Abstract: A method comprises: partitioning a region of interest into a plurality of soft bin regions that span the region of interest; estimating an integral over each soft bin region of a function defined over the region of interest; and outputting a value equal to or derived from the sum of the estimated integrals over the soft bin regions spanning the region of interest. The method may further comprise: integrating a Bayesian theorem function using the partitioning, estimating, and outputting operations, and classifying an object to be classified using a classifier trained using the Bayesian machine learning. The method may further comprise performing optimal control by iteratively minimizing a controlled system cost function to determine optimized control inputs using the partitioning, estimating, and outputting with the function equal to the controlled system cost function having the selected control inputs, and controlling the controlled system using the optimized control inputs.

Abstract: An information retrieval system is described for retrieving a list of documents such as web pages or other items from a document index in response to a user query. In an embodiment a prediction engine is used to predict both explicit relevance information such as judgment labels and implicit relevance information such as click data. In an embodiment the predicted relevance information is applied to a stored utility function that describes user satisfaction with a search session. This produces utility scores for proposed lists of documents. Using the utility scores one of the lists of documents is selected. In this way different sources of relevance information are combined into a single information retrieval system in a principled and effective manner which gives improved performance.

Abstract: Auction systems receive bids for items and select a winning item during each round of the auction. In an embodiment an automated on-line auction system for sponsored links is described. In the embodiment, for each advertisement a total expected utility is calculated over all advertisements and all anticipated future rounds of the auction. In an embodiment, an advertisement with the highest such total expected utility may be selected as the winner of the round of the auction and the advertiser is charged no matter whether the advertisement is clicked or not. In some embodiments the charge may be related to the externality that the winning advertisement imposes on the current round of the auction which can be thought of as the expected profits foregone by the other advertisers.

Abstract: There are many situations in which it is desired to predict outcomes of events. In an example, an event prediction system is described which receives variables for a proposed event. The system accesses learnt statistics describing belief about weights associated with the variables and uses the weights to determine probability information that the proposed event will have a specified outcome. The process involves combining the accessed statistics and mapping them into a number representing the probability. In another example, a machine learning process using assumed density filtering is used to learn the statistics from data about observed events. The event prediction system may be used as part of any suitable type of system such as an internet advertising system, an email filtering system, or a fraud detection system.