For quite a long time I've been trying to understand the paper "Bayesian Nonparametric Latent feature model" (by Zoubin Ghahramani et al.) [http://mlg.eng.cam.ac.uk/zoubin/papers/GhaGriSol06.pdf].

In a nut shell the following model is described:

  1. We have $N$ objects.
  2. A matrix $X$ of a size $N \times D$, where the row $x_i$ of this matrix consists of measurements of $D$ observable properties of the $i$-th object
  3. Each object is represented by a vector of latent features $f_i$ and the properties $x_i$ are generated from a distribution determined by those latent feature model.

$F=[f_1^T f_2^T ... f_N^T]^T$ indicates the latent feature values of all $N$ objects.

$p(F)$ a prior over features

$P(X|F)$ a distribution over observed property matrices conditioned on those features

The matrix $F$ can be break into two components:

  1. A binary matrix $Z$ indicating which features are possessed by each object, with $z_{ik}=1$ if object $i$ has the feature $k$ and $0$ otherwise.

  2. A second matrix $V$ indicating the value of each feature for each object.

$F$ is an element-wise product of $Z$ and $V$.

In the paper it is written that if the latent variable $f_i \in \{1, ..., K\}$ and $K$ then this is a description of finite mixture model.

A really don't see how. Could someone please clarify this to me


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