac12 ||y - Xw||^2 ). Compute the gradient ( \nabla L(w) ). a) ( X^T (Xw - y) ) b) ( X^T y - X^T X w ) c) Both a and b are equivalent. d) ( X X^T (y - Xw) )