Questions / Quant research, Regression & linear algebra
A tiny singular value amplifies noise
A design’s singular direction has singular value 0.01. The response component along the corresponding left singular vector is 0.02. What coefficient component does unregularized SVD least squares assign?
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Answer: 2 coefficient
- The coefficient component is the response projection divided by the singular value. It equals 0.02/0.01=2, so even a small response projection can imply a large coefficient.
Interview shortcut. SVD least squares: (uᵀy)/σ = 0.02/0.01.
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