Localized learning from a global model

1. A method comprising:

obtaining population-level training data associated with a particular activity, wherein the training data represents multiple observations associated with the particular activity performed by a collection of users;

mapping the population-level training data to an m-dimensional vector space, wherein each of the multiple observations is assigned to a vector mapped to the vector space having m orthogonal axes;

determining one or more principal axes based on the mapped population-level training data;

training a global model that represents the particular activity based on the one or more principal axes and the population-level training data to obtain a trained global model;

generating a representative global model from the trained global model, comprising generating from the global model the representative model that has a reduced number of vector space dimensions from the m-dimensional vector space, wherein the representative model is a compressed version of the global model;

providing the representative global model to a plurality of client devices, wherein on each device the representative global model is executed by the client device and the client device generates observations from one or more sensors on the client device, determines residuals from the predictions of the representative global model and the observations, and generates a respective local model based on the residuals and the representative global model;

receiving, from each of the client devices, a respective local model for a particular user of the client device, wherein each respective local model is different from each other respective local model and does not include private information about the particular user; and

determining, for each particular user, using the respective local model received from the client device of the particular user, particular expected data representing an expected observation associated with the particular activity performed by the user.

2. The method of claim 1 , wherein mapping the population-level training data comprises assigning each type of measurement as a dimension and mapping each observation to the m-dimensional vector space.

3. The method of claim 1 , wherein determining one or more principal axes comprises using principal component analysis to identify eigenvectors of covariance to determine the principal axes of the m-dimensional vector space.

4. The method of claim 1 , wherein the representative global model has a reduced number of vector space dimensions from the m-dimensional vector space.

5. The method of claim 4 , wherein one or more principal axes are removed from the vector space of the representative global model based on a determination of a variance along each principal axis.

6. The method of claim 1 , wherein the local model received for the particular user is a representative local model that does not include private information about the user.

7. The method of claim 1 , further comprising:

determining, using the local model, particular expected data representing an expected observation associated with the particular activity performed by the user.

8. 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 population-level training data associated with a particular activity, wherein the training data represents multiple observations associated with the particular activity performed by a collection of users;

mapping the population-level training data to an m-dimensional vector space, wherein each of the multiple observations is assigned to a vector mapped to the vector space having m orthogonal axes;

determining one or more principal axes based on the mapped population-level training data;

training a global model that represents the particular activity based on the one or more principal axes and the population-level training data to obtain a trained global model;

generating a representative global model from the trained global model, comprising generating from the global model the representative model that has a reduced number of vector space dimensions from the m-dimensional vector space;

providing the representative global model to a plurality of client devices, wherein on each device the representative global model is executed by the client device and the client device generates observations from one or more sensors on the client device, determines residuals from the predictions of the representative global model and the observations, and generates a respective local model based on the residuals and the representative global model;

receiving, from each of the client devices, a respective local model for a particular user of the client device, wherein each respective local model is different from each other respective local model and does not include private information about the particular user; and

determining, for each particular user, using the respective local model received from the client device of the particular user, particular expected data representing an expected observation associated with the particular activity performed by the user.

9. The system of claim 8 , wherein mapping the population-level training data comprises assigning each type of measurement as a dimension and mapping each observation to the m-dimensional vector space.

10. The system of claim 8 , wherein determining one or more principal axes comprises using principal component analysis to identify eigenvectors of covariance to determine the principal axes of the m-dimensional vector space.

11. The system of claim 8 , wherein the representative global model has a reduced number of vector space dimensions from the m-dimensional vector space.

12. The system of claim 11 , wherein one or more principal axes are removed from the vector space of the representative global model based on a determination of a variance along each principal axis.

13. The system of claim 8 , wherein the local model received for the particular user is a representative local model that does not include private information about the user.

14. The system of claim 8 , further comprising:

determining, using the local model, particular expected data representing an expected observation associated with the particular activity performed by the user.

15. One or more non-transitory computer-readable media 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 population-level training data associated with a particular activity, wherein the training data represents multiple observations associated with the particular activity performed by a collection of users;

mapping the population-level training data to an m-dimensional vector space, wherein each of the multiple observations is assigned to a vector mapped to the vector space having m orthogonal axes;

determining one or more principal axes based on the mapped population-level training data;

training a global model that represents the particular activity based on the one or more principal axes and the population-level training data to obtain a trained global model;

generating a representative global model from the trained global model, comprising generating from the global model the representative model that has a reduced number of vector space dimensions from the m-dimensional vector space;

providing the representative global model to a plurality of client devices, wherein on each device the representative global model is executed by the client device and the client device generates observations from one or more sensors on the client device, determines residuals from the predictions of the representative global model and the observations, and generates a respective local model based on the residuals and the representative global model;

receiving, from each of the client devices, a respective local model for a particular user of the client device, wherein each respective local model is different from each other respective local model and does not include private information about the particular user and is derived at the client device, in part, based on the representative global model; and

determining, for each particular user, using the respective local model received from the client device of the particular user, particular expected data representing an expected observation associated with the particular activity performed by the user.

16. The non-transitory computer-readable media of claim 15 , wherein mapping the population-level training data comprises assigning each type of measurement as a dimension and mapping each observation to the m-dimensional vector space.

17. The non-transitory computer-readable media of claim 15 , wherein determining one or more principal axes comprises using principal component analysis to identify eigenvectors of covariance to determine the principal axes of the m-dimensional vector space.

18. The non-transitory computer-readable media of claim 15 , wherein the representative global model has a reduced number of vector space dimensions from the m-dimensional vector space.

19. The non-transitory computer-readable media of claim 18 , wherein one or more principal axes are removed from the vector space of the representative global model based on a determination of a variance along each principal axis.

20. The non-transitory computer-readable media of claim 15 , wherein the local model received for the particular user is a representative local model that does not include private information about the user.

21. The non-transitory computer-readable media of claim 15 , further comprising:

determining, using the local model, particular expected data representing an expected observation associated with the particular activity performed by the user.