Understanding Logistic Regression In Machine Learning

This article details a basic concept of the Logistic Regression algorithm in Machine Learning and will cover the following.

  1. What is Logistic Regression?
  2. When to Use Logistic Regression?
  3. High-level steps to create a Logistic Regression Model
  4. Common Challenges in Logistic Regression

What is Logistic Regression?

Logistic Regression is a statistical method used for binary classification problems, where the outcome variable is categorical and has two classes.

The main objective behind Logistic Regression is to determine the relationship between features and the probability of an outcome.

We can solve classification problem statements which is a supervised machine learning technique using Logistic Regression.

For example, to predict whether an email is spam (1) or (0)

Logistic regression

The logistic regression model uses the logistic function, also known as the sigmoid function, to transform a linear combination of input features into a value between 0 and 1.

sigmoid function

The primary reason for utilizing the sigmoid function is its confinement to the range between 0 and 1. Consequently, it is particularly applicable in models where the objective is to forecast probability as an outcome. Given that probabilities only exist within the 0 to 1 range, the sigmoid function is a fitting choice. That is the basic idea of using the Sigmoid function in Logistic regression.

There are other key aspects of Logistic Regression.

Maximum Likelihood Estimation: The logistic regression model is trained by maximizing the likelihood function, which estimates the probability of observing the given set of outcomes. In other words, it finds the parameter values that make the observed data most probable.

Decision Boundary: Logistic Regression produces a decision boundary that separates the two classes in feature space. This boundary is determined by the weights assigned to each feature.

In logistic regression, the log(odds) of an outcome (say, defaulting on a credit card) is linearly related to the attributes x1, x2, etc.

log(odds of default)=β0+β1X1+β2X2+...βnXn

When to Use Logistic Regression?

Use logistic regression when the dependent or target variable is binary or categorical, and you aim to predict the probability of a specific input point belonging to a particular class. Consider logistic regression in the following situations:

  1. Binary Results: Logistic regression is the preferred approach for addressing binary classification challenges, including tasks like identifying spam, predicting customer churn, and diagnosing diseases.
  2. Estimating Probabilities: If you require quantifying the likelihood or risk of a specific event occurring based on the log odds.
  3. Understanding Impact: When seeking to comprehend the influence of multiple independent variables on a singular outcome variable.
  4. Non-Linear Boundaries: Logistic regression can handle non-linear effects as it doesn’t presume a linear association between the independent and dependent variables.

Here are some examples of problems for which Logistic Regression is well-suited.

  • Spam Email Detection
  • Credit Scoring
  • Customer Churn Prediction
  • Binary Image Classification
  • Fraud Detection

High-level steps to create a Logistic Regression Model

1. Importing the required libraries and reading the dataset.

2. Inspecting and cleaning up the data: Explore and analyze your data to understand the relationships between variables, identify patterns, and check for any outliers or anomalies.

3. Perform data encoding on categorical variables

4. Exploratory Data Analysis (EDA)

  • Data Visualization

5. Feature Engineering: Dropping of unwanted columns

6. Model Building

  • Performing train test split: Divide your dataset into two subsets: one for training the model and another for testing the model's performance. Common split ratios are 80/20 or 70/30, with the larger portion used for training.
  • Logistic Regression Model: Train the logistic regression model on the training dataset. The logistic regression model estimates the probability of the dependent variable belonging to a particular class based on the independent variables.

8. Model Validation (predictions): Evaluate the model's performance on the test dataset using appropriate metrics such as

  • Accuracy score
  • Confusion matrix
  • ROC and AUC
  • Recall score
  • Precision score
  • F1-score

9. Handling the unbalanced data

  • With balanced weights
  • Random weights
  • Adjusting imbalanced data
  • Using SMOTE

10. Feature Selection: Choose the relevant features (independent variables) that are likely to have an impact on the dependent variable. Feature selection can help improve the model's performance and reduce overfitting.

  • Barrier threshold selection
  • RFE method

Please refer to the sample reference Python Notebook for the implementation of Logistic Regression here.

Common Challenges in Logistic Regression

Here are some common challenges associated with Logistic Regression.

Challenges The issue Mitigation plan
class Imbalance When the classes in the target variable are imbalanced (one class significantly outnumbers the other), the model may be biased towards the majority class. Use techniques like oversampling, undersampling, or generating synthetic samples to balance the classes. Adjust class weights during model training.
Overfitting Logistic Regression models can be prone to overfitting, especially when the number of features is large compared to the number of observations. Regularization techniques, such as L1 or L2 regularization like Lasso and Ridge Regression, can be applied to penalize large coefficients and prevent overfitting.
Multicollinearity Logistic Regression assumes independence of features, and multicollinearity (high correlation between independent variables) can lead to unstable coefficient estimates. Identify and address multicollinearity by removing highly correlated variables or using dimensionality reduction techniques.
Assumption of Linearity Logistic Regression assumes a linear relationship between the independent variables and the log odds. If the true relationship is non-linear, Logistic Regression may not accurately capture the underlying patterns in the data. Consider adding interaction terms, and polynomial features, or using more complex models if non-linear relationships are significant.
Outliers Outliers in the dataset can disproportionately influence the model's coefficients and predictions. Identify and handle outliers appropriately, either by transforming the data or using robust regression techniques.
Inadequate Sample Size Logistic Regression performs better with a larger sample size, and inadequate data can lead to unreliable estimates. Ensure a sufficiently large sample size to obtain reliable parameter estimates and reduce the risk of overfitting.
Categorical Variable Encoding Logistic Regression requires categorical variables to be encoded properly, and inappropriate encoding can introduce bias. Use appropriate encoding methods, such as one-hot encoding, and handle categorical variables carefully to avoid biased results.

Happy Learning!

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