Feature selection for predictive analytics is the problem of identifying a minimal-size subset of features that is maximally predictive of an outcome of interest. To apply to molecular data, feature selection algorithms need to be scalable to tens of thousands of features. In this paper, we propose γ-OMP, a generalisation of the highly-scalable Orthogonal Matching Pursuit feature selection algorithm. γ-OMP can handle (a)various types of outcomes, such as continuous, binary, nominal, time-to-event, (b)discrete (categorical)features, (c)different statistical-based stopping criteria, (d)several predictive models (e.g., linear or logistic regression), (e)various types of residuals, and (f)different types of association. We compare γ-OMP against LASSO, a prototypical, widely used algorithm for high-dimensional data. On both simulated data and several real gene expression datasets, γ-OMP is on par, or outperforms LASSO in binary classification (case-control data), regression (quantified outcomes), and time-to-event data (censored survival times). γ-OMP is based on simple statistical ideas, it is easy to implement and to extend, and our extensive evaluation shows that it is also effective in bioinformatics analysis settings.