Julia package of loss functions for machine learning.
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October 2015


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

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Available Losses

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

Please consult the documentation for other losses.


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

This package provides a considerable amount of carefully implemented loss functions, as well as an API to query their properties (e.g. convexity). Furthermore, we expose methods to compute their values, derivatives, and second derivatives for single observations as well as arbitrarily sized arrays of observations. In the case of arrays a user additionally has the ability to define if and how element-wise results are averaged or summed over.


Check out the latest documentation

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

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


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

] add LossFunctions


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