LossFunctions

LossFunctions.jl is a Julia package that provides efficient andwell-tested implementations for a diverse set of loss functionsthat are commonly used in Machine Learning.

Available Losses

Distance-based (Regression)	Margin-based (Classification)

Please consult the documentationfor other losses.

Introduction

Typically, the loss functions we work with in Machine Learningfall into the category of supervised losses. These aremultivariate functions of two variables, the true target y,which represents the "ground truth" (i.e. correct answer), andthe predicted output ŷ, which is what our model thinks thetruth is. A supervised loss function takes these two variables asinput and returns a value that quantifies how "bad" ourprediction is in comparison to the truth. In other words: thelower the loss, the better the prediction.

This package provides a considerable amount of carefullyimplemented loss functions, as well as an API to query theirproperties (e.g. convexity). Furthermore, we expose methods tocompute their values, derivatives, and second derivatives forsingle observations as well as arbitrarily sized arrays ofobservations. In the case of arrays a user additionally has theability to define if and how element-wise results are averaged orsummed over.

Documentation

Check out the latest documentation

Additionally, you can make use of Julia's native docsystem.The following example shows how to get additional informationon HingeLoss within Julia's REPL:

?HingeLoss

search: HingeLoss L2HingeLoss L1HingeLoss SmoothedL1HingeLoss

  L1HingeLoss <: MarginLoss

  The hinge loss linearly penalizes every predicition where the
  resulting agreement a = y⋅ŷ < 1 . It is Lipschitz continuous
  and convex, but not strictly convex.

  L(a) = \max \{ 0, 1 - a \}

  --------------------------------------------------------------------

                Lossfunction                     Derivative
        ┌────────────┬────────────┐      ┌────────────┬────────────┐
      3 │'\.                      │    0 │                  ┌------│
        │  ''_                    │      │                  |      │
        │     \.                  │      │                  |      │
        │       '.                │      │                  |      │
      L │         ''_             │   L' │                  |      │
        │            \.           │      │                  |      │
        │              '.         │      │                  |      │
      0 │                ''_______│   -1 │------------------┘      │
        └────────────┴────────────┘      └────────────┴────────────┘
        -2                        2      -2                        2
                   y ⋅ ŷ                            y ⋅ ŷ

Installation

Get the latest stable release with Julia's package manager:

] add LossFunctions

License

This code is free to use under the terms of the MIT license.