Making recommendations in the presence of sparsity is known to present one of the most challenging problems faced by collaborative filtering methods. In this work we tackle this problem by exploiting the innately hierarchical structure of the item space following an approach inspired by the theory of Decomposability. We view the itemspace as a Nearly Decomposable system and we define blocks of closely related elements and corresponding indirect proximity components. We study the theoretical properties of the decomposition and we derive sufficient conditions that guarantee full item space coverage even in cold-start recommendation scenarios. A comprehensive set of experiments on the MovieLens and the Yahoo!R2Music datasets, using several widely applied performance metrics, support our model's theoretically predicted properties and verify that NCDREC outperforms several state-of-the-art algorithms, in terms of recommendation accuracy, diversity and sparseness insensitivity.

We present a unified framework for low-rank matrix estimation with nonconvex penalties. We first prove that the proposed estimator attains a faster statistical rate than the traditional low-rank matrix estimator with nuclear norm penalty. Moreover, we rigorously show that under a certain condition on the magnitude of the nonzero singular values, the proposed estimator enjoys oracle property (i.e., exactly recovers the true rank of the matrix), besides attaining a faster rate. As far as we know, this is the first work that establishes the theory of low-rank matrix estimation with nonconvex penalties, confirming the advantages of nonconvex penalties for matrix completion. Numerical experiments on both synthetic and real world datasets corroborate our theory.

In applications such as recommendation systems and revenue management, it is important to predict preferences on items that have not been seen by a user or predict outcomes of comparisons among those that have never been compared. A popular discrete choice model of multinomial logit model captures the structure of the hidden preferences with a low-rank matrix. In order to predict the preferences, we want to learn the underlying model from noisy observations of the low-rank matrix, collected as revealed preferences in various forms of ordinal data. A natural approach to learn such a model is to solve a convex relaxation of nuclear norm minimization. We present the convex relaxation approach in two contexts of interest: collaborative ranking and bundled choice modeling. In both cases, we show that the convex relaxation is minimax optimal. We prove an upper bound on the resulting error with finite samples, and provide a matching information-theoretic lower bound.

Collaborative filtering (CF) is a successful approach commonly used by many recommender systems. Conventional CF-based methods use the ratings given to items by users as the sole source of information for learning to make recommendation. However, the ratings are often very sparse in many applications, causing CF-based methods to degrade significantly in their recommendation performance. To address this sparsity problem, auxiliary information such as item content information may be utilized. Collaborative topic regression (CTR) is an appealing recent method taking this approach which tightly couples the two components that learn from two different sources of information. Nevertheless, the latent representation learned by CTR may not be very effective when the auxiliary information is very sparse. To address this problem, we generalize recent advances in deep learning from i.i.d. input to non-i.i.d. (CF-based) input and propose in this paper a hierarchical Bayesian model called collaborative deep learning (CDL), which jointly performs deep representation learning for the content information and collaborative filtering for the ratings (feedback) matrix. Extensive experiments on three real-world datasets from different domains show that CDL can significantly advance the state of the art.

Recommendation systems have been integrated into the majority of large online systems to filter and rank information according to user profiles. It thus influences the way users interact with the system and, as a consequence, bias the evaluation of the performance of a recommendation algorithm computed using historical data (via offline evaluation). This paper presents a new application of a weighted offline evaluation to reduce this bias for collaborative filtering algorithms.

Apple wants to control every aspect of your life -- as long as you choose to let it. The company on Monday showed off the newest updates to the software running on its iPhones and iPads, Macs and Apple Watches. One of the key characteristics of Apple's operating system releases over the past couple years -- including iOS 9 and Mac OS X 10.11 El Capitan revealed Monday at its developer conference -- is how well the software makes its devices work together. Last year's debut of Continuity and Handoff tied the iPhone and Mac computer more closely together, letting people start an email on their smartphone and finish it on their computer or even answer phone calls on their Macs. This year, Apple showed more ways it will extend its reach into our homes and cars, as well as how we listen to music and how we pay for goods.

The Cortana voice assistant is going a few steps further to ensure your next round of air travel goes as smoothly as possible. In a blog post Monday, Microsoft described several new ways that Cortana can help with almost every phase of your trip, from checking your flight-related emails to monitoring traffic on the way to the airport to figuring out how much you're spending if you travel abroad. The latest improvements come courtesy of an update to the software. Microsoft has grand ambitions for Cortana. Currently available only on Windows Phone 8.1, the voice assistant will expand to all Windows 10 devices -- PCs, tablets and phones -- in July.

Apple on Monday served up a veritable smorgasbord of digital delights for its fans, unveiling at its annual developers conference upgrades to its mobile and desktop software, showing off a gussied-up Siri with a new bag of tricks, and firing a shot over Spotify's bow with its new streaming Apple Music subscription service. "This is a truly revolutionary music service," Eddy Cue, Apple's senior vice president of Internet software and services, told the crowd of several thousand developers, designers and product managers at the 26th Worldwide Developers Conference, the annual Apple love fest at Moscone Center in San Francisco. "Apple Music will bring you all of your music all in one place." Revealed toward the end of a nearly three-hour extravaganza, the music feature was clearly Apple's rabbit out of a hat. It had been widely expected for months, ever since May last year when Apple bought subscription streaming music service Beats Music, and Beats Electronics, which makes the popular Beats headphones, speakers and audio software.

Apple on Monday served up a veritable smorgasbord of digital delights for its fans, unveiling at its annual developers conference upgrades to its mobile and desktop software, showing off a gussied-up Siri with a new bag of tricks, and firing a shot over Spotify's bow with its new streaming Apple Music subscription service. "This is a truly revolutionary music service," Eddy Cue, Apple's senior vice president of Internet software and services, told the crowd of several thousand developers, designers and product managers at the 26th Worldwide Developers Conference, the annual Apple love fest at Moscone Center in San Francisco. "Apple Music will bring you all of your music all in one place." Revealed toward the end of a nearly three-hour extravaganza, the music feature was clearly Apple's rabbit out of a hat. It had been widely expected for months, ever since May last year when Apple bought subscription streaming music service Beats Music, and Beats Electronics, which makes the popular Beats headphones, speakers and audio software.

At Apple's WWDC developers' conference keynote in San Francisco, the company's senior vice president of software engineering, Craig Federighi, highlighted a number of new tools coming to Apple's iOS 9 update. Some of these features include a native news aggregator (aptly called News); a refreshed user interface for the more "proactive" digital voice assistant Siri, and split-screen capabilities for the iPad. But similar to past WWDC events, Apple only spent time going through what it considered key upgrades. The other, less high-profile features were thrown onto a keynote slide and glossed over almost completely. Below are the 30 features Apple did not parse through during the presentation: One notable item on the list is "app thinning," which lets users download apps that are tailored to their iOS device.