Quantum-Inspired Classical Algorithm for Principal Component Regression
This provides a scalable solution for large datasets in regression tasks, though it is incremental as it builds on existing quantum-inspired techniques.
The paper tackles principal component regression by developing a classical algorithm that achieves polylogarithmic runtime relative to the number of data points, representing an exponential speedup over state-of-the-art methods under specific data structure assumptions.
This paper presents a sublinear classical algorithm for principal component regression. The algorithm uses quantum-inspired linear algebra, an idea developed by Tang. Using this technique, her algorithm for recommendation systems achieved runtime only polynomially slower than its quantum counterpart. Her work was quickly adapted to solve many other problems in sublinear time complexity. In this work, we developed an algorithm for principal component regression that runs in time polylogarithmic to the number of data points, an exponential speed up over the state-of-the-art algorithm, under the mild assumption that the input is given in some data structure that supports a norm-based sampling procedure. This exponential speed up allows for potential applications in much larger data sets.