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This Julia package provides a collection of predictors and loss functions, mainly to support the implementation of (regularized) empirical risk minimization methods.
Test Status:
Currently, the following higher-level packages are depending on EmpiricalRisks:
Regression: solving moderate-size problem using conventional optimization techniques.
SGDOptim: solving large-scale problem using stochastic gradient descent or its variants.
Overview
This package provides basic components for implementing regularized empirical risk minimization:
Prediction modelsu = f(x; θ)
linear prediction
affine prediction
multivariate linear prediction
multivariate affine prediction
Loss functionsloss(u, y)
squared loss
absolute loss
quantile loss
huber loss
hinge loss
squared hinge loss
smoothed hinge loss
logistic loss
sum squared loss (for multivariate prediction)
multinomial logistic loss
Notes:
For each loss function, we provide methods to compute the loss value, the derivative/gradient, or both (at the same time).
For each (consistent) combination of loss function and prediction model (which together are referred to as a risk model), we provide methods to compute the total risk and the gradient w.r.t. the parameter.
Regularizers
squared L2
L1
elastic net (L1 + squared L2)
Notes:
For each regularizer, we provide methods to evaluate the regularization value, the gradient, and the proximal operator.
Remarks: All functions in this package are carefully optimized and tested.