Quantum Recommendation Systems

A recommendation system uses the past purchases or ratings of $n$ products by a group of $m$ users, in order to provide personalized recommendations to individual users. The information is modeled as an $m \times n$ preference matrix which is assumed to have a good rank-$k$ approximation, for a small constant $k$. In this work, we present a quantum algorithm for recommendation systems that has running time $O(\text{poly}(k)\text{polylog}(mn))$. All known classical algorithms for recommendation systems that work through reconstructing an approximation of the preference matrix run in time polynomial in the matrix dimension. Our algorithm provides good recommendations by sampling efficiently from an approximation of the preference matrix, without reconstructing the entire matrix. For this, we design an efficient quantum procedure to project a given vector onto the row space of a given matrix. This is the first algorithm for recommendation systems that runs in time polylogarithmic in the dimensions of the matrix and provides an example of a quantum machine learning algorithm for a real world application.Comment: 22 page

BoostFM: Boosted Factorization Machines for Top-N Feature-based Recommendation

Feature-based matrix factorization techniques such as Factorization Machines (FM) have been proven to achieve impressive accuracy for the rating prediction task. However, most common recommendation scenarios are formulated as a top-N item ranking problem with implicit feedback (e.g., clicks, purchases)rather than explicit ratings. To address this problem, with both implicit feedback and feature information, we propose a feature-based collaborative boosting recommender called BoostFM, which integrates boosting into factorization models during the process of item ranking. Specifically, BoostFM is an adaptive boosting framework that linearly combines multiple homogeneous component recommenders, which are repeatedly constructed on the basis of the individual FM model by a re-weighting scheme. Two ways are proposed to efficiently train the component recommenders from the perspectives of both pairwise and listwise Learning-to-Rank (L2R). The properties of our proposed method are empirically studied on three real-world datasets. The experimental results show that BoostFM outperforms a number of state-of-the-art approaches for top-N recommendation

Retrospective Higher-Order Markov Processes for User Trails

Users form information trails as they browse the web, checkin with a geolocation, rate items, or consume media. A common problem is to predict what a user might do next for the purposes of guidance, recommendation, or prefetching. First-order and higher-order Markov chains have been widely used methods to study such sequences of data. First-order Markov chains are easy to estimate, but lack accuracy when history matters. Higher-order Markov chains, in contrast, have too many parameters and suffer from overfitting the training data. Fitting these parameters with regularization and smoothing only offers mild improvements. In this paper we propose the retrospective higher-order Markov process (RHOMP) as a low-parameter model for such sequences. This model is a special case of a higher-order Markov chain where the transitions depend retrospectively on a single history state instead of an arbitrary combination of history states. There are two immediate computational advantages: the number of parameters is linear in the order of the Markov chain and the model can be fit to large state spaces. Furthermore, by providing a specific structure to the higher-order chain, RHOMPs improve the model accuracy by efficiently utilizing history states without risks of overfitting the data. We demonstrate how to estimate a RHOMP from data and we demonstrate the effectiveness of our method on various real application datasets spanning geolocation data, review sequences, and business locations. The RHOMP model uniformly outperforms higher-order Markov chains, Kneser-Ney regularization, and tensor factorizations in terms of prediction accuracy

Learning to Customize Network Security Rules

Security is a major concern for organizations who wish to leverage cloud computing. In order to reduce security vulnerabilities, public cloud providers offer firewall functionalities. When properly configured, a firewall protects cloud networks from cyber-attacks. However, proper firewall configuration requires intimate knowledge of the protected system, high expertise and on-going maintenance. As a result, many organizations do not use firewalls effectively, leaving their cloud resources vulnerable. In this paper, we present a novel supervised learning method, and prototype, which compute recommendations for firewall rules. Recommendations are based on sampled network traffic meta-data (NetFlow) collected from a public cloud provider. Labels are extracted from firewall configurations deemed to be authored by experts. NetFlow is collected from network routers, avoiding expensive collection from cloud VMs, as well as relieving privacy concerns. The proposed method captures network routines and dependencies between resources and firewall configuration. The method predicts IPs to be allowed by the firewall. A grouping algorithm is subsequently used to generate a manageable number of IP ranges. Each range is a parameter for a firewall rule. We present results of experiments on real data, showing ROC AUC of 0.92, compared to 0.58 for an unsupervised baseline. The results prove the hypothesis that firewall rules can be automatically generated based on router data, and that an automated method can be effective in blocking a high percentage of malicious traffic.Comment: 5 pages, 5 figures, one tabl

Top-k Route Search through Submodularity Modeling of Recurrent POI Features

We consider a practical top-k route search problem: given a collection of points of interest (POIs) with rated features and traveling costs between POIs, a user wants to find k routes from a source to a destination and limited in a cost budget, that maximally match her needs on feature preferences. One challenge is dealing with the personalized diversity requirement where users have various trade-off between quantity (the number of POIs with a specified feature) and variety (the coverage of specified features). Another challenge is the large scale of the POI map and the great many alternative routes to search. We model the personalized diversity requirement by the whole class of submodular functions, and present an optimal solution to the top-k route search problem through indices for retrieving relevant POIs in both feature and route spaces and various strategies for pruning the search space using user preferences and constraints. We also present promising heuristic solutions and evaluate all the solutions on real life data.Comment: 11 pages, 7 figures, 2 table