Mathematical Optimization for Machine Learning · Introduction

Introduction

What this guide covers

Introduction Linear Algebra and Multivariable Calculus

Overview

Topics covered

Introduction
General introduction and formalization of problems
1.1 Structure and taxonomy of optimizers
Topology and Geometry of Loss Functions
2.1 Convexity: the ideal scenario
2.2 Critical points and spectral analysis of the Hessian

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

R(\theta) = \mathbb{E}_{(x,y) \sim \mathcal{P}} \left[ \mathcal{L}(f_\theta(x), y) \right] = \int_{\mathcal{X} \times \mathcal{Y}} \mathcal{L}(f_\theta(x), y) \, d\mathcal{P}(x,y)

View LaTeX source

R(\theta) = \mathbb{E}_{(x,y) \sim \mathcal{P}} \left[ \mathcal{L}(f_\theta(x), y) \right] = \int_{\mathcal{X} \times \mathcal{Y}} \mathcal{L}(f_\theta(x), y) \, d\mathcal{P}(x,y)