Minimize a function over an interval:

Use the resulting BayesianMinimizationObject[…] to get the estimated minimum configuration:

Get the estimated minimum function value:

Minimize a function over a set of configurations:

Get the minimum configuration over the set:

Minimize a function over a domain defined by a random generator:

Get the estimated minimum value:

Minimize a function over a region:

Get the list of available properties to query:

Get the history of evaluations:

Get information about the method used to determine the configurations to explore:

Get the current probabilistic model of the function (this is a PredictorFunction):

Find the best configuration to explore if the minimization were continued:

Find a list of properties simultaneously:

Visualize how well the function is modeled, particularly near the minimum:

Minimize a function with initial configurations over a domain defined by a random neighborhood configuration generator:

Get the model of the function:

Visualize the model's performance near the minimum:

Define a function that takes an image and computes the negative probability returned by ImageIdentify of identifying the image as the entity , with the domain defined by a random generator over a corpus of images:

Minimize the function above:

Get the minimum configuration:

Get the evaluation history:

Define a training set to train predictor functions using the Predict function and a test set to measure their performance:

Create a "loss" function to test the performance of different methods in Predict:

Minimize the loss function over a domain defined by a list of different methods for Predict:

Examine the evaluation history:

Find the best configuration to explore next:

Load Fisher's Iris dataset and divide it into a training set and a validation set:

Create "blackbox" functions. Here the functions are the loss (negative log-likelihood) functions for two different methods used in the Classify function. The arguments of the functions are known as hyperparameters.

Train a logistic regression classifier with two hyperparameters, the L1 and L2 regularization coefficients:

Minimize the loss function for the logistic regression classifier over a domain defined by a rectangular region in the logarithm of the hyperparameters:

Get the model of the function:

Visualize the model of the loss function of the classifier together with the estimated minimum:

Now train a support vector machine (SVM) classifier with two hyperparameters, the soft margin parameter and the gamma scaling parameter:

Minimize the loss function for the SVM classifier over a domain defined by a rectangular region in the logarithm of the hyperparameters:

Get the model of the function:

Visualize the model of the loss function together with the estimated minimum:

When the domain of the objective function is defined by an initial configuration set and a neighborhood configuration generator, the results depend on the quality of the generator provided.

Minimize a function where the domain is defined as above:

Get the model of the function:

Since the starting initial configurations are "far" from the global minimum and the generator takes relatively small steps, the algorithm could converge to a local minimum:

If the neighborhood configuration generator takes steps that are "too large" or "too small", this could lead to problems:

In this case, at each step the generator gives a configuration value that is square of the previous one, so the values quickly become extremely large and the probabilistic model does not work properly.