# What does "intractable" mean for this function in latent Dirichlet allocation (LDA)?

In the original paper Latent Dirichlet Allocation, the authors said that the function

$$p(\mathbf{w} \mid \alpha, \beta)=\frac{\Gamma\left(\sum_{i} \alpha_{i}\right)}{\prod_{i} \Gamma\left(\alpha_{i}\right)} \int\left(\prod_{i=1}^{k} \theta_{i}^{\alpha_{i}-1}\right)\left(\prod_{n=1}^{N} \sum_{i=1}^{k} \prod_{j=1}^{V}\left(\theta_{i} \beta_{i j}\right)^{w_{n}^{j}}\right) d \theta$$

is intractable due to the coupling between $$\theta$$ and $$\beta$$ in the summation over latent topics. Then they went on with "the posterior distribution is intractable for exact inference". IMHO, the exact estimation of $$\alpha,\beta$$ is not possible because we do not observe $$\theta$$.

Can you explain what "intractable" means in this case?

## 1 Answer

It means that it's not possible to calculate in a reasonable amount of time with a computer. In this case, it's probably because it iterates over a very large number of elements.