Feature Network Models (FNM) are graphical structures that represent proximity data in a discrete space with the use of features. A statistical inference theory is introduced, based on the additivity properties of networks and the linear regression framework. Considering features as predictor variables leads in a natural way to a univariate multiple regression problem with positivity restrictions on the parameters, which represent edge lengths in the network representation. Theoretical standard errors and confidence intervals are obtained for the parameters and their performance is evaluated by Monte Carlo simulation. When the feature structure is not known in advance, a strategy is proposed to select an adequate subset of features that takes into account a good compromise between model fit and model complexity using Gray codes and the positive lasso. The same statistical inference theory also holds for additive trees that are special cases of FNM. Standard errors and confidence intervals, model tests and prediction error are obtained for the estimates of the branch lengths of additive trees. The dissertation concludes by demonstrating that there exists a universal network representation of city-block models based on key elements of the network representation consisting of betweenness, metric segmental additivity and internal nodes.
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