Latent Dirichlet Allocation vs. pLSA In the original LDA paper it is stated that: 

The parameters for a k-topic pLSI model are k multinomial distributions of size V and M mixtures over the k hidden topics. This gives kV +kM parameters and therefore linear growth in M. The linear growth in parameters suggests that the model is prone to overfitting and, empirically, overfitting is indeed a serious problem[.]

Also: 

LDA is a well-defined generative model and generalizes easily to new documents. Furthermore, the k+kV parameters in a k-topic LDA model do not grow with the size of the training corpus.

But what I understand is that LDA also has those $kV + kM$ parameters but not as hyper-parameters. So this is irrelevant to overfitting. I.e., in pLSA these posteriors must be estimated ($M$ is the number of documents):
$p(z|d): kM$ parameters,
$p(w|z): kV$ parameters,
and in LDA the following posteriors have to be estimated:
$p(\Theta_d|\alpha): kM$ parameters ($\Theta_d$ is $k$-dimensional),
$p(w|z): kV$ parameters,
and two parameters $\alpha$ and $\eta$, (called hyperparameters).
Thus, the number of posteriors to be estimated is approximately the same. Why LDA is claimed to have solved overfitting problem of pLSA? I agree that since Dirichlet distribution with a low $\alpha$ tends to generate sparser distributions than Dirichlet with $\alpha=1$ (or uniform) as in pLSA, and this sparsity might help reducing the overfitting a bit, but still the number of parameters are similar.
 A: We see that pLSI describes a process for generating documents with topic distributions p(z | d) seen in a particular document in the collection as opposed to generating documents with arbitrary topic proportions from a prior probability distribution.
This may not be crucial in information retrieval where the current document collection to be stored can be viewed as a ﬁxed collection. However, in applications such as text categorization, it is crucial to have a model ﬂexible enough to properly handle text that has not been seen before.
Thus probability of documents in pLSI are points (one point - one document from your collection), while in LDA, there is full topic simplex to use (of course, after training you have dirichlet distribution), so there are no problems to take new document.
A: To the question of parameters, in LDA the parameters to be learned are:


*

*$\alpha$, the $k$-dimensional corpus-level Dirichlet parameter from which each $\theta_d$ is drawn.

*$\beta$, the $k \times V$ matrix built such that $\beta_{i,j} = p(w^j | z^i)$. Put another way, the $i$-th row of $\beta$ is the parameter for a categorical distribution of a word for topic $z^i$.


These are the $k + kV$ parameters referenced in the paper, and the only ones the model needs to learn. In other words, each $\theta_d$ is drawn from a Dirichlet with the learned parameter $\alpha$; it is not itself learned as part of training the model. (Software packages implementing LDA do allow you to represent a document as its distribution over topics, but this is a consequence of the trained model, not a prerequisite for it.)
There's a clue to this in the LDA paper in section 5.3:

In particular, given a corpus of documents $D = {\bf{w}_1,\bf{w}_2,...,\bf{w}_M}$, we wish to find parameters $\alpha$ and $\beta$ that maximize the (marginal) log likelihood of the data...

One potential source of confusion is that $\alpha$ itself has a prior, the tuning of which can effect topical sparsity.
