Starting the doc

Author: bthirion

docs/src/high_dimension.rst

@@ -3,4 +3,24 @@
 
 ===========================
 Inference in high dimension
-===========================
+===========================
+
+Naive inference in high dimension is ill-posed
+----------------------------------------------
+
+In some cases, data represent high-dimensional measurements of some phenomenon of interest (e.g. imaging or genotyping). The common characteristic of these problems is to be very high-dimensional and lead to correlated features. Both aspects are clearly detrimental to conditional inference, making it both expensive and powerless:
+
+* Expensive: most learers are quadratic or cubic in the number of features. Moreover per-feature inference generally entails a loop over features
+* powerless: As dimensionality and correlation increase, it  becomes harder and harder to isolate the contribution of each variable, meaning that conditional inference is ill-posed.
+
+This is illustrated in the above example, where the Desparsified Lasso struggles
+to identify relevant features
+
+
+
+.. topic:: **Full example**
+
+    See the following example for a full file running the analysis:
+    :ref:`https://hidimstat.github.io/dev/generated/gallery/examples/plot_2D_simulation_example.html#`
+
+