$\def\prob{p} \def\vocab{V} \def\params{\boldsymbol{\theta}} \def\argmax{\mathop{\arg\,\max}} \def\param{\theta} \def\bpi{\boldsymbol{\pi}} \def\balpha{\boldsymbol{\alpha}} \def\bbeta{\boldsymbol{\beta}} \def\perplexity{PP} \def\x{\mathbf{x}} \def\y{\mathbf{y}} \def\Xs{\mathcal{X}} \def\Ys{\mathcal{Y}} \def\perplexity{PP} \def\train{\mathcal{D}_\mathit{train}} \def\counts#1#2{\#_{#1}(#2)} \def\RR{\bf R} \def\length#1{\mathop{length}(#1)} \def\aligns{\mathbf{a}} \def\align{a} \def\source{\mathbf{s}} \def\ssource{s} \def\target{\mathbf{t}} \def\starget{t}$