Explain SVM kernels and complexity
Overview
This question evaluates understanding of Support Vector Machines, including support vectors and primal/dual formulations, the kernel trick and why Gram matrices must be positive semidefinite, computational scaling of linear versus kernel SVMs, and the roles of hyperparameters and their effects on imbalanced data.
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Oct 13, 2025, 9:49 PM
Data Scientist
Onsite
Machine Learning
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Support Vector Machines – Core Concepts and Practice
You are interviewing for a Data Scientist role. Answer the following about Support Vector Machines (SVMs):
(a) Support vectors and primal/dual formulations
- Define support vectors.
- Write the soft-margin SVM primal and dual formulations and interpret key variables.
(b) Kernel trick and PSD requirement
- Explain the kernel trick: what it does and how it is used in SVMs.
- Explain why the kernel (Gram) matrix must be positive semidefinite (PSD).
- State a condition under which a function is a valid kernel (Mercer condition).
(c) Computational scaling
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State how training time, inference time, and memory scale with number of samples n and features p for:
- Linear SVM
- Kernel SVM (e.g., RBF, polynomial)
(d) Hyperparameters and robust search on imbalanced data
- Interpret the roles of C, γ (RBF), and degree (polynomial).
- Propose a robust hyperparameter search plan for an imbalanced dataset.
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