Methods and apparatus to construct histograms and wavelet synopses for probabilistic data

An apparatus to select wavelet coefficients to represent probabilistic data, comprising:

• a processor;
• and
• a memory storing machine readable instructions that, when executed by the processor, cause the processor to perform operations comprising:
• generating a wavelet coefficient quantity exceeding a target error value;
• iteratively generating different wavelet coefficient quantities until an error measure of a selected one of the different wavelet coefficient quantities is less than or equal to the target error value, the different wavelet coefficient quantities generated based on items represented by probabilistic data having uncertainties as to information of a data transmission that the probabilistic data represents, and each wavelet coefficient quantity representing different ones of the items by multiplying corresponding wavelet vectors;
• for the different wavelet coefficient quantities, determining the error measure by determining a probabilistic expected error for each of the coefficients of the different wavelet coefficient quantities, the probabilistic expected error indicative of an accuracy with which a synopsis represents items associated with a respective one of the coefficients;
• selecting the selected one of the different wavelet coefficient quantities based on its associated error measure;
• and
• displaying parameter information associated with the selected wavelet coefficient quantity to represent the probabilistic data, the parameter information to reduce data loss associated with at least one of noisy data transmissions or dropped data transmissions.

A tangible machine readable storage medium comprising instructions which, when executed, cause a machine to perform a method, comprising:

• generating a wavelet coefficient quantity exceeding a target error value;
• iteratively generating different wavelet coefficient quantities until an error measure of a selected one of the different wavelet coefficient quantities is less than or equal to the target error value, the different wavelet coefficient quantities generated based on items represented by probabilistic data having uncertainties as to information of a data transmission that the probabilistic data represents, and each wavelet coefficient quantity representing different ones of the items by multiplying corresponding wavelet vectors;
• for the different wavelet coefficient quantities, determining the error measure by determining a probabilistic expected error for each of the coefficients of the different wavelet coefficient quantities, the probabilistic expected error indicative of an accuracy with which a synopsis represents items associated with a respective one of the coefficients;
• selecting the selected one of the different wavelet coefficient quantities based on its associated error measure;
• and
• displaying parameter information associated with the selected wavelet coefficient quantity to represent the probabilistic data, the parameter information to reduce data loss associated with at least one of noisy data transmissions or dropped data transmissions.