How to implement the bayesain optimization in NN model structured with back propagation algorithm?

I am working in predicting the weld ead geometry based on the input parameter. On input layer power, welding speed, stand off distance are considered and bead width, bead height and penetration depth wer given in output layer. Two hiden layer with 5 node in each hidden layer and trained using back propagation algorithm. I have no control on weight and bias. I have to optimize the weight and bias using bayesain optimizaqtion. how to incorparate bayesain optimization which could help to identify the optimum weight and bais for each layer.

Answer 1

[recent works]

Bayesian optimization is a technique for finding the optimal hyperparameters of a machine learning model. It works by constructing a probabilistic model of the hyperparameters and their relationship to the model's performance. This model is then used to select the next set of hyperparameters to try, in a way that maximizes the expected improvement in performance.

To incorporate Bayesian optimization into your neural network, you would first need to define a probabilistic model of the hyperparameters. This model could be a Gaussian process, a Bayesian neural network, or another type of probabilistic model.

Once you have defined the model, you can use it to select the next set of hyperparameters to try. You can do this by maximizing the expected improvement in performance, or by minimizing the expected regret.

The expected improvement is the expected difference in performance between the current model and the model with the best hyperparameters. The expected regret is the expected difference in performance between the current model and the best model that could have been found if you had known the optimal hyperparameters from the beginning.

You can use a Bayesian optimization library to automate the process of selecting hyperparameters. Some popular Bayesian optimization libraries include:

• GPyOpt
• Spearmint
• Optuna

These libraries provide a variety of features for defining probabilistic models, selecting hyperparameters, and evaluating model performance.

Here are the steps on how to incorporate Bayesian optimization into your neural network to identify the optimum weight and bias for each layer:

1. Define a probabilistic model of the hyperparameters.
2. Use the model to select the next set of hyperparameters to try.
3. Train the neural network with the new hyperparameters.
4. Evaluate the performance of the neural network.
5. Repeat steps 2-4 until the desired performance is achieved.

The number of iterations required to achieve the desired performance will depend on the complexity of the neural network and the difficulty of the optimization problem.

Example of how to incorporate Bayesian optimization into a neural network in MATLAB using the bayesopt function

function [weights, biases, best_loss] = bayesopt_neural_network(X, y)

% Define the hyperparameters to optimize.

hyperparameters = {

'learning_rate', 'momentum', 'weight_decay'};

% Define the objective function.

objective_function = @(hyperparameters) ...

train_neural_network(X, y, hyperparameters);

% Run Bayesian optimization.

results = bayesopt(objective_function, hyperparameters);

% Get the best weights and biases.

weights = results.best_params.Weights;

biases = results.best_params.Biases;

% Get the best loss.

best_loss = results.best_value;

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