+\begin{equation}
+\label{mixturemodel1}
+\PP_{\theta}(Y=1\vert X=x)=\sum^{K}_{k=1}\omega_k g(<\beta_k,x>+b_k).
+\end{equation}
+
+## Algorithm, theoretical garantees
+
+The algorithm uses spectral properties of some tensor matrices to estimate the model
+parameters $\Theta = (\omega, \beta, b)$. Under rather mild conditions it can be
+proved that the algorithm converges to the correct values (its speed is known too).
+For more informations on that subject, however, please refer to our article [XX].
+In this vignette let's rather focus on package usage.
+
+## Usage
+<!--We assume that the random variable $X$ has a Gaussian distribution.
+We now focus on the situation where $X\sim \mathcal{N}(0,I_d)$, $I_d$ being the
+identity $d\times d$ matrix. All results may be easily extended to the situation
+where $X\sim \mathcal{N}(m,\Sigma)$, $m\in \R^{d}$, $\Sigma$ a positive and
+symetric $d\times d$ matrix. ***** TODO: take this into account? -->
+
+The two main functions are:
+ * computeMu(), which estimates the parameters directions, and
+ * optimParams(), which builds an object \code{o} to estimate all other parameters
+ when calling \code{o$run()}, starting from the directions obtained by the
+ previous function.
+A third function is useful to run Monte-Carlo or bootstrap estimations using
+different models in various contexts: multiRun(). We'll show example for all of them.
+
+### Estimation of directions
+
+In a real situation you would have (maybe after some pre-processing) the matrices
+X and Y which contain vector inputs and binary output.
+However, a function is provided in the package to generate such data following a
+pre-defined law:
+
+io <- generateSampleIO(n=10000, p=1/2, beta=matrix(c(1,0,0,1),ncol=2), b=c(0,0), link="probit")
+
+n is the total number of samples (lines in X, number of elements in Y)
+p is a vector of proportions, of size d-1 (because the last proportion is deduced from
+ the others: p elements sums to 1) [TODO: omega or p?]
+beta is the matrix of linear coefficients, as written above in the model.
+b is the vector of intercepts (as in linear regression, and as in the model above)
+link can be either "logit" or "probit", as mentioned earlier.
+
+This function outputs a list containing in particular the matrices X and Y, allowing to
+use the other functions (which all require either these, or the moments).
+
+TODO: computeMu(), explain input/output
+
+### Estimation of other parameters
+
+TODO: just run optimParams$run(...)
+
+### Monte-Carlo and bootstrap
+
+TODO: show example comparison with flexmix, show plots.