You are in a machine learning project to improve the performance of some basic supervised learning algorithms in a real$-$world application. Please give the solutions for the following situations.

$($a$)$ Suppose now you are required to compare the performance of a simple model $($e$.$g$.,$ linear model$)$ and a complex model $($e$.$g$.,$ neural network$)$ in the project. Given the model performance in the following table, which one $($simple or complex$)$ is more suitable for the project. Please give the reason for your choice.

Simple Model:

Training Accuracy: $75\%,$ Test Accuracy: $65\%$

Complex Model:

Training Accuracy:$90\%,$Test Accuracy: $40\%$

$($b$)$ Please explain the reason for the results of the complex model $($from the view of the hypothesis space$).$

The results of the complex model show that it is overfitting of the training data.

$($c$)$ If you are required to use the complex model, you could adopt what kinds of techniques to boost the final performance.