ONLINE LEARNING OF MODEL PARAMETERS

• US 20200134495A1
• Filed: 10/29/2018
• Published: 04/30/2020
• Est. Priority Date: 10/29/2018
• Status: Active Application

• Current Assignee: International Business Machines Corporation
• Original Assignee: International Business Machines Corporation
• Inventors: Osogami, Takayuki
• Application Number:
  US16/173,582
• Publication Number:
  US 20200134495A1
• Time in Patent Office: Days
• CPC Class Codes: G06F 17/13 Differential equations using digital differential analysers G06F7/64
• CPC Class Codes: G06F 17/16 Matrix or vector computation , e.g. matrix-matrix or matrix-vector multiplication, matrix factorization matrix transposition G06F7/78
• CPC Class Codes: G06N 20/00 Machine learning
• CPC Class Codes: G06N 7/00 Computing arrangements based on specific mathematical models

Abstract

Online learning of model parameters is performed by obtaining a first target value in a target sequence and a feature vector corresponding to the first target value. The feature vector includes a plurality of elements. The feature vector can be modified to obtain a modified feature vector by reducing an absolute value of at least one element of the feature vector. An inverse Hessian matrix can be generated recursively from a previous inverse Hessian matrix using at least the feature vector and the modified feature vector. Parameters of a model can be updated using the inverse Hessian matrix.

Claims

1. A computer-implemented method comprising:

obtaining a first target value in a target sequence and a feature vector corresponding to the first target value, the feature vector including a plurality of elements;

modifying the feature vector to obtain a modified feature vector by reducing an absolute value of at least one element of the feature vector;

generating an inverse Hessian matrix recursively from a previous inverse Hessian matrix using at least the feature vector and the modified feature vector; and

updating parameters of a model using the inverse Hessian matrix.

2. The computer-implemented method of claim 1, further comprising predicting a future target value in the target sequence by using the updated parameters and a feature vector corresponding to the future target value.

3. The computer-implemented method of claim 2, wherein predicting the future target value includes calculating an inner product of the updated parameters and the feature vector corresponding to the future target value.

4. The computer implemented method of claim 1, further comprising calculating a first vector recursively from a previous first vector using the first target value and the feature vector, wherein updating parameters of the model further uses the first vector to update the parameters.

5. The computer implemented method of claim 4, wherein updating parameters of the model includes calculating the parameters by multiplying the inverse Hessian matrix and the first vector.

6. The computer-implemented method of claim 1, wherein modifying the feature vector includes changing the at least one element of the feature vector to 0.

7. The computer-implemented method of claim 6, wherein the at least one element of the feature vector includes at least one intercept component of the model.

8. The computer-implemented method of claim 1, wherein generating the inverse Hessian matrix includes:

generating, for a second target value preceding the first target value in the target sequence, a Hessian matrix recursively from a previous Hessian matrix by using a feature vector corresponding to the second target value; and

inverting the Hessian matrix for the second target value to obtain the inverse Hessian matrix.

9. The computer-implemented method of claim 1, wherein generating the inverse Hessian matrix includes:

calculating a temporal inverse Hessian matrix from the previous inverse Hessian matrix by using the feature vector; and

calculating the inverse Hessian matrix from the temporal inverse Hessian matrix and the previous inverse Hessian matrix by using the modified feature vector.

10. The computer-implemented method of claim 9, wherein calculating the inverse Hessian matrix from the temporal inverse Hessian matrix and the previous inverse Hessian matrix includes calculating the inverse Hessian matrix by the following formula:

11. A computer program product including one or more computer readable storage mediums collectively storing program instructions that are executable by a processor or programmable circuitry to cause the processor or programmable circuitry to perform operations comprising:

obtaining a first target value in a target sequence and a feature vector corresponding to the first target value, the feature vector including a plurality of elements;

modifying the feature vector to obtain a modified feature vector by reducing an absolute value of at least one element of the feature vector;

generating an inverse Hessian matrix recursively from a previous inverse Hessian matrix using at least the feature vector and the modified feature vector; and

updating parameters of a model using the inverse Hessian matrix.

12. The computer program product of claim 11, comprising predicting a future target value in the target sequence by using the updated parameters and a feature vector corresponding to the future target value.

13. The computer program product of claim 11, wherein modifying the feature vector includes changing the at least one element of the feature vector to 0.

14. The computer program product of claim 13, wherein the at least one element of the feature vector includes at least one intercept component of the model.

15. The computer program product of claim 11, wherein generating the inverse Hessian matrix includes:

calculating a temporal inverse Hessian matrix from the previous inverse Hessian matrix by using the feature vector; and

calculating the inverse Hessian matrix from the temporal inverse Hessian matrix and the previous inverse Hessian matrix by using the modified feature vector.

16. An apparatus comprising:

a processor or a programmable circuitry; and

one or more computer readable mediums collectively including instructions that, when executed by the processor or the programmable circuitry, cause the processor or the programmable circuitry to;

obtain a first target value in a target sequence and a feature vector corresponding to the first target value, the feature vector including a plurality of elements;

modify the feature vector to obtain a modified feature vector by reducing an absolute value of at least one element of the feature vector;

generate an inverse Hessian matrix recursively from a previous inverse Hessian matrix using at least the feature vector and the modified feature vector; and

update parameters of a model using the inverse Hessian matrix.

17. The apparatus of claim 16, further comprising instructions, that when executed by the processor or the programmable circuitry, cause the processor or the programmable circuitry to predict a future target value in the target sequence by using the updated parameters and a feature vector corresponding to the future target value.

18. The apparatus of claim 16, wherein the processor or the programmable circuitry modifies the feature vector by executing instructions that cause the processor or the programmable circuitry to at least change the at least one element of the feature vector to 0.

19. The apparatus of claim 16, wherein the at least one element of the feature vector includes at least one intercept component of the model.

20. The apparatus of claim 16, wherein the processor or the programmable circuitry generates the inverse Hessian matrix by executing instructions that cause the processor or the programmable circuitry to at least:

calculate a temporal inverse Hessian matrix from the previous inverse Hessian matrix by using the feature vector; and

calculate the inverse Hessian matrix from the temporal inverse Hessian matrix and the previous inverse Hessian matrix by using the modified feature vector.