Figure A6.

The top row shows the results for the normal IB Lagrangian, and the bottom row for the exponential IB Lagrangian with $\eta =1$, both in the California housing dataset. In each row, from left to right it is shown (i) the information plane, where the region of possible solutions of the IB problem is shadowed in light orange and the information-theoretic limits are the dashed orange line; (ii) $I(T;Y)$ as a function of ${\beta }_u$; and (iii) the compression $I(X;T)$ as a function of ${\beta }_u$. In all plots, the red crosses joined by a dotted line represent the values computed with the training set and the blue dots the values computed with the validation set. Moreover, in all plots, it is indicated $I(X;Y)$ as the empirical value obtained maximizing $I(T;Y)$ without compression limitations as in [26]. All values are shown in bits.