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High-dimensional Bayesian inference via the Unadjusted Langevin Algorithm

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Academic year: 2021

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Table 1: Dependencies of the number of iterations n ε to get W 2 (δ x ⋆ R γ n ε ε , π) ≤ ε For simplicity, consider sequences (γ k ) k≥1 defined for all k ≥ 1 by γ k = γ 1 k −α , for γ 1 < 1/(m + L) and α ∈ (0, 1]
Table 3: Bound for the MSE for γ k = γ 1 k −α for fixed γ 1 and N under H1 and H2 Bound for the MSE
Table 5: Optimal bound for the MSE by choosing γ 1
Table 8: Order of the step size γ ε > 0 and the number of iterations n ε ∈ N ∗ to get k δ x ⋆ R nγ ε ε − π k TV ≤ ε for ε > 0.
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