Outliers in a training set can have various impacts on model training. Here are some ways outliers can affect the training process and the resulting model:

  1. Bias in model estimation: Outliers can significantly distort the model's estimated parameters. Most statistical learning algorithms aim to minimize the sum of squared errors or maximize the likelihood of the observed data. Outliers with extreme values can heavily influence these objectives, leading to biased parameter estimates.

  2. Incorrect relationship identification: Outliers may create the illusion of significant relationships between input features and the target variable. When a model is trained on a dataset containing outliers, it may assign them undue importance in determining the model's decision boundaries or regression coefficients. As a result, the model may generate incorrect relationships when applied to new data without outliers.

  3. Increased model complexity: Outliers can increase the complexity of the model needed to fit the training data accurately. In an attempt to capture the outliers, the model may become more complex by introducing additional parameters or decision rules. This can lead to overfitting, where the model becomes overly specialized to the training data and performs poorly on unseen data.

  4. Reduced generalization performance: The presence of outliers in the training set can degrade the model's ability to generalize. If outliers are rare and not representative of the underlying data distribution, the model may learn to overreact to similar but non-outlying points in the future. Consequently, its performance may suffer when faced with new data that does not contain outliers.

  5. Sensitivity to noisy data: Outliers are often considered as noise that hinders the learning process. Outliers can introduce significant variations in the observed data, leading to increased error rates and reduced robustness of the model. Training a model on data contaminated with outliers may result in poor performance and unreliable predictions.

  To mitigate the impact of outliers, it is essential to preprocess the training data by detecting and handling outliers appropriately. Various techniques such as winsorizing, trimming, or using robust estimators can be employed to minimize the influence of outliers during model training.