Contents

Objective function

Some classification algorithms are designed to minimize the selected objective function. On each iteration its’ gradient and sometimes hessian is calculated and model weights are updated using this information.

Operation

Computational methods

Programming Interface

dense_batch

dense_batch

compute(…)

compute_input

compute_result

Supported objective functions

Mathematical formulation

Computing

Algorithm takes dataset \(X = \{ x_1, \ldots, x_n \}\) with \(n\) feature vectors of dimension \(p\), vector with correct class labels \(y = \{ y_1, \ldots, y_n \}\) and coefficients vector w = { w_0, ldots, w_p }`of size :math:`p + 1 as input. Then it calculates logistic loss, its gradient or hessian.

Value

\(L(X, w, y)\) - value of objective function.

Gradient

\(\overline{grad} = \frac{\partial L}{\partial w}\) - gradient of objective function.

Hessian

\(H = (h_{ij}) = \frac{\partial L}{\partial w \partial w}\) - hessian of objective function.

Computation method: dense_batch

The method computes value of objective function, its gradient or hessian for the dense data. This is the default and the only method supported.

Programming Interface

Refer to API Reference: Objective Function.

Distributed mode

Currently algorithm does not support distributed execution in SMPD mode.

Examples: Logistic Loss

Batch Processing:

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Logistic Loss