Statistical Query Lower Bound

Statistical Query (SQ) lower bounds research investigates the fundamental limits of learning algorithms that only access data through statistical queries, rather than directly observing individual data points. Current research focuses on establishing tight SQ lower bounds for various learning problems, including those involving Gaussian mixtures, sparse vectors, and neural networks, often comparing these bounds to the performance of existing algorithms like stochastic gradient descent. These lower bounds provide crucial insights into the computational hardness of different learning tasks, guiding the development of more efficient algorithms and informing the design of practically feasible machine learning systems. The ultimate goal is to understand the inherent difficulty of learning problems, independent of specific algorithmic choices.