Practical Optimization for Stats Nerds

Audience level:

Intermediate

Description

Many models important to inferential statistics and machine learning use some form of optimization under the hood. For example, least squares regression and support vector machines are both implemented as simple optimization models. With the right tools in your hands, optimization can do so much more! This talk shows how to implement familiar statistical models directly using optimization solvers.

Abstract

Practical Optimization for Stats Nerds

Introduction

Format of the talk

This talk takes familiar stats models and explores them from an optimization perspective. It then shows how those same optimization technologies can be used in decision modeling.

Key take-aways

Many statistical techniques are based on some sort of optimization.
Optimization has lots of uses, such as solving decision models.
Learning to structure problems you already know for optimization solvers is a great way to understand them!

Model 1: Least Squares

Data generation and problem statement
Least squares using scikit-learn
Least squares using calculus
Least squares using cvxopt and quadratic optimization

Application 1: Portfolio Optimization

Extends the quadratic optimization model used to solve least squares to solve Markowitz portfolio optimization.

Model 2: Support Vector Machines

Data generation and problem statement
SVMs using scikit-learn
SVMs using PuLP and linear optimization

Interlude: Problem Shapes

What is general problem structure in statistical inferences problems? How does that differ from problem structure of optimization problems? How do we convert these to problems we can solve?

Model 3: Clustering

Data generation and problem statement
Clustering using scikit-learn
Clustering using PuLP and integer optimization

Application 2: Pedicab Sharing

Demonstrates a realistic approach to solving vehicle routing using integer optimization and Python.

Thursday 10:45 AM–11:30 AM in Track 3 - Hood