Summary: In streamwise feature selection, new features are sequentially considered for addition to a predictive model. When the space of potential features is large, streamwise feature selection offers many advantages over traditional feature selection methods, which assume that all features are known in advance. Features can be generated dynamically, focusing the search for new features on promising subspaces, and overfitting can be controlled by dynamically adjusting the threshold for adding features to the model. In contrast to traditional forward feature selection algorithms, such as stepwise regression, in which at each step all possible features are evaluated and the best one is selected, streamwise feature selection only evaluates each feature once when it is generated. We describe information-investing and \(\alpha\)-investing, two adaptive complexity penalty methods for streamwise feature selection which dynamically adjust the threshold on the error reduction required for adding a new feature. These two methods give false discovery rate style guarantees against overfitting. They differ from standard penalty methods such as AIC, BIC and RIC, which always drastically over- or under-fit in the limit of infinite numbers of non-predictive features. Empirical results show that streamwise regression is competitive with (on small data sets) and superior to (on large data sets) much more compute-intensive feature selection methods such as stepwise regression, and allows feature selection on problems with millions of potential features.