🐛Logistic Regression & Regularization for Smarter Predictions🐛
Logistic regression is a cornerstone of statistical modeling and machine learning when dealing with binary classification problems. It bridges between simple linear regression and modern classification techniques to provide a way to predict probabilities and make decisions based on binary outcomes.
🐜The Basics
Logistic regression uses a logistic function, sigmoid curve, to model binary outcomes like is a tumor malignant/benign. While linear regression can predict values outside the range of 0 to 1, logistic regression maps predictions to probabilities, ideal for binary classification.Logit Transformation converts probabilities into a linear scale using the log-odds.Maximum Likelihood Estimation or MLE gets the parameters that maximize the likelihood of observed data. Accuracy, confusion matrices, and ROC curves help evaluate model effectiveness.
🍃The Overfitting Dilemma
With datasets with numerous features, overfitting is a challenge. Gene expression data having more predictors than samples may lead to a model that fits the training data but performs poorly on new data.
Markers of Overfitting are high training accuracy (100%) but poor test accuracy, and poor generalization on new data.
🌞Regularization: A Cure for Overfitting
Regularization techniques introduce a bias to the model, limiting its flexibility and improving generalization. By modifying the loss function with a penalty term, regularization helps prevent overfitting.
🌻Ridge Regression (L2 Regularization)
Adds a penalty proportional to the square of the coefficients. It shrinks coefficients but retains all predictors. Ideal for multicollinearity. Ensures no coefficients are zero.
🌹Lasso Regression (L1 Regularization)
Adds a penalty proportional to the absolute value of the coefficients. It can shrink some coefficients to zero, effectively performing feature selection. Useful when you need a sparse model.
💐Elastic Net Regularization
combines L1 and L2 penalties to balance feature selection and multicollinearity handling.
Implement with caret and glmnet packages from R or scikit-learn from Python.