Online learning of model parameters
View Patent ↗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.
1 . A computer-implemented method for enhancing performance of a trained machine learning model by additional machine learning model training after initial machine learning model deployment, 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 having new data patterns;
dynamically adjusting the feature vector responsive to time-variant characteristic data of the target sequence and the feature vector to generate a modified feature vector by:
reducing an absolute value of at least one element of the feature vector using a multiplication reducing factor between 0 to 1 responsive to an intercept component as at least one element of the feature vector being a constant feature; and
updating the intercept component of the trained machine learning model to zero;
iteratively optimizing the trained machine learning model by reducing processing time and processor resource utilization for continuous online training of the trained machine learning model trained for predicting an anomaly with newly detected time-variant characteristic data by applying training processes of a previous training to each data pattern in available historical data at each time step only once while regularizing model parameters of the trained machine learning model to maintain model parameters reflecting previous training including:
generating an inverse Hessian matrix recursively, based on the previous training from a previous inverse Hessian matrix using a difference of a temporal inverse Hessian matrix and a proportion based on at least the feature vector, the modified feature vector, a transpose of the modified feature vector, the previous inverse Hessian matrix, and a regularization weight, the inverse Hessian matrix maintains the model parameters proportional to a weighted mean squared error between the target sequence and a future target value to avoid overfitting;
updating the model parameters of the trained machine learning model for continuous online training with only newly detected time-variant characteristic data from the target sequence using the modified feature vector and the recursively generated inverse Hessian matrix;
predicting a future target value in the target sequence based on an inner product of the updated model parameters and a feature vector corresponding to the future target value; and
minimizing the weighted mean squared error between the target sequence and the future target value.
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 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 machine learning model further uses the first vector to update the machine learning model parameters.
4 . The computer-implemented method of claim 3 , wherein updating parameters of the machine learning model includes calculating the parameters by multiplying the inverse Hessian matrix and the first vector.
5 . The computer-implemented method of claim 1 , wherein the at least one element of the feature vector includes at least one intercept component of the machine learning model.
6 . 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.
7 . The computer-implemented method of claim 1 , wherein generating the inverse Hessian matrix includes:
calculating the 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.
8 . The computer-implemented method of claim 7 , 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:
H
t
+
1
-
1
←
H
t
+
1
′
-
1
-
λ
ϕ
^
t
ϕ
^
t
T
1
+
λ
ϕ
^
t
T
H
t
-
1
ϕ
^
t
where
H
t
+
1
-
1
is the inverse Hessian matrix,
H
t
+
1
′
-
1
is the temporal inverse Hessian matrix,
H
t
-
1
is the previous inverse Hessian matrix, {circumflex over (φ)} t is the modified feature vector, and λ is a weight for regularization.
9 . A computer program product including one or more non-transitory 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 for enhancing performance of a trained machine learning model by additional machine learning model training after initial machine learning model deployment, 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 having new data patterns;
dynamically adjusting the feature vector responsive to time-variant characteristic data of the target sequence and the feature vector to generate a modified feature vector by:
reducing an absolute value of at least one element of the feature vector using a multiplication reducing factor between 0 to 1 responsive to an intercept component as at least one element of the feature vector being a constant feature; and
updating the intercept component of the trained machine learning model to zero;
iteratively optimizing the trained machine learning model by reducing processing time and processor resource utilization for continuous online training of the trained machine learning model trained for predicting an anomaly with newly detected time-variant characteristic data by applying training processes of a previous training to each data pattern in available historical data at each time step only once while regularizing model parameters of the trained machine learning model to maintain model parameters reflecting previous training including:
generating an inverse Hessian matrix recursively, based on the previous training from a previous inverse Hessian matrix using a difference of a temporal inverse Hessian matrix and a proportion based on at least the feature vector, the modified feature vector, a transpose of the modified feature vector, the previous inverse Hessian matrix, and a regularization weight, the inverse Hessian matrix maintains the model parameters proportional to a weighted mean squared error between the target sequence and a future target value to avoid overfitting;
updating model parameters of the trained machine learning model for continuous online training with only newly detected time-variant characteristic data from the target sequence using the modified feature vector and the recursively generated inverse Hessian matrix
predicting a future target value in the targe t sequence based on an inner product of the updated model parameters and a feature vector corresponding to the future target value; and
minimizing the weighted mean squared error between the target sequence and the future target value.
10 . The computer program product of claim 9 , 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.
11 . The computer program product of claim 9 , wherein modifying the feature vector includes changing the at least one element of the feature vector to 0.
12 . The computer program product of claim 11 , wherein the at least one element of the feature vector includes at least one intercept component of the machine learning model.
13 . The computer program product of claim 9 , wherein generating the inverse Hessian matrix includes:
calculating the 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.
14 . An apparatus for additional machine learning model training after initial machine learning model deployment, 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 having new data patterns;
dynamically adjust the feature vector responsive to time-variant characteristic data of the target sequence and the feature vector to generate a modified feature vector by:
reducing an absolute value of at least one element of the feature vector using a multiplication reducing factor between 0 to 1 responsive to an intercept component as at least one element of the feature vector being a constant feature; and
updating the intercept component of the trained machine learning model to zero;
iteratively optimize the trained machine learning model by reducing processing time and processor resource utilization for continuous online training of the trained machine learning model trained for predicting an anomaly with newly detected time-variant characteristic data by applying training processes of a previous training to each data pattern in available historical data at each time step only once while regularizing model parameters of the trained machine learning model to maintain model parameters reflecting previous training including:
generating an inverse Hessian matrix recursively, based on previous training from a previous inverse Hessian matrix using a difference of a temporal inverse Hessian matrix and a proportion based on at least the feature vector, the modified feature vector, a transpose of the modified feature vector, the previous inverse Hessian matrix, and a regularization weight, the inverse Hessian matrix maintains the model parameters proportional to a weighted mean squared error between the target sequence and a future target value to avoid overfitting;
updating model parameters of the trained machine learning model for continuous online training with only newly detected time-variant characteristic data from the target sequence using the modified feature vector and the recursively generated inverse Hessian matrix;
predicting a future target value in the target sequence based on an inner product of the updated model parameters and a feature vector corresponding to the future target value; and
minimizing the weighted mean squared error between the target sequence and the future target value.
15 . The apparatus of claim 14 , 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.
16 . The apparatus of claim 14 , 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.
17 . The apparatus of claim 14 , wherein the at least one element of the feature vector includes at least one intercept component of the machine learning model.
18 . The apparatus of claim 14 , 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 the 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.