2023/01/15 by Yigit Efe Erginbas, Justin Kang, Erginbas, Yigit Efe +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #Algorithms and Data Compression #FOS: Computer and information sciences #FOS: Electrical engineering #Machine Learning (cs.LG) #Machine Learning and Algorithms #Machine Learning in Bioinformatics #Signal Processing (eess.SP) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2301.06200
openalex publication_date 2023/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Fourier transformations of pseudo-Boolean functions are popular tools for analyzing functions of binary sequences. Real-world functions often have structures that manifest in a sparse Fourier transform, and previous works have shown that under the assumption of sparsity the transform can be computed efficiently. But what if we want to compute the Fourier transform of functions defined over a q-ary alphabet? These types of functions arise naturally in many areas including biology. A typical workaround is to encode the q-ary sequence in binary, however, this approach is computationally inefficient and fundamentally incompatible with the existing sparse Fourier transform techniques. Herein, we develop a sparse Fourier transform algorithm specifically for q-ary functions of length n sequences, dubbed q-SFT, which provably computes an S-sparse transform with vanishing error as qn → ∞ in O(Sn) function evaluations and O(S n2 log q) computations, where S = qnδ for some δ< 1. Under certain assumptions, we show that for fixed q, a robust version of q-SFT has a sample complexity of O(Sn2) and a computational complexity of O(Sn3) with the same asymptotic guarantees. We present numerical simulations on synthetic and real-world RNA data, demonstrating the scalability of q-SFT to massively high dimensional q-ary functions.