Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for obtaining a global model for a particular activity, the global model derived based on input data representing multiple observations associated with the particular activity performed by a collection of users; determining, using the global model, expected data representing an expected observation associated with the particular activity performed by a particular user; receiving, by a computing device operated by the particular user, particular data representing an actual observation associated with the particular activity performed by the particular user; determining, by the computing device and using (i) the expected data and (ii) the particular data, residual data of the particular user; and deriving a local model of the particular user based on the residual data.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A computer-implemented method, comprising: obtaining a global model for a particular activity, the global model derived based on input data representing multiple observations associated with the particular activity performed by a collection of users; determining, using the global model, expected data representing an expected observation associated with the particular activity performed by a particular user; receiving, by a computing device operated by the particular user, particular data representing an actual observation associated with the particular activity performed by the particular user; determining, by the computing device and using (i) the expected data and (ii) the particular data, residual data of the particular user; and deriving a local model of the particular user based on the residual data. 2. The method of claim 1, wherein determining the residual data using (i) the expected data and (ii) the particular data comprises determining the residual data based on a difference between the expected data and the particular data. 3. The method of claim 1, comprising: determining, using the local model, particular expected data representing an expected observation associated with the particular activity performed by the particular user, wherein the particular expected data determined by the local model substantially matches the particular data. 4. The method of claim 1, wherein the local model is derived by the computing device, and wherein the method further comprises: transmitting, from the computing device to one or more remote computers, the local model of the particular user as a representation of the particular user. 5. The method of claim 1, wherein deriving the local model of the particular user comprises: transmitting, from the computing device to one or more remote computers, the residual data; and deriving the local model by the one or more remote computers. 6. The method of claim 1, wherein the global model includes a first vector space constructed by first multiple principal axes, and wherein the local model includes a second vector space constructed by second multiple principal axes that are different from the first multiple principal axes. 7. The method of claim 1, comprising: obtaining a second global model for a second activity that is different from the particular activity, the second global model derived based on second input data representing multiple observations associated with the second activity performed by a collection of users; determining, using the second global model, second expected data representing an expected observation associated with the second activity performed by the particular user; receiving, by the computing device operated by the particular user, second particular data representing an actual observation associated with the second activity performed by the particular user; and determining, by the computing device and using (i) the second expected data and (ii) the second particular data, second residual data of the particular user. 8. The method of claim 7, wherein deriving the local model of the particular user comprises deriving the local model of the particular user based at least on (i) the residual data and (ii) the second residual data. 9. The method of claim 1, comprising: receiving second particular data associated with the particular activity; determining, by the computing device and using (i) the expected data and (ii) the second particular data, second residual data; determining that the second residual data does not substantially match the residual data; and in response to determining that the second residual data does not substantially match the residual data, determining that an identity of the particular user is not verified. 10. A computer-readable medium storing software having stored thereon instructions, which, when executed by one or more computers, cause the one or more computers to perform operations of: obtaining a global model for a particular activity, the global model derived based on input data representing multiple observations associated with the particular activity performed by a collection of users; determining, using the global model, expected data representing an expected observation associated with the particular activity performed by a particular user; receiving particular data representing an actual observation associated with the particular activity performed by the particular user; determining, using (i) the expected data and (ii) the particular data, residual data of the particular user; and deriving a local model of the particular user based on the residual data. 11. The computer-readable medium of claim 10, wherein the operations comprise: determining, using the local model, particular expected data representing an expected observation associated with the particular activity performed by the particular user, wherein the particular expected data determined by the local model substantially matches the particular data. 12. The computer-readable medium of claim 10, wherein the operations comprise: transmitting, to one or more remote computers, the local model of the particular user as a representation of the particular user. 13. The computer-readable medium of claim 10, wherein the global model includes a first vector space constructed by first multiple principal axes, and wherein the local model includes a second vector space constructed by second multiple principal axes that are different from the first multiple principal axes. 14. The computer-readable medium of claim 10, wherein the operations comprise: obtaining a second global model for a second activity that is different from the particular activity, the second global model derived based on second input data representing multiple observations associated with the second activity performed by a collection of users; determining, using the second global model, second expected data representing an expected observation associated with the second activity performed by the particular user; receiving second particular data representing an actual observation associated with the second activity performed by the particular user; and determining, using (i) the second expected data and (ii) the second particular data, second residual data of the particular user. 15. The computer-readable medium of claim 10, wherein the operations comprise: receiving second particular data associated with the particular activity; determining, by the computing device and using (i) the expected data and (ii) the second particular data, second residual data; determining that the second residual data does not substantially match the residual data; and in response to determining that the second residual data does not substantially match the residual data, determining that an identity of the particular user is not verified. 16. A system comprising: one or more processors and one or more computer storage media storing instructions that are operable, when executed by the one or more processors, to cause the one or more processors to perform operations comprising: obtaining a global model for a particular activity, the global model derived based on input data representing multiple observations associated with the particular activity performed by a collection of users; determining, using the global model, expected data representing an expected observation associated with the particular activity performed by a particular user; receiving particular data representing an actual observation associated with the particular activity performed by the particular user; determining, using (i) the expected data and (ii) the particular data, residual data of the particular user; and deriving a local model of the particular user based on the residual data. 17. The system of claim 16, wherein the operations comprise: determining, using the local model, particular expected data representing an expected observation associated with the particular activity performed by the particular user, wherein the particular expected data determined by the local model substantially matches the particular data. 18. The system of claim 16, wherein the operations comprise: transmitting, to one or more remote computers, the local model of the particular user as a representation of the particular user. 19. The system of claim 16, wherein the operations comprise: obtaining a second global model for a second activity that is different from the particular activity, the second global model derived based on second input data representing multiple observations associated with the second activity performed by a collection of users; determining, using the second global model, second expected data representing an expected observation associated with the second activity performed by the particular user; receiving second particular data representing an actual observation associated with the second activity performed by the particular user; and determining, using (i) the second expected data and (ii) the second particular data, second residual data of the particular user. 20. The system of claim 16, wherein the operations comprise: receiving second particular data associated with the particular activity; determining, by the computing device and using (i) the expected data and (ii) the second particular data, second residual data; determining that the second residual data does not substantially match the residual data; and in response to determining that the second residual data does not substantially match the residual data, determining that an identity of the particular user is not verified.