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Logistic Regression From Scratch Your First Step Into Ml

Leo Migdal
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logistic regression from scratch your first step into ml

Logistic regression is a statistical method used for binary classification tasks where we need to categorize data into one of two classes. The algorithm differs in its approach as it uses curved S-shaped function (sigmoid function) for plotting any real-valued input to a value between 0 and 1. To understand it better we will implement logistic regression from scratch in this article. We will import required libraries from python: We define a class LogisticRegressionScratch that implements logistic regression using gradient descent. We’ll generate a random dataset and standardize it:

📬 Receive new lessons straight to your inbox (once a month) and join 40K+ developers in learning how to responsibly deliver value with ML. Logistic regression is an extension on linear regression (both are generalized linear methods). We will still learn to model a line (plane) that models \(y\) given \(X\). Except now we are dealing with classification problems as opposed to regression problems so we'll be predicting probability distributions as opposed to discrete values. We'll be using the softmax operation to normalize our logits (\(XW\)) to derive probabilities. Our goal is to learn a logistic model \(\hat{y}\) that models \(y\) given \(X\).

(*) bias term (\(b\)) excluded to avoid crowding the notations This function is known as the multinomial logistic regression or the softmax classifier. The softmax classifier will use the linear equation (\(z=XW\)) and normalize it (using the softmax function) to produce the probability for class y given the inputs. Understanding machine learning algorithms at their core is crucial for any data scientist. In this comprehensive tutorial, we’ll build logistic regression entirely from scratch using Python and NumPy. No black-box libraries, just the math implemented in code.

We’ll use everything from the sigmoid function and cross-entropy loss to gradient descent optimization. Finally, we’ll test our implementation on the classic “moons” dataset to validate our approach. Logistic regression transforms linear combinations of features into probabilities using the sigmoid function: Model: z = w^T x + b Prediction: ŷ = σ(z) = 1 / (1 + e^(-z)) Loss: L = -[y log(ŷ) + (1-y) log(1-ŷ)] Our implementation follows a modular approach with separate functions for each mathematical component: July 7, 2025 · Machine Learning · 2 min read

Logistic Regression is a fundamental algorithm used for classification problems in machine learning. Unlike linear regression, which predicts continuous outcomes, logistic regression predicts categorical outcomes, often binary (0 or 1, Yes or No). Use logistic regression when you need to: Logistic regression uses the sigmoid function to convert the output of a linear equation into a probability between 0 and 1, which can then be mapped to classes. where z = w₀ + w₁x₁ + w₂x₂ + ... + wₙxₙ.

Logistic Regression is one of the most fundamental algorithms in machine learning, often serving as the first step into the world of classification problems. Despite its simplicity, it provides a strong foundation for understanding more complex models like neural networks. In this post, we’ll explore what Logistic Regression is, how it works, and how to implement it using PyTorch. We’ll also cover how to set up the project using Poetry and provide a link to the GitHub repository for you to try it out yourself! Logistic Regression is a statistical method used for binary classification. It predicts the probability that a given input belongs to a particular class (e.g., spam or not spam, fraud or not fraud).

Unlike linear regression, which predicts continuous values, Logistic Regression outputs probabilities between 0 and 1 using the sigmoid function. Sigmoid Function: The sigmoid function maps any real-valued number into the range [0, 1]. Formula: Failed to render LaTeX expression — no expression found Failed to render LaTeX expression — no expression found

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Logistic regression is a statistical method used for binary classification tasks where we need to categorize data into one of two classes. The algorithm differs in its approach as it uses curved S-shaped function (sigmoid function) for plotting any real-valued input to a value between 0 and 1. To understand it better we will implement logistic regression from scratch in this article. We will impor...

📬 Receive New Lessons Straight To Your Inbox (once A

📬 Receive new lessons straight to your inbox (once a month) and join 40K+ developers in learning how to responsibly deliver value with ML. Logistic regression is an extension on linear regression (both are generalized linear methods). We will still learn to model a line (plane) that models \(y\) given \(X\). Except now we are dealing with classification problems as opposed to regression problems ...

(*) Bias Term (\(b\)) Excluded To Avoid Crowding The Notations

(*) bias term (\(b\)) excluded to avoid crowding the notations This function is known as the multinomial logistic regression or the softmax classifier. The softmax classifier will use the linear equation (\(z=XW\)) and normalize it (using the softmax function) to produce the probability for class y given the inputs. Understanding machine learning algorithms at their core is crucial for any data sc...

We’ll Use Everything From The Sigmoid Function And Cross-entropy Loss

We’ll use everything from the sigmoid function and cross-entropy loss to gradient descent optimization. Finally, we’ll test our implementation on the classic “moons” dataset to validate our approach. Logistic regression transforms linear combinations of features into probabilities using the sigmoid function: Model: z = w^T x + b Prediction: ŷ = σ(z) = 1 / (1 + e^(-z)) Loss: L = -[y log(ŷ) + (1-y) ...

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Logistic Regression is a fundamental algorithm used for classification problems in machine learning. Unlike linear regression, which predicts continuous outcomes, logistic regression predicts categorical outcomes, often binary (0 or 1, Yes or No). Use logistic regression when you need to: Logistic regression uses the sigmoid function to convert the output of a linear equation into a probability be...