+## 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")