Introduction Low-rank matrix estimation Confidence areas Bayesian
Bayesian treatment of SVD
X = µ + ε = UDV + ε
• Josse et al. (2013): disregarding the constraints
uis ∼ N (0, 1) vjs ∼ N (0, 1) (ds)s=1...S
∼ N 0, s2
λ
• more random variables than required
• posteriors do not meet the constraints
• posterior for µ: draw µ1, ..., µB ⇒ postprocessing step
SVD on each matrix µ1 = U1D1V 1, ..., µB = UBDBV B
⇒ Point estimate ˆ
µ (regularized) - Uncertainty (µ1, ..., µB)
⇒ Opportunist bayesian?
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