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EmpiricalRisks

Julia implementation of predictors and loss functions for empirical risk minimization

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EmpiricalRisks

This Julia package provides a collection of predictors and loss functions, mainly to support the implementation of (regularized) empirical risk minimization methods.

Test Status: Build Status EmpiricalRisks EmpiricalRisks

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:

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  • Prediction models u = f(x; θ)

    • [x] linear prediction
    • [x] affine prediction
    • [x] multivariate linear prediction
    • [x] multivariate affine prediction
  • Loss functions loss(u, y)

    • [x] squared loss
    • [x] absolute loss
    • [x] quantile loss
    • [x] huber loss
    • [x] hinge loss
    • [x] squared hinge loss
    • [x] smoothed hinge loss
    • [x] logistic loss
    • [x] sum squared loss (for multivariate prediction)
    • [x] 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
  • [x] squared L2

  • [x] L1

  • [x] 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.

Documentation

Here is the Detailed Documentation.

First Commit

04/16/2015

Last Touched

4 months ago

Commits

83 commits

Requires:

Used By: