15. A computer-readable medium having instructions stored thereon that, when executed by data processing apparatus, cause the data processing apparatus to perform operations comprising: receiving input data and a request for a predictive output from a client computing system; generating the predictive output using a first trained predictive model from a repository of trained predictive models and a second trained predictive model from the repository of trained predictive models; providing the predictive output to the client computing system; and apportioning a fee received from the client computing system to generate the predictive output to a first client computing system and to a second client computing system, wherein the first client computing system provided a first set of training data that was used to train the first trained predictive model and the second client computing system provided a second set of training data that was used to train the second trained predictive model.
15. A computer-readable medium having instructions stored thereon that, when executed by data processing apparatus, cause the data processing apparatus to perform operations comprising: receiving input data and a request for a predictive output from a client computing system; generating the predictive output using a first trained predictive model from a repository of trained predictive models and a second trained predictive model from the repository of trained predictive models; providing the predictive output to the client computing system; and apportioning a fee received from the client computing system to generate the predictive output to a first client computing system and to a second client computing system, wherein the first client computing system provided a first set of training data that was used to train the first trained predictive model and the second client computing system provided a second set of training data that was used to train the second trained predictive model. 16. The computer-readable medium of claim 15 , wherein the operations further comprise: receiving a plurality of sets of predictive modeling training data from a first plurality of client computing systems; for each set of plurality of sets of predictive modeling training data: using the training data and a plurality of training functions to train a plurality of predictive models; generating a respective score for each of the plurality of trained predictive models, where each score represents an estimation of the effectiveness of the trained predictive model; and selecting a trained predictive model from among the plurality of trained predictive models based on the generated scores; wherein a plurality of trained predictive models are thereby generated and selected; storing the plurality of selected trained predictive models in the repository of trained predictive models.