Logarithmic loss minimization leads to well-behaved probabilistic outputs.

Hinge loss leads to some (not guaranteed) sparsity on the dual, but it doesn't help at probability estimation. Instead, it punishes misclassifications (that's why it's so useful to determine margins): diminishing hinge-loss comes with diminishing across margin misclassifications.

So, summarizing:

  • Logarithmic loss ideally leads to better probability estimation at the cost of not actually optimizing for accuracy

  • Hinge loss ideally leads to better accuracy and some sparsity at the cost of not actually estimating probabilities

In ideal scenarios, each respective method would excel in their domain (accuracy vs probability estimation). However, due to the No-Free-Lunch Theorem, it is not possible to know, a priori, if the model choice is optimal.

Answer from Firebug on Stack Exchange
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Quora
quora.com › What-is-the-advantage-disadvantage-of-Hinge-loss-compared-to-cross-entropy
What is the advantage/disadvantage of Hinge-loss compared to cross-entropy? - Quora
Answer (1 of 2): Cross Entropy (or Log Loss), Hing Loss (SVM Loss), Squared Loss etc. are different forms of Loss functions. Log Loss in the classification context gives Logistic Regression, while the Hinge Loss is Support Vector Machines. Logistic ...
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Medium
medium.com › @hatodi0945 › a-comparison-between-mse-cross-entropy-and-hinge-loss-4d4fe63cca12
A comparison between MSE, Cross Entropy, and Hinge Loss | by abc xyz | Medium
October 2, 2023 - The main difference between the hinge loss and the cross entropy loss is that the former arises from trying to maximize the margin between our decision boundary and data points — thus attempting to ensure that each point is correctly and ...
Discussions
machine learning - hinge loss vs logistic loss advantages and disadvantages/limitations - Cross Validated
12 Is there a Good Illustrative Example where the Hinge Loss (SVM) Gives a Higher Accuracy than the Logistic Loss · 3 Disadvantages of cross entropy loss comparing to SVM loss More on stats.stackexchange.com
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April 14, 2015
machine learning - softmax+cross entropy compared with square regularized hinge loss for CNNs - Cross Validated
SVM is actually a single layer ... with gradients. In addition, squared regularized hinge loss can be transformed into dual form to induce kernel and find the support vector. Compared with softmax+cross entropy, squared regularized hinge loss has better convergence and ... More on stats.stackexchange.com
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October 15, 2021
DailyML 28: MSE, Hinge Loss, and cross-entropy are all types of ___________.
To add a little more fun and learning, I think I'm going to try out giving awards to helpful/engaging comments on the DailyML a few times a week. Do we like the idea? More on reddit.com
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April 21, 2022
Why do we use log-loss in logistic regression instead of just taking the absolute difference between expected probability and actual value for each instance?
You can try it and see if it works🤷‍♂️ Absolute is usually avoided because makes a "V" shaped gradient. Sharp corners are bad in general for gradient based optimization. Same reason we use MSE or RMSE instead of absolute error for regression tasks. More on reddit.com
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April 26, 2023
Videos
03:15
🌐 YouTube
What Is Hinge Loss? - The Friendly Statistician - YouTube
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Perceptron Loss Function | Hinge Loss | Binary Cross Entropy | ...
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Week 4 Lecture 25 SVM - Hinge Loss Formulation - YouTube
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05:53
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Loss Functions and its types |Log Loss |Cross Entropy Loss |Hinge ...
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Hinge Loss, SVMs, and the Loss of Users - YouTube
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Hinge Loss for Binary Classifiers - YouTube
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Topcoder
topcoder.com › thrive › articles › Concepts of Loss Functions - What, Why and How
Concepts of Loss Functions - What, Why and How
Hinge loss is easier to compute than the cross-entropy loss. It is faster to train via gradient descent since a lot of the time the gradient is 0 so you don’t have to update the weights.
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Medium
medium.com › @noorfatimaafzalbutt › understanding-perceptron-loss-function-hinge-loss-binary-cross-entropy-and-the-sigmoid-function-bbb42d128ef6
Understanding Perceptron Loss Function, Hinge Loss, Binary Cross Entropy, and the Sigmoid Function | by Noor Fatima | Medium
July 24, 2024 - The realm of machine learning and neural networks is vast, and understanding foundational concepts is crucial for building robust models. In this article, we will explore four fundamental concepts: the Perceptron loss function, Hinge loss, Binary Cross Entropy, and the Sigmoid function.
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Baeldung
baeldung.com › home › artificial intelligence › machine learning › differences between hinge loss and logistic loss
Differences Between Hinge Loss and Logistic Loss | Baeldung on Computer Science
February 28, 2025 - Consequently, this makes the function less suitable for large-scale problems which require an algorithm that uses linear memory usage (e.g. LBFGS). Logistic loss (also known as the cross-entropy ...
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Rohanvarma
rohanvarma.me › Loss-Functions
Picking Loss Functions - A comparison between MSE, Cross Entropy, and Hinge Loss
The main difference between the hinge loss and the cross entropy loss is that the former arises from trying to maximize the margin between our decision boundary and data points - thus attempting to ensure that each point is correctly and confidently classified*, while the latter comes from ...
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Stack Exchange
stats.stackexchange.com › questions › 146277 › hinge-loss-vs-logistic-loss-advantages-and-disadvantages-limitations
machine learning - hinge loss vs logistic loss advantages and disadvantages/limitations - Cross Validated
Top answer
1 of 3
34

Logarithmic loss minimization leads to well-behaved probabilistic outputs.

Hinge loss leads to some (not guaranteed) sparsity on the dual, but it doesn't help at probability estimation. Instead, it punishes misclassifications (that's why it's so useful to determine margins): diminishing hinge-loss comes with diminishing across margin misclassifications.

So, summarizing:

  • Logarithmic loss ideally leads to better probability estimation at the cost of not actually optimizing for accuracy

  • Hinge loss ideally leads to better accuracy and some sparsity at the cost of not actually estimating probabilities

In ideal scenarios, each respective method would excel in their domain (accuracy vs probability estimation). However, due to the No-Free-Lunch Theorem, it is not possible to know, a priori, if the model choice is optimal.

2 of 3
6

@Firebug had a good answer (+1). In fact, I had a similar question here.

What are the impacts of choosing different loss functions in classification to approximate 0-1 loss

I just want to add more on another big advantages of logistic loss: probabilistic interpretation. An example, can be found in UCLA - Advanced Research - Statistical Methods and Data Analysis - Computing Logit Regression | R Data Analysis Examples

Specifically, logistic regression is a classical model in statistics literature. (See, What does the name "Logistic Regression" mean? for the naming.) There are many important concept related to logistic loss, such as maximize log likelihood estimation, likelihood ratio tests, as well as assumptions on binomial. Here are some related discussions.

Likelihood ratio test in R

Why isn't Logistic Regression called Logistic Classification?

Is there i.i.d. assumption on logistic regression?

Difference between logit and probit models

Find elsewhere
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Stack Exchange
stats.stackexchange.com › questions › 299876 › softmaxcross-entropy-compared-with-square-regularized-hinge-loss-for-cnns
machine learning - softmax+cross entropy compared with square regularized hinge loss for CNNs - Cross Validated
Top answer
1 of 1
2

Rohan Varma - Picking Loss Functions - A Comparison between MSE, Cross Entropy and Hinge Loss does an excellent job of working through the math and explanations from intuition and first principles. Take a peek.

tl;dr
Hinge stops penalizing errors after the result is "good enough," while cross entropy will penalize as long as the label and predicted distributions are not identical. The choice of cross-entropy entails that we aiming at the asymptote of perfection, not the threshold of "good enough."

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DataMonje
datamonje.com › a beginner’s guide to loss functions for classification algorithms
A Beginner's Guide to Loss functions for Classification Algorithms - DataMonje
November 18, 2022 - import numpy as np def ... values: [0 0 1 0 0] # Cross Entropy loss: 20.67 ... Hinge Loss is a specific loss function used by Support Vector Machines (SVM)....
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Milvus
milvus.io › ai-quick-reference › what-are-some-common-loss-functions
What are some common loss functions?
For regression tasks with outliers, ... sensitive to extreme values. Cross-entropy is ideal for probabilistic classification, while hinge loss suits models aiming for clear decision boundaries....
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Kaggle
kaggle.com › c › jigsaw-unintended-bias-in-toxicity-classification › discussion › 90793
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April 27, 2019 - Checking your browser before accessing www.kaggle.com · Click here if you are not automatically redirected after 5 seconds
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Kaggle
kaggle.com › code › viveknimsarkar › hands-on-guide-to-loss-functions
Hands-On Guide To Loss Functions
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Medium
medium.com › analytics-vidhya › overview-of-loss-functions-for-machine-learning-61829095fa8a
Overview of loss functions for Machine Learning | by Elizabeth Van Campen | Analytics Vidhya | Medium
February 18, 2021 - The activator used with this loss ... 0.5 is one class and below is the other. ... Hinge loss is used for Support Vector Machines and classifies with -1 and 1 rather than 0 and 1....
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ScienceDirect
sciencedirect.com › topics › engineering › hinge-loss-function
Hinge Loss Function - an overview | ScienceDirect Topics
Although the hinge loss function ... for example. The hinge loss encourages the network to maximize the margin around the decision boundary separating the two classes, which can lead to better generalization performance than using cross-entropy....
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Reddit
reddit.com › r/learnmachinelearning › dailyml 28: mse, hinge loss, and cross-entropy are all types of ___________.
r/learnmachinelearning on Reddit: DailyML 28: MSE, Hinge Loss, and cross-entropy are all types of ___________.
April 21, 2022 -

Yesterday's answer in the comments

Top answer
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To add a little more fun and learning, I think I'm going to try out giving awards to helpful/engaging comments on the DailyML a few times a week. Do we like the idea?
2 of 5
15
Imo cost functions aren't explored enough, at least on novice-intermediate level. Some custom loss functions, and exploration of cumulative cost functions via custom layers is def something to explore.
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CS231n
cs231n.github.io › linear-classify
CS231n Deep Learning for Computer Vision
Possibly confusing naming conventions. To be precise, the SVM classifier uses the hinge loss, or also sometimes called the max-margin loss. The Softmax classifier uses the cross-entropy loss.
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MachineLearningMastery
machinelearningmastery.com › home › blog › how to choose loss functions when training deep learning neural networks
How to Choose Loss Functions When Training Deep Learning Neural Networks - MachineLearningMastery.com
August 25, 2020 - Line Plots of Cross Entropy Loss and Classification Accuracy over Training Epochs on the Two Circles Binary Classification Problem · An alternative to cross-entropy for binary classification problems is the hinge loss function, primarily developed ...
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DataCamp
datacamp.com › tutorial › loss-function-in-machine-learning
Loss Functions in Machine Learning Explained | DataCamp
December 4, 2024 - Loss: This is a mathematical quantification of the margin/difference between the prediction of a machine learning algorithm and the actual target value. Entropy: A simple definition of entropy is that it is a calculation of the degree of randomness or disorder within a system · Cross Entropy: This is a term commonly utilised in information theory, and it measures the differences between two probability distributions that can be used to identify an observation.
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Wikipedia
en.wikipedia.org › wiki › Loss_functions_for_classification
Loss functions for classification - Wikipedia
January 12, 2026 - {\displaystyle p(1\mid x)\neq 0.5} , which matches that of the 0–1 indicator function. This conclusion makes the hinge loss quite attractive, as bounds can be placed on the difference between expected risk and the sign of hinge loss function.
Bayes consistencyProper loss functions, loss margin and regularizationSquare lossLogistic lossExponential lossSavage lossTangent lossHinge lossGeneralized smooth hinge loss
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Quora
quora.com › Why-do-people-prefer-Cross-Entropy-Loss-to-Hinge-Loss-in-classification-task
Why do people prefer Cross Entropy Loss to Hinge Loss in classification task? - Quora
Answer: I think, this derives heavily from the notion of the nature of classification labels to begin with. See, when you are talking about Hinge Loss - you are running Maximization of Information Metrics in terms of Vectorial dynamics, correct? Assuming, that you are accounting for the Hamming...
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