Reducing Overfitting in Logistic Regression

What

Overfitting occurs when the model fits the training data too closely, to the point that it captures noise and random fluctuations in data rather than the underlying patterns. This can lead to poor generalization performance on new, unseen data.

When Overfitting occurs

Overfitting can occur when

1. The model is too complex for the size of the dataset, it can fit the training data too closely and fail to generalize to new data.
2. When the model includes so many irrelevant or redundant features, it can become too flexible and fit the noise in the data rather than the underlying patterns.

Detection

Overfitting can be detected by evaluating the performance of the model on a held-out test set. If the model performs well on the training set but poorly on the test set, it's a sign that the model is overfitting to the training data.

Ways of Reducing Overfitting

1. Simplifyng the model through various techniques:
   1. Regularization techniques which add a penalty term to the logistic regression objective function and thus discouraging large weights that can lead to overfitting. By tuning the strength of the regularization parameter, you can find the optimal set of features that balances the tradeoff between fitting the training data well and not overfitting to noise in the data.
      1. L1 regularization - adds a penalty term proportional to the absolute value of the weights
      2. L2 regularization - adds a penalty term proportional to the square of the weights
2. Reducing features - using feature selection techniques that aim to identify a subset of relevant features for the model while discarding irrelevant or redundant features
   1. Forward selection - starts with an empty set of features and iteratively adds the most significant feature, as determined by a statistical test or some other criterion until a stopping criterion is met
   2. Backward elimination - starts with the full set of features and iteratively removes the least significant feature, as determined by a statistical test or some other criterion, until a stopping criterion is met.
   3. Recursive feature elimination - recursively removes the least significant feature, as determined by a statistical test or some other criterion, until a stopping criterion is met. This is often used in conjunction with cross-validation to find the optimal number of features.

Other Techniques

There are other techniques that can help reduce overfitting and these are:

1. Cross-validation - This is a technique that helps to estimate the generalization performance of a model. It involves partitioning the data into training and validation sets and evaluating the model on the validation set. This process is repeated multiple times, with different partitions of the data, and the results are averaged. Cross-validation can help to prevent overfitting by providing an estimate of how well the model will perform on new, unseen data.
2. Early stopping - is a technique that stops the training process of the logistic regression model before it overfits to the training data. This is typically achieved by monitoring the performance of the model on a validation set during training and stopping the training process when the performance on the validation set starts to degrade.
3. Dropout - is a regularization technique that randomly drops out a fraction of the features during training. This helps to prevent the model from relying too heavily on any one feature and encourages the model to learn more robust representations of the data. 
4. Data augmentation - is a technique that artificially increases the size of the training data by generating new examples from the existing data. This can help to reduce overfitting by providing the model with more diverse examples to learn from.
5. Ensemble methods - this involves combining multiple models to create a single, more powerful model. One example is the random forest , which uses a collection of decision trees to make predictions. They can help to reduce overfitting by averaging out the predictions of multiple models.
6. Feature Engineering - this involves creating new features from the existing data that can help the model better capture the underlying patterns in the data. For example, if you are working with text data, you might create new features based on the frequency of certain words or the length of the text. Feature engineering can be a powerful way to improve the performance of the logistic regression model, but it can also be time-consuming and requires domain expertise.
7. Dimensionality reduction - examples such as principle component analysis (PCA) and singular value decomposition (SVD) , can be used to reduce the number of features in the data while preserving the most important information. This can help to reduce overfitting by simplifying the model and reducing the risk of overfitting to noise in the data.
8. Bayesian methods - this involves placing priors on the model parameters, which can help to regularize the model and prevent overfitting. Bayesian logistic regression models can be trained using techniques such as Markov Chains Monte Carlo (MCMC) or variational inference.
9. Batch normalization - is a technique that normalizes the input to each layer of the model which can help to reduce overfitting. Normalizing the input helps to ensure that the activations in each layer are centered around zero and have a similar scale, which can help to prevent the model from becoming too sensitive to the magnitude of the input features.
10. Data preprocessing techniques - Data preprocessing techniques, such as scaling or normalization of the input features, can help to reduce the risk of overfitting by ensuring that the input features have similar scales and distributions.

Practical Notebooks

• Students enrolling for any AI related course from Carnegie Training Institute have access to jupyter notebook, class exercises illustrating this reasoning.

Sources