The article introduces a new method for reducing the complexity of data in a way that is more efficient than existing techniques. This method, called weak conditional expectation, allows for a more flexible approach to analyzing data, especially when dealing with functions or vectors of functions. By using this new statistical construction, researchers were able to develop dimension reduction methods that do not rely on estimating conditional mean and variance. This approach was found to be effective in various scenarios, as shown through simulations and real-world applications.