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

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.

This package provides basic components for implementing regularized empirical risk minimization:

**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.

Here is the Detailed Documentation.

04/16/2015

4 months ago

83 commits