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Optimization for Machine Learning with NumPy and SciPy

Partial Derivatives and Gradients

Explore the concept of partial derivatives and gradients for multivariate functions and understand their significance in optimization. Learn how to compute gradients using Python libraries, visualize them, and apply the chain rule for functions dependent on multiple variables.

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What are gradients?

A multivariate function in mathematics is a function that takes more than one input variable and produces one or more output variables. For example, the volume of a cylinder f(x,y)=πx2yf(x, y) = \pi x^2y is a multivariate function because it takes two inputs: the radius xx and the height yy of the cylinder.

For multivariate functions f(x)=f(x1,x2,...,xm)f(x) = f(x_1, x_2, ..., x_m) ...