523.523. Wide and Deep Learning

Wide and Deep Learning is a type of neural network architecture used in recommender systems. It combines the strengths of linear models (wide) and deep learning models (deep) to predict user-item interactions. **Example:** Suppose we have a user-item interaction matrix where each entry represents the rating given by a user to an item. We can use Wide and Deep Learning to learn both the linear and nonlinear interactions between users and items. **Constraints:** The user-item interaction matrix is sparse, meaning most users have interacted with few items. The number of users and items is large. The ratings are mostly binary (0 or 1).

Your task is to implement a Wide and Deep Learning model using NumPy to predict the ratings given by users to items.