</> Code with Papers by Syntology

Methods › General › Loss Functions › Huber loss

Huber loss

77 papers tagged archive 2025-07-28

archive 2025-07-28 Description, source and code snippet are the archive's method entry.

The Huber loss function describes the penalty incurred by an estimation procedure f. Huber (1964) defines the loss function piecewise by[1]

L δ ( a ) = { 1 2 a 2 for  | a | ≤ δ , δ ⋅ ( | a | − 1 2 δ ) , otherwise. {\displaystyle L_{\delta }(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\\delta \cdot \left(|a|-{\frac {1}{2}}\delta \right),&{\text{otherwise.}}\end{cases}}}

This function is quadratic for small values of a, and linear for large values, with equal values and slopes of the different sections at the two points where | a | = δ |a|=\delta . The variable a often refers to the residuals, that is to the difference between the observed and predicted values a = y − f ( x ) a=y-f(x), so the former can be expanded to[2]

L δ ( y , f ( x ) ) = { 1 2 ( y − f ( x ) ) 2 for  | y − f ( x ) | ≤ δ , δ   ⋅ ( | y − f ( x ) | − 1 2 δ ) , otherwise. {\displaystyle L_{\delta }(y,f(x))={\begin{cases}{\frac {1}{2}}(y-f(x))^{2}&{\text{for }}|y-f(x)|\leq \delta ,\\\delta \ \cdot \left(|y-f(x)|-{\frac {1}{2}}\delta \right),&{\text{otherwise.}}\end{cases}}}

The Huber loss is the convolution of the absolute value function with the rectangular function, scaled and translated. Thus it "smoothens out" the former's corner at the origin.

.. math:: \ell(x, y) = L = {l_1, ..., l_N}^T

with

.. math::
    l_n = \begin{cases}
    0.5 (x_n - y_n)^2, & \text{if } |x_n - y_n| < delta \\
    delta * (|x_n - y_n| - 0.5 * delta), & \text{otherwise }
    \end{cases}

Papers archive 2025-07-28

30 shown of 77, newest first. Repository counts are the archive's code-links table. A Syntology line states what Syntology ran from that paper's harvested code; it is per sample and not a correctness claim.

Tasks archive 2025-07-28

20 shown of 71 tasks the archive attaches to papers tagged with this method, by distinct papers. A task without a page in the catalog is plain text.

TaskPapers
regression23
Matrix Completion5
quantile regression5
Reinforcement Learning (RL)4
Prediction3
Reinforcement Learning3
Vocal Bursts Intensity Prediction3
reinforcement-learning3
Clustering2
Deep Learning2
Dimensionality Reduction2
Distributional Reinforcement Learning2
General Classification2
Low-Rank Matrix Completion2
Multi-Task Learning2
Object2
Object Detection2
Q-Learning2
Time Series2
compressed sensing2

Usage over time archive 2025-07-28

Papers per year tagged with Huber loss: 2015 to 2025, peak 14 14 0 2015: 2 papers 2015 2016: 3 papers 2016 2017: 1 paper 2017 2018: 5 papers 2018 2019: 6 papers 2019 2020: 8 papers 2020 2021: 10 papers 2021 2022: 14 papers 2022 2023: 14 papers 2023 2024: 7 papers 2024 2025: 7 papers 2025
Papers per year the archive tags with this method, by the paper's archive date (77 dated). Bars are counts, not a trend claim.

Components: the archive holds no method-to-method composition, so PwC's Components table cannot be rebuilt; the Papers list carries no Results column for the same reason (the archive does not join its leaderboard rows to method tags).

Categories archive 2025-07-28

Loss Functions

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections