Bayesian Regularization in Artificial Neural Networks: A Comprehensive Review

Artificial neural networks (ANNs) are computational models inspired by human brains’ neural structures and functions. Bayesian regularized ANNs (BRANNs) combine the principles of Bayesian inference with ANNs, adding an extra term to the loss function during training to smooth out network responses. BRANNs have several advantages over traditional ANNs, including improved generalization ability and reduced overfitting.
To understand how BRANNs work, imagine a large network of interconnected nodes (artificial neurons) in an ANN. Each node receives inputs from other nodes and applies weights to these inputs before passing them through an activation function to produce an output. The goal of the network is to minimize the difference between its predictions and the actual outputs, which is achieved by adjusting the weights and biases during training.
BRANNs introduce Bayesian regularization into this process by adding a penalty term to the loss function for large weights. This encourages the network to have smaller weights, which leads to a smoother response. Think of it like a teacher giving a student a reward for using smaller handwriting, making their work easier to read and appreciate.
During training, the BRANN adjusts the weights and biases to minimize the loss function, which is a measure of how well the network’s predictions match the actual outputs. The learning process can be expressed mathematically as:
y = f(Wx + b)
Where y is the output vector; f is the activation function; x is the input vector; W and b are the weight matrix and bias parameter, respectively.
In summary, BRANNs are a type of ANN that combines Bayesian inference with traditional neural network architecture to improve generalization ability and reduce overfitting. By adding a penalty term to the loss function, BRANNs encourage the network to have smaller weights, resulting in a smoother response.