Information Criterion

Information criteria are statistical metrics used to select the best-fitting model from a set of candidates, balancing model complexity with goodness-of-fit. Current research focuses on adapting existing criteria (like AIC and BIC) and developing novel ones (e.g., UBIC, NICc, LS, IIC) to address challenges posed by high-dimensional data, overparameterized models, and complex data structures such as clustered or time-series data. These advancements are crucial for improving model selection in diverse fields, including PDE discovery, deep learning, and federated learning, leading to more accurate and reliable scientific inferences and practical applications. The development of robust information criteria is particularly important in situations with noisy or incomplete data, where traditional methods may fail.