the multiplcation between word distribution among all topics and the corresponding doc distribution among all topics: p(w)=\sum_{k}{p(k|d)*p(w|k)}= \sum_{k}{\frac{{n}_{kw}+{\beta }_{w}} {{n}_{k}+\bar{\beta }} \frac{{n}_{kd}+{\alpha }_{k}}{\sum{{n}_{k}}+ \bar{\alpha }}}
the multiplcation between word distribution among all topics and the corresponding doc distribution among all topics: p(w)=\sum_{k}{p(k|d)*p(w|k)}= \sum_{k}{\frac{{n}_{kw}+{\beta }_{w}} {{n}_{k}+\bar{\beta }} \frac{{n}_{kd}+{\alpha }_{k}}{\sum{{n}_{k}}+ \bar{\alpha }}}
\bar{\alpha }}} \sum_{k} \frac{{\alpha }_{k}{\beta }_{w} + {n}_{kw}{\alpha }_{k} + {n}_{kd}{\beta }_{w} + {n}_{kw}{n}_{kd}} {{n}_{k}+\bar{\beta }} \frac{1}{\sum{{n}_{k}}+\bar{\alpha }}} \exp^{-(\sum{\log(p(w))})/N} N is the number of tokens in corpus
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