Abstract: A computationally efficient method and apparatus is disclosed for machine learning an unknown, n-dimensional ?-margin halfspace to accuracy 1?? in the presence of malicious noise, when the noise rate is allowed to be as high as ? ? ( ?? ? log ? ( 1 / ? ) ) . A smooth boosting module repeatedly calls a weak learner module that generates candidate classifiers based on a majority vote of randomly-generated classifiers.

Abstract: A method and apparatus is disclosed for machine learning an unknown n-dimensional ?-margin halfspace. The method and apparatus can be implemented using parallel processing. In one embodiment, the method includes generating a random d-dimensional projection of the set of examples. The random projection is generated by rounding the examples, taking a projection and then rounding the results. A set of m examples are drawn from the d-dimensional projection. Linear programs are then solved with m constraints based on the m examples using multiple stages of Newton's method. Parallel algorithms for linear algebra can be used to carry out at least some stages of Newton's method.

Abstract: Boosting algorithms are provided for accelerated machine learning in the presence of misclassification noise. In an exemplary embodiment, a machine learning method having multiple learning stages is provided. Each learning stage may include partitioning examples into bins, choosing a base classifier for each bin, and assigning an example to a bin by counting the number of positive predictions previously made by the base classifier associated with the bin.

Abstract: Presented are methods and systems for highly efficient proofs of correctness of computations that preserve secrecy of the input values and calculations. One embodiment includes a method for verifiably determining at least one output for a secrecy preserving computations where the method includes acts of calculating an output from submitted inputs according to an announced calculation, translating a value in the calculation into two components that are a randomized representation of that value, publishing commitments to the at least two components, revealing a portion of the randomized representation in response to a verification request, and enabling verification of the calculation of the output using the revealed portion of the randomized representation. According to one aspect of the secrecy preserving verification the numbers involved in the secrecy preserving calculation are represented by a randomly constructed representing pair.

Abstract: Boosting algorithms are provided for accelerated machine learning in the presence of misclassification noise. In an exemplary embodiment, a machine learning method having multiple learning stages is provided. Each learning stage may include partitioning examples into bins, choosing a base classifier for each bin, and assigning an example to a bin by counting the number of positive predictions previously made by the base classifier associated with the bin.