System and method for approximating numerical features via cubic splines and applications thereof

1 . A method implemented on at least one processor, a memory, and a communication platform for online advertising, comprising:

obtaining, via machine learning, based on training data indicative of effectiveness of online advertisements on various websites among different users, a set of weights each of which is associated with one of a plurality of basis functions;

receiving a value of a numerical feature including a plurality of features;

transforming, via a transform function, the value into a transformed value within a fixed range;

with respect to each of the plurality of basis functions for approximating a non-linear relationship between the numerical feature and a prediction of a model associated with online advertising, computing a respective basis function value of the basis function based on the transformed value;

retrieving the set of weights;

generating an approximated value of the numerical feature to facilitate assessment on which advertisement is to be displayed to which user and on which platform, wherein the approximated value of the numeral feature depends on a sum of the plurality of basis function values weighted respectively by each corresponding one of the set of the weights, wherein the approximated value of the numerical feature also depends on interactions among the plurality of features, and wherein the approximated value of the numerical feature is used to select an online advertisement for display on an online platform; and

adjusting, via machine learning and based on a discrepancy between an actual value of the numerical feature included in the training data and the approximated value of the numerical feature, the set of weights for more accurate approximation.

2 . The method of claim 1 , wherein

the value of the numerical feature is not bounded; and

the transformed value is bounded in the fixed range.

3 . The method of claim 1 , wherein the plurality of basis functions correspond to spline functions.

4 . The method of claim 1 , wherein the transform function is determined based on a cumulative distribution of the numerical feature and modeling thereof.

5 . The method of claim 1 , wherein the machine learning to obtain the set of weights is performed by:

initializing the set of weights, each of which is to be associated with a respective one of the plurality of basis functions;

accessing numerical feature values of the numerical feature from the training data; and

with respect to each of the numerical feature values,

generating an approximated numerical feature value based on a weighted sum of basis function values, each of which is weighed using a corresponding one of the set of weights and computed using a corresponding one of the plurality of basis functions based on a transformed numerical feature value associated with the numerical feature value, and

adjusting the set of weights based on the numerical feature value and the approximated numerical feature value.

6 . The method of claim 5 , wherein the step of generating the approximated numerical feature value comprises:

transforming the numerical feature value using the transform function to generate the transformed numerical feature value;

calculating the respective basis function values of the plurality of basis functions based on the transformed numerical feature value;

applying each of the set of weights to a corresponding one of the respective basis function values to generate a weighted basis function value; and

computing the approximated numerical feature value based on a sum of the weighted basis function values.

7 . The method of claim 1 , further comprising:

receiving values of additional features and corresponding additional weights involved in a factorization machine formulation; and

computing a value of the factorization machine formulation based on the approximated value of the numerical feature, the values of the additional features, as well as the corresponding additional weights.

8 . Machine readable and non-transitory medium having information recorded thereon for online advertising, wherein the information, once read by the machine, causes the machine to perform the following steps:

obtaining, via machine learning, based on training data indicative of effectiveness of online advertisements on various websites among different users, a set of weights each of which is associated with one of a plurality of basis functions;

receiving a value of a numerical feature including a plurality of features;

transforming, via a transform function, the value into a transformed value within a fixed range;

with respect to each of the plurality of basis functions for approximating a non-linear relationship between the numerical feature and a prediction of a model associated with online advertising, computing a respective basis function value of the basis function based on the transformed value;

retrieving the set of weights;

generating an approximated value of the numerical feature to facilitate assessment on which advertisement is to be displayed to which user and on which platform, wherein the approximated value of the numeral feature depends on a sum of the plurality of basis function values weighted respectively by each corresponding one of the set of the weights, wherein the approximated value of the numerical feature also depends on interactions among the plurality of features, and wherein the approximated value of the numerical feature is used to select an online advertisement for display on an online platform; and

adjusting, via machine learning and based on a discrepancy between an actual value of the numerical feature included in the training data and the approximated value of the numerical feature, the set of weights for more accurate approximation.

9 . The medium of claim 8 , wherein

the value of the numerical feature is not bounded; and

the transformed value is bounded in the fixed range.

10 . The medium of claim 8 , wherein the plurality of basis functions correspond to spline functions.

11 . The medium of claim 8 , wherein the transform function is determined based on a cumulative distribution of the numerical feature and modeling thereof.

12 . The medium of claim 8 , wherein the machine learning to obtain the set of weights is carried out by:

initializing the set of weights, each of which is to be associated with a respective one of the plurality of basis functions;

accessing numerical feature values of the numerical feature from the training data;

with respect to each of the numerical feature values,

generating an approximated numerical feature value based on a weighted sum of basis function values, each of which is weighed using a corresponding one of the set of weights and computed using a corresponding one of the plurality of basis functions based on a transformed numerical feature value associated with the numerical feature value,

adjusting the set of weights based on the numerical feature value and the approximated numerical feature value.

13 . The medium of claim 12 , wherein the step of generating the approximated numerical feature value comprises:

transforming the numerical feature value using the transform function to generate the transformed numerical feature value;

calculating the respective basis function values of the plurality of basis functions based on the transformed numerical feature value;

applying each of the set of weights to a corresponding one of the respective basis function values to generate a weighted basis function value;

computing the approximated numerical feature value based on a sum of the weighted basis function values.

14 . The medium of claim 8 , wherein the information, once read by the machine, further causes the machine to perform the step of:

receiving values of additional features and corresponding additional weights involved in a factorization machine formulation;

computing a value of the factorization machine formulation based on the approximated value of the numerical feature, the values of the additional features, as well as the corresponding additional weights.

15 . A system for online advertising, comprising:

a machine learning mechanism configured for obtaining, via machine learning, based on training data indicative of effectiveness of online advertisements on various websites among different users, a set of weights each of which is associated with one of a plurality of basis functions;

a training data processor configured for receiving a value of a numerical feature including a plurality of features;

a data transformation unit configured for transforming, via a transform function, the value into a transformed value within a fixed range;

a basis function value generator configured for computing, with respect to each of the plurality of basis functions for approximating a non-linear relationship between the numerical feature and a prediction of a model associated with online advertising, a respective basis function value of the basis function based on the transformed value, wherein

the set of weights are used for generating an approximated value of the numerical feature to facilitate assessment on which advertisement is to be displayed to which user and on which platform, wherein the approximated value of the numeral feature depends on a sum of the plurality of basis function values weighted respectively by each corresponding one of the set of the weights, wherein the approximated value of the numerical feature also depends on interactions among the plurality of features, and wherein the approximated value of the numerical feature is used to select an online advertisement for display on an online platform, and

the set of weights is adjusted for more accurate approximation via machine learning and based on a discrepancy between an actual value of the numerical feature included in the training data and the approximated value of the numerical feature.

16 . The system of claim 15 , wherein

the value of the numerical feature is not bounded; and

the transformed value is bounded in the fixed range.

17 . The system of claim 16 , wherein the transformed function is determined based on a cumulative distribution of the numerical feature and modeling thereof.

18 . The system of claim 15 , wherein the plurality of basis functions correspond to spline functions.

19 . The system of claim 15 , wherein the machine learning to obtain the set of weights is performed by:

initializing the set of weights, each of which is to be associated with a respective one of the plurality of basis functions;

accessing numerical feature values of the numerical feature from the training data;

with respect to each of the numerical feature values,

generating an approximated numerical feature value based on a weighted sum of basis function values, each of which is weighed using a corresponding one of the set of weights and computed using a corresponding one of the plurality of basis functions based on a transformed numerical feature value associated with the numerical feature value,

adjusting the set of weights based on the numerical feature value and the approximated numerical feature value.

20 . The system of claim 19 , wherein the step of generating the approximated numerical feature value comprises:

transforming the numerical feature value using the transform function to generate the transformed numerical feature value;

calculating the respective basis function values of the plurality of basis functions based on the transformed numerical feature value;

applying each of the set of weights to a corresponding one of the respective basis function values to generate a weighted basis function value;

computing the approximated numerical feature value based on a sum of the weighted basis function values.