Training instances from a target domain are represented by feature vectors storing values for a set of features, and are labeled by labels from a set of labels. Both a noise marginalizing transform and a weighting of one or more source domain classifiers are simultaneously learned by minimizing the expectation of a loss function that is dependent on the feature vectors corrupted with noise represented by a noise probability density function, the labels, and the one or more source domain classifiers operating on the feature vectors corrupted with the noise. An input instance from the target domain is labeled with a label from the set of labels by operations including applying the learned noise marginalizing transform to an input feature vector representing the input instance and applying the one or more source domain classifiers weighted by the learned weighting to the input feature vector representing the input instance.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A device comprising: a computer programmed to perform a machine learning method operating on training instances from a target domain, the training instances represented by feature vectors storing values for a set of features and labeled by labels from a set of labels, the machine learning method including the operations of: optimizing a loss function dependent on all of: the feature vectors representing the training instances from the target domain corrupted with noise, the labels of the training instances from the target domain, and one or more source domain classifiers operating on the feature vectors representing the training instances from the target domain corrupted with the noise, to simultaneously learn both a noise marginalizing transform and a weighting of the one or more source domain classifiers; and generating a label prediction for an unlabeled input instance from the target domain that is represented by an input feature vector storing values for the set of features by operations including applying the learned noise marginalizing transform to the input feature vector and applying the one or more source domain classifiers weighted by the learned weighting to the input feature vector. 2. The device of claim 1 wherein the loss function is not dependent on any training instance from any domain other than the target domain. 3. The device of claim 1 wherein the loss function is a quadratic loss function, the one or more source domain classifiers are linear classifiers, and the optimizing of the quadratic loss function comprises evaluating a closed form solution of the loss function for a vector representing parameters of the noise marginalizing transform and the weighting of the one or more source domain classifiers. 4. The device of claim 3 wherein the closed form solution is dependent upon the statistical expectation and variance values of the training instances from the target domain corrupted with the noise represented by a noise probability density function (noise pdf). 5. The device of claim 1 wherein the loss function is an exponential loss function, the one or more source domain classifiers are linear classifiers, and the optimizing of the exponential loss function is performed analytically using statistical values of the training instances from the target domain corrupted with the noise represented by a noise probability density function (noise pdf). 6. The device of claim 1 wherein the loss function L is optimized by optimizing: ℒ  ( w , z ) = ∑ n = 1 N     [ L  ( x ~ n , f , y n ; w , z ) ] p  ( x ~ n | x n ) where xn, n=1, . . . , N are the feature vectors representing the training instances from the target domain, {tilde over (x)}n, n=1, . . . , N are the feature vectors representing the training instances from the target domain corrupted with the noise, p({tilde over (x)}n|xn) is a noise probability density function (noise pdf) representing the noise, f represents the one or more source domain classifiers, w represents parameters of the noise marginalizing transform, z represents the weighting of the one or more source domain classifiers, and is the statistical expectation. 7. The device of claim 6 wherein generating the label prediction for the unlabeled input instance from the target domain comprises computing the label prediction ŷin according to: ŷin=(w*)Txin+(z*)Tf(xin) where xin is the input feature vector representing the unlabeled input instance from the target domain, w* represents the learned parameters of the noise marginalizing transform, and z* represents the learned weighting of the one or more source domain classifiers. 8. The device of claim 1 wherein the loss function L is a quadratic loss function and the optimizing of the quadratic loss function L comprises minimizing: ℒ  ( w , z ) = 1 N  ∑ n = 1 N     [ ( w T  x ~ n + z T  f  ( x ~ n ) - y n ) 2 ] p  ( x ~ n | x n ) where xn, n=1, . . . , N are the feature vectors representing the training instances from the target domain, {tilde over (x)}n, n=1, . . . , N are the feature vectors representing the training instances from the target domain corrupted with the noise, p({tilde over (x)}n|xn) is a noise probability density function (noise pdf) representing the noise, f represents the one or more source domain classifiers, w represents parameters of the noise marginalizing transform, z represents the weighting of the one or more source domain classifiers, and is the statistical expectation. 9. The device of claim 8 wherein the one or more source domain classifiers f are linear classifiers, and the minimizing comprises evaluating a closed form solution of (w,z) for a vector [ w * z * ] where w* represents the learned parameters of the noise marginalizing transform and z* represents the learned weighting of the one or more source domain classifiers. 10. The device of claim 1 wherein the loss function L is an exponential loss function and the optimizing of the exponential loss function L comprises minimizing: ℒ  ( w , z ) = ∑ n = 1 N     [ e - y n  ( w T  x ~ n + z T  f  ( x ~ n ) ) ] p  ( x ~ n | x n ) where xn, n=1, . . . , N are the feature vectors representing the training instances from the target domain, {tilde over (x)}n, n=1, . . . , N are the feature vectors representing the training instances from the target domain corrupted with the noise, p({tilde over (x)}n|xn) is a noise probability density function (noise pdf) representing the noise, f represents the one or more source domain classifiers, w represents parameters of the noise marginalizing transform, z represents the weighting of the one or more source domain classifiers, and is the statistical expectation. 11. The device of claim 1 wherein one of: each training instance from the target domain represents a corresponding image, the set of features is a set of image features, the one or more source domain classifiers are one or more source domain image classifiers, and the machine learning method includes the further operation of generating each training instance from the target domain by extracting values for the set of image features from the corresponding image; and each training instance from the target domain represents a corresponding text-based document, the set of features is a set of text features, the one or more source domain classifiers are one or more source domain document classifiers, and the machine learning method includes the further operation of generating each training instance from the target domain by extracting values for the set of text features from the corresponding text-based document. 12. A non-transitory storage medium storing instructions executable by a computer to perform a machine learning method operating on N training instances from a target domain, the training instances represented by feature vectors xn, n=1, . . . , N storing values for a set of features and labeled by labels yn, n=1, . . . , N from a set of labels, the machine learning method including the operations of: optimizing the function (w,z) given by: ℒ  ( w , z ) = ∑ n = 1 N     [ L  ( x ~ n , f , y n ; w , z ) ] p  ( x ~ n | x n ) with respect to w and z where {tilde over (x)}n, n=1, . . . , N are the feature vectors representing the training instances from the target domain corrupted with noise, p({tilde over (x)}n|xn) is a noise probability density function (noise pdf) representing the noise, f represents one or more source domain classifiers, L is a loss function, w represents parameters of a noise marginalizing transform, z represents a weighting of the one or more source domain classifiers, and is the statistical expectation, to generate learned parameters w* of the noise marginalizing transform and a learned weighting z* of the one or more source domain classifiers; and generating a label prediction ŷin for an unlabeled input instance from the target domain represented by input feature vector xin by operations including applying the noise marginalizing transform with the learned parameters w* to the input feature vector xin and applying the one or more source domain classifiers weighted by the learned weighting z* to the input feature vector xin. 13. The non-transitory storage medium of claim 12 wherein the loss function L is the quadratic loss function (wT{tilde over (x)}in+zTf({tilde over (x)}n)−yn)2. 14. The non-transitory storage medium of claim 12 wherein the loss function L is a quadratic loss function, the one or more source domain classifiers f are linear classifiers, and the optimizing comprises evaluating a closed form solution of (w,z) for a vector [ w * z * ] where w* represents the learned parameters of the noise marginalizing transform and z* represents the learned weighting of the one or more source domain classifiers. 15. The non-transitory storage medium of claim 12 wherein the loss function L is the exponential loss function e−yn(wT{tilde over (x)}n+zTf({tilde over (x)}n)). 16. The non-transitory storage medium of claim 12 wherein each training instance from the target domain represents a corresponding image, the set of features is a set of image features, the one or more source domain classifiers are one or more source domain image classifiers, and the machine learning method includes the further operation of: generating the feature vector xn representing each training instance by extracting values for the set of image features from the corresponding image. 17. The non-transitory storage medium of claim 12 wherein each training instance from the target domain represents a corresponding text-based document, the set of features is a set of text features, the one or more source domain classifiers are one or more source domain document classifiers, and the machine learning method includes the further operation of: generating the feature vector xn representing each training instance by extracting values for the set of text features from the corresponding text-based document. 18. A machine learning method operating on training instances from a target domain, the training instances represented by feature vectors storing values for a set of features and labeled by labels from a set of labels, the machine learning method comprising: simultaneously learning both a noise marginalizing transform and a weighting of one or more source domain classifiers by minimizing the expectation of a loss function dependent on the feature vectors corrupted with noise represented by a noise probability density function, the labels, and the one or more source domain classifiers operating on the feature vectors corrupted with the noise; and labeling an unlabeled input instance from the target domain with a label from the set of labels by operations including applying the learned noise marginalizing transform to an input feature vector representing the unlabeled input instance and applying the one or more source domain classifiers weighted by the learned weighting to the input feature vector representing the unlabeled input instance; wherein the simultaneous learning and the labeling are performed by a computer. 19. The method of claim 18 wherein the loss function is not dependent on any feature vector representing a training instance from any domain other than the target domain. 20. The method of claim 18 wherein the loss function is a quadratic loss function and the simultaneous learning comprises evaluating a closed form solution of the loss function for a vector representing parameters of the noise marginalizing transform and the weighting of the one or more source domain classifiers.