ECCC-Report TR18-128https://eccc.weizmann.ac.il/report/2018/128Comments and Revisions published for TR18-128en-usWed, 11 Jul 2018 11:38:28 +0300
Paper TR18-128
| A quantum-inspired classical algorithm for recommendation systems |
Ewin Tang
https://eccc.weizmann.ac.il/report/2018/128A recommendation system suggests products to users based on data about user preferences. It is typically modeled by a problem of completing an $m\times n$ matrix of small rank $k$. We give the first classical algorithm to produce a recommendation in $O(\text{poly}(k)\text{polylog}(m,n))$ time, which is an exponential improvement on previous algorithms that run in time linear in $m$ and $n$. Our strategy is inspired by a quantum algorithm by Kerenidis and Prakash: like the quantum algorithm, instead of reconstructing a user's full list of preferences, we only seek a randomized sample from the user's preferences. Our main result is an algorithm that samples high-weight entries from a low-rank approximation of the input matrix in time independent of $m$ and $n$, given natural sampling assumptions on that input matrix. As a consequence, we show that Kerenidis and Prakash's quantum machine learning (QML) algorithm, one of the strongest candidates for provably exponential speedups in QML, does not in fact give an exponential speedup over classical algorithms.Wed, 11 Jul 2018 11:38:28 +0300https://eccc.weizmann.ac.il/report/2018/128