Logistic Regression: Formulation
📰 Dev.to · Ethan Davis
Learn the formulation of logistic regression and its application in machine learning, including expressiveness delineation and model specification.
Action Steps
- Understand the logistic regression model and its desire to model posterior probabilities of classes via linear function in x
- Apply the log-odds or logit transformations to ensure probabilities sum to one and remain in [0,1]
- Specify the model in terms of K-1 log-odds or logit transformations, reflecting the constraint that probabilities sum to one
- Use the last class as the denominator in the odds-ratios, noting that the choice of denominator is arbitrary
- Implement logistic regression using a library such as scikit-learn in Python, using the LogisticRegression class and its methods
Who Needs to Know This
Data scientists and machine learning engineers can benefit from understanding logistic regression formulation to improve their models and predictions.
Key Insight
💡 Logistic regression models posterior probabilities of classes via linear function in x, using log-odds or logit transformations to ensure probabilities sum to one and remain in [0,1].
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📊 Learn logistic regression formulation and improve your machine learning models! 🚀
Key Takeaways
Learn the formulation of logistic regression and its application in machine learning, including expressiveness delineation and model specification.
Full Article
Title: Logistic Regression: Formulation
URL Source: https://dev.to/davisethan/logistic-regression-formulation-25af
Published Time: 2026-07-11T15:57:00Z
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[Ethan Davis](https://dev.to/davisethan)
Posted on Jul 11
# Logistic Regression: Formulation
[#machinelearning](https://dev.to/t/machinelearning)[#datascience](https://dev.to/t/datascience)[#statistics](https://dev.to/t/statistics)[#tutorial](https://dev.to/t/tutorial)
> _Adapted from an appendix of my MS thesis._
# [](https://dev.to/davisethan/logistic-regression-formulation-25af#logistic-regression) Logistic Regression
## [](https://dev.to/davisethan/logistic-regression-formulation-25af#expressiveness-delineation) Expressiveness Delineation
The logistic regression model arises from the desire to model the posterior probabilities of $K$K classes via linear function in $x$x , while at the same time ensuring that they sum to one and remain in $\left[\right. 0 , 1 \left]\right.$[0,1] . The model has the following form. It is specified in terms of $K - 1$K−1 log-odds or logit transformations, reflecting the constraint that the probabilities sum to one. Although the model uses the last class as the denominator in the odds-ratios, the choice of denominator is arbitrary in that the estimates are equivalent under this choice [1].
$$
log \frac{P \
URL Source: https://dev.to/davisethan/logistic-regression-formulation-25af
Published Time: 2026-07-11T15:57:00Z
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[Ethan Davis](https://dev.to/davisethan)
Posted on Jul 11
# Logistic Regression: Formulation
[#machinelearning](https://dev.to/t/machinelearning)[#datascience](https://dev.to/t/datascience)[#statistics](https://dev.to/t/statistics)[#tutorial](https://dev.to/t/tutorial)
> _Adapted from an appendix of my MS thesis._
# [](https://dev.to/davisethan/logistic-regression-formulation-25af#logistic-regression) Logistic Regression
## [](https://dev.to/davisethan/logistic-regression-formulation-25af#expressiveness-delineation) Expressiveness Delineation
The logistic regression model arises from the desire to model the posterior probabilities of $K$K classes via linear function in $x$x , while at the same time ensuring that they sum to one and remain in $\left[\right. 0 , 1 \left]\right.$[0,1] . The model has the following form. It is specified in terms of $K - 1$K−1 log-odds or logit transformations, reflecting the constraint that the probabilities sum to one. Although the model uses the last class as the denominator in the odds-ratios, the choice of denominator is arbitrary in that the estimates are equivalent under this choice [1].
$$
log \frac{P \
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