Explain linear regression and Transformer fundamentals

Q: Explain linear regression and Transformer fundamentals

This question evaluates core competencies in statistical modeling and deep learning architecture, specifically linear regression (optimization objective, estimation and interpretability under common failure modes) and Transformer fundamentals (self-attention mechanics, positional encodings, multi-head computation and long-sequence scaling trade-offs). It is commonly asked in Machine Learning interviews for Data Scientist roles to probe foundational understanding of modeling assumptions, probabilistic interpretation, model interpretability and algorithmic complexity; domain: Machine Learning; level: primarily conceptual understanding with practical-application reasoning.

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Question

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Answer the following conceptual questions:

Part A — Linear Regression

What objective does linear regression optimize, and what is the closed-form solution? When might you avoid the closed form?
What assumptions connect least squares to maximum likelihood?
How do you interpret coefficients, and what breaks that interpretation?
What are common failure modes (multicollinearity, outliers, heteroscedasticity), and how do you address them?

Part B — Transformers

What problem does self-attention solve compared to RNNs/CNNs?
Walk through the computations of (scaled dot-product) self-attention and multi-head attention.
Why are positional encodings needed? Name at least two approaches.
What are the main complexity bottlenecks, and what are common strategies to scale to long sequences?

Explain linear regression and Transformer fundamentals

Quick Overview

Part A — Linear Regression

Part B — Transformers

Solution

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