Elaborate on techniques that can be applied to detect and mitigate overfitting and underfitting in a machine learning model.

Overfitting and underfitting are two common challenges in machine learning that impact a model's ability to generalize to new data. Overfitting occurs when a model learns the training data too well, capturing noise and random variations rather than the underlying patterns. This results in a model that performs excellently on the training data but poorly on unseen data. Underfitting, on the other hand, happens when a model fails to capture the underlying patterns in the training data, resulting in poor performance on both the training and the unseen data. It essentially is too simple for the underlying complexity of the data. Here are techniques that can be used to detect and mitigate both overfitting and underfitting:

Detecting Overfitting:
1. Performance Discrepancy: The most common way to detect overfitting is to see the difference in performance between the training set and the validation set. If a model performs very well on the training data but poorly on the validation or test set, this is a strong indication of overfitting. For example, in a regression problem, if the model achieves very low RMSE on the training set but much higher RMSE on the test set, overfitting has likely occurred. Similarly, in a classification problem, a model might achieve an accuracy of 99% on the training set, but only 70% on the test set, showing the same pattern.
2. Learning Curves: Learning curves are plots that show how the training and validation performance metrics change as the training set size increases. With overfitting, the training performance remains high while the validation performance plateaus or even declines as the training size increases. The gap between the curves would also show the level of overfitting, with larger gaps indicating more overfitting. On the other hand, with underfitting the training and validation curves both plateau at a low performance level.
3. Model Complexity: Overfitted models are often overly complex, having too many parameters for the amount of data available, this usually leads to overfitting. For instance, a deep neural network with many layers may overfit on a small dataset due to its high complexity, whereas a simple linear regression might underfit on the same data set, because it is too simple.
4. High Variance: Overfitting is also associated with high variance, meaning the model is highly sensitive to small changes in the training data. This can be assessed using cross-validation where the scores between folds will have high variance. If performance differs significantly across different validation folds, it could be an indication of high variance and overfitting.

Mitigating Overfitting:

1. Simplify the Model: Reduce the model complexity to reduce overfitting, which can be done by using simpler algorithms, reducing the number of layers in neural networks, or reducing the degree of a polynomial in regression. For instance, when using a decision tree model, the maximum depth of the tree can be reduced. If there is a model that uses too many features, the number of features can be reduced using feature selection techniques.
2. Regularization: Regularization techniques add a penalty term to the model's loss function to discourage complex models. L1 and L2 regularization are common, where L1 shrinks some coefficients to zero (feature selection) and L2 shrinks all coefficients to smaller values. In a logistic regression model, adding an L1 penalty can reduce the number of features by setting some coefficient values to zero.
3. Cross-Validation: Use cross-validation to train and evaluate the model and find better models, this is crucial for detecting and preventing overfitting. If there is significant overfitting, cross-validation will show the high variance in model performances across the folds. Use k-fold cross-validation to evaluate the model performance by training and testing on different folds and to fine tune parameters for better results.
4. Data Augmentation: Augment the training data by artificially creating new training samples based on existing data. This can be achieved by adding noise, rotating, cropping, or flipping images in image processing or by resampling or jittering time series data. Data augmentation can help the model learn more robust features by generalizing across several different versions of the data.
5. Early Stopping: Monitor the model’s performance during the training process, stop the training process early if there is no more improvement on the validation dataset to prevent overfitting. For example, when training neural networks, monitor the validation loss and stop training when the validation loss starts to increase, even if the training loss is still decreasing.
6. Feature Selection: Select only the most relevant features and remove the others that add noise to the training. Feature selection techniques can reduce model complexity by reducing the number of inputs, and this will reduce the chance of the model overfitting the data.

Detecting Underfitting:

1. Low Performance: If the model performs poorly on both the training and the test data, this suggests underfitting. For example, in a regression problem, if a model has a high mean absolute error on both the training and validation sets, this implies that it is unable to capture the relationship between the input features and the output.
2. Learning Curves: In underfitting, both the training and the validation learning curves converge at low performance. The performance stays low even with increased training sizes. This implies that the model is unable to learn from any of the data, even with more training samples.
3. Model Simplicity: Underfitting occurs when a model is too simplistic for the underlying complexity of the data. For example, using linear regression to model a non-linear relationship between data points can cause underfitting. In the same way, a shallow neural network with only a few neurons may be too simple for a very complex dataset.
4. High Bias: Underfitting is associated with high bias, which means that the model has made strong assumptions about the data that are not correct, which results in poor model performance on the dataset. A model with high bias will not perform well on any subset of data, because the simplifying assumptions have prevented it from learning from the data, even if there is a pattern.

Mitigating Underfitting:
1. Model Complexity: Increase the model complexity to improve its ability to capture the underlying patterns in the training data. For decision trees, this might mean increasing the depth of the tree, for neural networks, adding more layers or neurons per layer might increase the complexity. Use a more complex model that better captures underlying features of the data, and thus reduces underfitting.
2. Feature Engineering: Create additional features using techniques such as interaction terms, polynomial features, or other transformations to capture more complex patterns in the data. More advanced feature engineering techniques might be necessary to extract features that can reduce underfitting.
3. More Training Data: Provide more training data, because a model underfits often when not enough data is used in training. More data allows models to better learn the underlying patterns, reducing bias and allowing the model to fit more accurately to the underlying distribution of the data.
4. Reduce Regularization: If regularization techniques are used, reducing or removing them can help a model to learn more complex patterns. Regularization, while helping with overfitting, can prevent a model from learning more complex patterns if the regularization is too strong, leading to underfitting.
5. Increase Training Time: Train a model for a longer period to allow it to learn more effectively, although this must be used cautiously, as too long training might lead to overfitting. Increasing the number of epochs can help to reduce underfitting if the model hasn't yet converged to the optimal solution.

In summary, effectively addressing overfitting and underfitting requires careful analysis of the model's performance, the data, and the learning process. It is also important to iterate on these techniques, and change or apply the techniques as necessary until the models perform as expected. The goal is to achieve a balance, where the model can generalize effectively to new data, while not overfitting or underfitting.