Abstract: A Software optimization method, system, and computer program product, include defining a vocabulary of tokens to yield admissible inputs of a system, generating random test inputs based on combining inputs and input tuples, followed by application of these inputs into the system, and analyzing the correlations between system failures and the tokens present in respective inputs to localize failures to particular inputs and input tuples.

Abstract: A method, system, and computer program product including generating random test inputs as a number of queries using a token and analyzing a correlation between a system failure and a token present in respective inputs to localize the system failure.

Abstract: A Software optimization method, system, and computer program product, include defining a vocabulary of tokens to yield admissible inputs of a system, generating random test inputs based on combining inputs and input tuples, followed by application of these inputs into the system, and analyzing the correlations between system failures and the tokens present in respective inputs to localize failures to particular inputs and input tuples.

Abstract: Risk management is facilitated by tracking and forecasting multivariate data using nonparametric statistical procedures. Enhanced matrix factorization is used for developing a nonparametric tracking and forecasting algorithm, based on Kalman smoothing, that applies a state space model to both (i) factor loading, and (ii) factor time series of multivariate data in the matrix factorization. One example of use is tracking and forecasting financial risk according to a yield curve based on multivariate financial data. The forecasted yield curve change forms the bases, for example, of risk exposure adjustments associated with US Treasury bond investment.