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{{alias}}( N[, options] )
Returns an accumulator function which incrementally performs binary
classification using stochastic gradient descent (SGD).
If provided a feature vector and response value, the accumulator function
updates a binary classification model and returns updated model
coefficients.
If not provided a feature vector and response value, the accumulator
function returns the current model coefficients.
Stochastic gradient descent is sensitive to the scaling of the features. One
is advised to either scale each feature to `[0,1]` or `[-1,1]` or to
transform the features into z-scores with zero mean and unit variance. One
should keep in mind that the same scaling has to be applied to training data
in order to obtain accurate predictions.
In general, the more data provided to an accumulator, the more reliable the
model predictions.
Parameters
----------
N: integer
Number of features.
options: Object (optional)
Function options.
options.intercept: boolean (optional)
Boolean indicating whether to include an intercept. Default: true.
options.lambda: number (optional)
Regularization parameter. Default: 1.0e-4.
options.learningRate: ArrayLike (optional)
Learning rate function and associated (optional) parameters. The first
array element specifies the learning rate function and must be one of
the following:
- ['constant', ...]: constant learning rate function. To set the
learning rate, provide a second array element. By default, when the
learn rate function is 'constant', the learning rate is set to 0.02.
- ['basic']: basic learning rate function according to the formula
`10/(10+t)` where `t` is the current iteration.
- ['invscaling', ...]: inverse scaling learning rate function according
to the formula `eta0/pow(t, power_t)` where `eta0` is the initial
learning rate and `power_t` is the exponent controlling how quickly the
learning rate decreases. To set the initial learning rate, provide a
second array element. By default, the initial learning rate is 0.02. To
set the exponent, provide a third array element. By default, the
exponent is 0.5.
- ['pegasos']: Pegasos learning rate function according to the formula
`1/(lambda*t)` where `t` is the current iteration and `lambda` is the
regularization parameter.
Default: ['basic'].
options.loss: string (optional)
Loss function. Must be one of the following:
- hinge: hinge loss function. Corresponds to a soft-margin linear
Support Vector Machine (SVM), which can handle non-linearly separable
data.
- log: logistic loss function. Corresponds to Logistic Regression.
- modifiedHuber: Huber loss function variant for classification.
- perceptron: hinge loss function without a margin. Corresponds to the
original Perceptron by Rosenblatt.
- squaredHinge: squared hinge loss function SVM (L2-SVM).
Default: 'log'.
Returns
-------
acc: Function
Accumulator function.
acc.predict: Function
Predicts response values for one ore more observation vectors. Provide a
second argument to specify the prediction type. Must be one of the
following: 'label', 'probability', or 'linear'. Default: 'label'.
Note that the probability prediction type is only compatible with 'log'
and 'modifiedHuber' loss functions.
Examples
--------
// Create an accumulator:
> var opts = {};
> opts.intercept = true;
> opts.lambda = 1.0e-5;
> var acc = {{alias}}( 3, opts );
// Update the model:
> var buf = new {{alias:@stdlib/array/float64}}( [ 2.3, 1.0, 5.0 ] );
> var x = {{alias:@stdlib/ndarray/array}}( buf );
> var coefs = acc( x, 1 )
<ndarray>
// Create a new observation vector:
> buf = new {{alias:@stdlib/array/float64}}( [ 2.3, 5.3, 8.6 ] );
> x = {{alias:@stdlib/ndarray/array}}( buf );
// Predict the response value:
> var yhat = acc.predict( x )
<ndarray>
See Also
--------
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