Curse of Dimensionality in Finance - Quant Trader Interview Question
Difficulty: Medium
Category: Data Science
Practice quant interview questions from top firms including Jane Street, Citadel, Two Sigma, DE Shaw, and other leading quantitative finance companies.
Topics: curse-of-dimensionality, machine-learning, distance-metrics, high-dimensional-data
Problem Description
Consider a unit hypercube (all sides have length 1) in $d$ dimensions. We want to understand the implications of increasing the number of dimensions in our financial models.
Specifically, what happens to the fraction of the hypercube's volume that lies within a distance of 0.01 from its boundary as $d$ increases? How does this phenomenon, known as the "curse of dimensionality", affect the reliability of distance-based machine learning models in finance, where we often deal with a large number
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