Bayesian Optimization, also known as Sequential Model-Based Optimization (SMBO), is a probabilistic search technique that is predominantly used to find the global maximum or minimum of an unknown objective function that is costly to evaluate. This algorithm is a robust and efficient approach to optimizing black-box functions with high-dimension, non-linear or non-convex optimization landscapes. Bayesian Optimization is a much sought-after technique, particularly in the field of Machine Learning (ML), when it comes to hyperparameter tuning.
Hyperparameters are model parameters that cannot be learned from the training data, and need to be set manually. These hyperparameters include learning rates, regularization coefficients, weight init. function, etc. The accurate selection of hyperparameters is a complex and time-consuming process since there may be several ways to impact the performance of machine learning models. And that is why Bayesian Optimization comes into the picture of hyperparameter tuning in Machine Learning.
In this article, we will cover the basics of Bayesian Optimization, the Bayesian Optimization process, its application in Machine Learning, and some examples to explore various Bayesian Optimization techniques.
Bayesian Optimization works by constructing a probability model, which describes how the objective function is estimated given the hyperparameters. The constructed model then guides the selection of hyperparameters for the objective function. The model is updated iteratively, by evaluating the objective function at promising hyperparameters at each iteration, until either the number of iterations allowed gets exhausted or the model can’t obtain any further improvement.
To be more precise, the Bayesian Optimization process can be summarized as:
Bayesian Optimization for Machine Learning is an iterative process used to find the optimal set of hyperparameters for a specific task. In ML, Bayesian Optimization has been applied for hyperparameter tuning in various models, including neural networks, Random Forests, Gradient Boosting, SVMs, etc.
Hyperparameter tuning is the process of trying out different hyperparameter settings in a machine learning model, to get the best possible results. In training machine learning models, sometimes subtle changes in hyperparameters lead to significant changes in the score. Traditional methods of hyperparameter optimization like random search, grid search, manual search, etc., cannot guarantee optimal results or prevent overfitting, and are hence wasteful and time-consuming. Bayesian Optimization, on the other hand, is much more effective when it comes to hyperparameter optimization.
Let’s take an example of hyperparameter tuning for a Support Vector Machine (SVM) model for the classification task. The SVM algorithm has several hyperparameters that need to be set, including kernel type, regularization parameter, and gamma. To find the best hyperparameters, we can use Bayesian Optimization processes as follows:
The above five steps form a complete Bayesian Optimization process applied to solve the hyperparameter tuning problem in SVMs. The process can be modified and applied to any other models as well.
Acquisition Functions are the functions that drive the Bayesian Optimization process by guiding the selection of the best set of hyperparameters. There are numerous types of Acquisition Functions available, but we will briefly discuss the most popular ones here: -
Below are a few examples of Bayesian Optimization in action for hyperparameter tuning in different ML models
Gradient Boosting: It is a popular ensemble-based ML method which relies on decision trees, and Bayesian Optimization can be used to identify the best set of hyperparameters for an effective Gradient Boosting model.
To identify the optimal parameters for Gradient Boosting, one can use Bayesian Optimization with the acquisition function chosen as Expected Improvement (EI), as follows:
Random Forests: Random Forest is a robust, tree-based ensemble ML method that has several hyperparameters, including the number of estimators, bootstrapping technique, criterion function, max depth, max features, bootstrap, etc. We can use Bayesian Optimization techniques to find the optimal set of hyperparameters for the Random Forest model.
To identify the optimal hyperparameters, one can use Bayesian Optimization with the acquisition function chosen as Expected Improvement (EI) as follows:
Bayesian Optimization has numerous advantages, including:
However, Bayesian Optimization has a few disadvantages which must be considered, including:
Bayesian Optimization is an efficient, model-based approach to optimizing complex objective functions with costly function evaluations. It is a much sought-after technique, particularly in the field of Machine Learning for hyperparameter tuning. The Bayesian Optimization process involves several steps, including defining a probability model and selecting a suitable acquisition function, and iterating the process until either the desired improvement is achieved or the maximum number of iterations is exceeded. There are several types of Acquisition Functions available, each with its strengths and weaknesses. Bayesian Optimization, like any other technique, has its advantages and drawbacks, but the benefits outweigh the shortcomings when used correctly. Remember, the faster we tune in hyperparameters, the faster we can iterate model improvement and achieve a better overall model performance.
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