Scale And Translation Invariant Collaborative Filtering Systems

Collaborative filtering systems are prediction algorithms over sparse data sets of user preferences. We modify a wide range of state-of-the-art collaborative filtering systems to make them scale and translation invariant and generally improve their accuracy without increasing their computational cost. Using the EachMovie and the Jester data sets, we show that learning-free constant time scale and translation invariant schemes outperforms other learning-free constant time schemes by at least 3% and perform as well as expensive memory-based schemes (within 4%). Over the Jester data set, we show that a scale and translation invariant Eigentaste algorithm outperforms Eigentaste 2.0 by 20%. These results suggest that scale and translation invariance is a desirable property

Beyond Low Rank + Sparse: Multi-scale Low Rank Matrix Decomposition

We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often exhibit local correlations in multiple scales. Concretely, we propose a multi-scale low rank modeling that represents a data matrix as a sum of block-wise low rank matrices with increasing scales of block sizes. We then consider the inverse problem of decomposing the data matrix into its multi-scale low rank components and approach the problem via a convex formulation. Theoretically, we show that under various incoherence conditions, the convex program recovers the multi-scale low rank components \revised{either exactly or approximately}. Practically, we provide guidance on selecting the regularization parameters and incorporate cycle spinning to reduce blocking artifacts. Experimentally, we show that the multi-scale low rank decomposition provides a more intuitive decomposition than conventional low rank methods and demonstrate its effectiveness in four applications, including illumination normalization for face images, motion separation for surveillance videos, multi-scale modeling of the dynamic contrast enhanced magnetic resonance imaging and collaborative filtering exploiting age information

Transfer Learning via Contextual Invariants for One-to-Many Cross-Domain Recommendation

The rapid proliferation of new users and items on the social web has aggravated the gray-sheep user/long-tail item challenge in recommender systems. Historically, cross-domain co-clustering methods have successfully leveraged shared users and items across dense and sparse domains to improve inference quality. However, they rely on shared rating data and cannot scale to multiple sparse target domains (i.e., the one-to-many transfer setting). This, combined with the increasing adoption of neural recommender architectures, motivates us to develop scalable neural layer-transfer approaches for cross-domain learning. Our key intuition is to guide neural collaborative filtering with domain-invariant components shared across the dense and sparse domains, improving the user and item representations learned in the sparse domains. We leverage contextual invariances across domains to develop these shared modules, and demonstrate that with user-item interaction context, we can learn-to-learn informative representation spaces even with sparse interaction data. We show the effectiveness and scalability of our approach on two public datasets and a massive transaction dataset from Visa, a global payments technology company (19% Item Recall, 3x faster vs. training separate models for each domain). Our approach is applicable to both implicit and explicit feedback settings.Comment: SIGIR 202

RACOFI: A Rule-Applying Collaborative Filtering System

In this paper we give an overview of the RACOFI (Rule-Applying Collaborative Filtering) multidimensional rating system and its related technologies. This will be exemplified with RACOFI Music, an implemented collaboration agent that assists on-line users in the rating and recommendation of audio (Learning) Objects. It lets users rate contemporary Canadian music in the five dimensions of impression, lyrics, music, originality, and production. The collaborative filtering algorithms STI Pearson, STIN2, and the Per Item Average algorithms are then employed together with RuleML-based rules to recommend music objects that best match user queries. RACOFI has been on-line since August 2003 at http://racofi.elg.ca.

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.Comment: 30 page