Abstract: Data structures for collaborative filtering systems are described. In an embodiment sketches which extremely concisely represent a list of items that a user has rated are created and stored for use by a collaborative filtering system to recommend items. For example, the sketches are created by using several versions of a cryptographic hash function to permute the item list and store a minimal value from each permutation in the sketch together with a user rating. In examples the sketches are used to compute estimates of similarity measures between pairs of users such as rank correlations including Spearman's Rho and Kendall's Tau. For example, the similarity measures are used by a collaborative filtering system to accurately and efficiently recommend items to users. For example the sketches are so concise that massive amounts of data can be taken into account in order to give high quality recommendations in a practical manner.

Abstract: A method includes receiving first online messages regarding a financial instrument, and first objective quantitative data that reflect respective first values of a target variable associated with the financial instrument. The first messages are analyzed to generate respective first sentiment scores reflecting respective sentiments expressed in the first messages regarding the financial instrument. An initial prediction model is generated for the target variable by analyzing the first sentiment scores and the associated first values of the target variable. Second messages and objective quantitative data are received and analyzed to generate second sentiment scores and an incremental prediction model. A refined prediction model is generated by combining the initial model with the incremental model. Third messages are received and analyzed to generate third sentiment scores, which are used as input to the refined model to predict a future value of the target variable, which is reported to a user.