This disclosure relates to learning with transformed data such as determining multiple training samples from multiple data samples. Each of the multiple data samples comprises one or more feature values and a label that classifies that data sample. A processor determines each of the multiple training samples by randomly selecting a subset of the multiple data samples, and combining the feature values of the data samples of the subset based on the label of each of the data samples of the subset. Since the training samples are combinations of randomly chosen data samples, the training samples can be provided to third parties without disclosing the actual training data. This is an advantage over existing methods in cases where the data is confidential and should therefore not be shared with a learner of a classifier, for example.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A computer implemented method for determining multiple training samples from multiple data samples, each of the multiple data samples comprising one or more feature values and a label that classifies that data sample, the method comprising: determining each of the multiple training samples by randomly selecting a subset of the multiple data samples, and combining the feature values of the data samples of the subset based on the label of each of the data samples of the subset. 2. The method of claim 1, wherein randomly selecting the subset of the multiple data samples comprises multiplying each of the multiple data samples by a random selection value that is unequal to zero to select that data sample or equal to zero to deselect that data sample. 3. The method of claim 1, wherein combining the feature values of the data samples comprises determining a sum of the feature values of the data samples such that the feature value of a feature of the training sample is the sum of the feature values of that feature of the data samples. 4. The method of claim 3, wherein determining the sum comprises determining a weighted sum that is weighted based on the label of each of the data samples. 5. The method of claim 3, wherein determining the sum comprises determining a weighted sum that is weighted based on the number of data samples in the subset of the multiple data samples. 6. The method of claim 4, wherein the weighted sum is weighted based on a random number such that randomly selecting the subset of the multiple data samples is performed simultaneously with combining the feature values. 7. The method of claim 1, wherein randomly selecting a subset of multiple data samples comprises randomly selecting a subset of multiple data samples based on a non-uniform distribution. 8. The method of claim 1, wherein the data samples have signed real values as features values, and the label is one of ‘−1’ and ‘+1’. 9. The method of claim 1, wherein determining each of the multiple training samples comprises determining each of the multiple training samples such that each of the multiple training samples is based on at least a predetermined number of data samples. 10. The method of claim 9, wherein randomly selecting a subset of the multiple data samples comprises randomly selecting a subset of the multiple data samples that comprises at least a predetermined number of data samples. 11. A computer implemented method for determining multiple training samples, the method comprising: receiving a training sample according to claim 1; and determining for each feature value of the training sample a random value and adding the random value to that feature value to determine a modified training sample. 12. A non-transitory computer readable medium comprising computer-executable instructions stored thereon, that when executed by a processor, causes the processor to perform the method of claim 1. 13. A computer system for determining multiple training samples from multiple data samples, the computer system comprising: an input port to receive the multiple data samples, each of the multiple data samples comprising one or more feature values and a label that classifies that data sample; and a processor to determining each of the multiple training samples by randomly selecting a subset of the multiple data samples, and combining the feature values of the data samples of the subset based on the label of each of the data samples of the subset. 14. A computer implemented method for determining a classifier coefficient associated with a feature index, the method comprising: receiving multiple training values associated with the feature index, each training value being based on a combination of a subset of multiple data values based on multiple data labels, each of the multiple data labels being associated with one of the multiple data values; determining a correlation value based on the multiple training values, such that the correlation value is indicative of a correlation between each of the multiple data values and the data label associated with that data value; and determining the classifier coefficient based on the correlation value. 15. The method of claim 14, further comprising determining for each of the multiple training values a training value weight associated with that training value, wherein determining the correlation value is based on the training value weight associated with each of the multiple training values. 16. The method of claim 15, wherein determining the correlation value comprises determining a sum of training values weighted by the training value weight associated with each of the multiple training values. 17. The method of claim 16, wherein determining the correlation value comprises: determining a maximum training value; and dividing the sum by the maximum training value. 18. The method of claim 15, wherein determining the training value weight associated with each of the training values comprises determining the training value weight associated with each of the multiple training values based on the correlation value. 19. The method of claim 18, wherein determining each training value weight associated with one of the multiple training values comprises: determining a maximum training value; and determining the training value weight based on a fraction of the one of the multiple training values over the maximum training value. 20. The method of claim 14, further comprising performing multiple repetitions of the method to determine multiple classifier coefficients, each classifier coefficient being associated with one of multiple feature indices. 21. The method of claim 20, wherein determining the training value weight comprises determining the training value weight based on a difference between a first value of a regularization function of a current repetition and a second value of the regularization function of a previous repetition. 22. The method of claim 21, wherein the regularization function depends on the multiple classifier coefficients associated with the corresponding repetition. 23. The method of claim 21, wherein determining the training value weight comprises determining the training value weight based on an exponential function having an exponent by adding the difference to the exponent. 24. The method of claim 21, wherein the regularization function comprises one or more of: ridge function; lasso function; L∞-regularization; and SLOPE regularisation. 25. The method of claim 21, further comprising selecting the feature index based on an ordering of multiple feature indices, wherein the ordering is based on the difference. 26. The method of claim 20, wherein repeating the method comprises repeating the method to optimise a cost function of the multiple data values. 27. The method of claim 14, further comprising: receiving test values; and determining a classification of the test values based on the classifier coefficients. 28. A non-transitory computer readable medium comprising computer-executable instructions stored thereon, that when executed by a processor, causes the processor to perform the method of claim 14. 29. A computer system for determining a classifier weight associated with a feature index, the computer system comprising: an input port to receive multiple training values associated with the feature index, each training value being based on a combination of a subset of multiple data values based on multiple data labels, each of the multiple data labels being associated with one of the multiple data values; and a processor to determine a correlation value based on the multiple training values, such that the correlation value is indicative of a correlation between each of the multiple data values and the data label associated with that data value, and to determine the classifier coefficient based on the correlation value. 30. A computer implemented method for training a machine learning system, the method comprising optimising a convex loss function, the convex loss function being based on training samples as determined according to the method of claim 1.