CertNexus Certified Artificial Intelligence Practitioner (CAIP) Practice Exam

The notable downside of using the closed-form normal equation in linear regression is its inefficiency for large datasets. The closed-form solution involves calculating the inverse of the matrix derived from the features of the dataset, specifically the Gram matrix (X^TX). As the number of features and data points increases, the computational load becomes substantial. This process requires O(n^3) operations for matrix inversion, which can be prohibitively expensive when dealing with high-dimensional datasets.

As a result, the closed-form normal equation is not scalable for large datasets, making iterative methods, such as gradient descent, often more practical in such scenarios. These iterative methods can efficiently handle larger datasets by using smaller batches of data and optimizing parameters incrementally, thus avoiding the heavy computation associated with directly solving the normal equations. Understanding this nuance is crucial for practitioners working with machine learning and regression in real-world applications, where data volume can significantly impact the choice of algorithm and method used for model training.