For a Gaussian prior P(θ)∼N(0,τ)P(\theta) \sim \mathcal N(0, \tau)P(θ)∼N(0,τ) so F(θ)=1τ2∑iθi2F(\theta) = \frac{1}{\tau^2} \sum_i \theta_i^2F(θ)=τ21∑iθi2 while for a Laplace prior P(θ)∼Laplace(0,τ)P(\theta) \sim \mathrm{Laplace}(0, \tau)P(θ)∼Laplace(0,τ), then F(θ)=1τ∑i∣θi∣F(\theta) = \frac{1}{\tau} \sum_i |\theta_i|F(θ)=τ1∑i∣θi∣. So all along, these two regularization techniques were just different choices of Bayesian priors!
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#Trigram Decomposition