In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain connectomes or words' embedding, represented by graphs. We present a formulation of CNNs in the context of spectral graph theory, which provides the necessary mathematical background and efficient numerical schemes to design fast localized convolutional filters on graphs. Importantly, the proposed technique offers the same linear computational complexity and constant learning complexity as classical CNNs, while being universal to any graph structure. Experiments on MNIST and 20NEWS demonstrate the ability of this novel deep learning system to learn local, stationary, and compositional features on graphs.

Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering

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Convolutional neural networks on graphs with fast localized spectral filtering

Data integration is the problem of combining data residing at different sources, and providing the user with a unified view of these data. The problem of designing data integration systems is important in current real world applications, and is characterized by a number of issues that are interesting from a theoretical point of view. This document presents on overview of the material to be presented in a tutorial on data integration. The tutorial is focused on some of the theoretical issues that are relevant for data integration. Special attention will be devoted to the following aspects: modeling a data integration application, processing queries in data integration, dealing with inconsistent data sources, and reasoning on queries.

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Data integration: a theoretical perspective

Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.

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The knowledge complexity of interactive proof-systems

Over the last decade, we have seen a revolution in connectivity between computers, and a resulting paradigm shift from centralized to highly distributed systems. With massive scale also comes massive instability, as node and link failures become the norm rather than the exception. For such highly volatile systems, decentralized gossip-based protocols are emerging as an approach to maintaining simplicity and scalability while achieving fault-tolerant information dissemination. In this paper, we study the problem of computing aggregates with gossip-style protocols. Our first contribution is an analysis of simple gossip-based protocols for the computation of sums, averages, random samples, quantiles, and other aggregate functions, and we show that our protocols converge exponentially fast to the true answer when using uniform gossip. Our second contribution is the definition of a precise notion of the speed with which a node's data diffuses through the network. We show that this diffusion speed is at the heart of the approximation guarantees for all of the above problems. We analyze the diffusion speed of uniform gossip in the presence of node and link failures, as well as for flooding-based mechanisms. The latter expose interesting connections to random walks on graphs.

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Gossip-based computation of aggregate information

We present Symphony, a novel protocol for maintaining distributed hash tables in a wide area network. The key idea is to arrange all participants along a ring and equip them with long distance contacts drawn from a family of harmonic distributions. Through simulation, we demonstrate that our construction is scalable, flexible, stable in the presence of frequent updates and offers small average latency with only a handful of long distance links per node. The cost of updates when hosts join and leave is small.

Symphony: distributed hashing in a small world

We consider the problem of indexing high-dimensional data for answering (approximate) similarity-search queries. Similarity indexes prove to be important in a wide variety of settings: Web search engines desire fast, parallel, main-memory-based indexes for similarity search on text data; database systems desire disk-based similarity indexes for high-dimensional data, including text and images; peer-to-peer systems desire distributed similarity indexes with low communication cost. We propose an indexing scheme called LSH Forest which is applicable in all the above contexts. Our index uses the well-known technique of locality-sensitive hashing (LSH), but improves upon previous designs by (a) eliminating the different data-dependent parameters for which LSH must be constantly hand-tuned, and (b) improving on LSH's performance guarantees for skewed data distributions while retaining the same storage and query overhead. We show how to construct this index in main memory, on disk, in parallel systems, and in peer-to-peer systems. We evaluate the design with experiments on multiple text corpora and demonstrate both the self-tuning nature and the superior performance of LSH Forest.

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LSH forest: self-tuning indexes for similarity search

Recent trends towards database outsourcing, as well as concerns and laws governing data privacy, have led to great interest in enabling secure database services. Previous approaches to enabling such a service have been based on data encryption, causing a large overhead in query processing. We propose a new, distributed architecture that allows an organization to outsource its data management to {\em two} untrusted servers while preserving data privacy. We show how the presence of two servers enables efficient partitioning of data so that the contents at any one server are guaranteed not to breach data privacy. We show how to optimize and execute queries in this architecture, and discuss new challenges that emerge in designing the database schema.

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Two Can Keep a Secret: A Distributed Architecture for Secure Database Services

We consider the problem of horizontally partitioning a dynamic relation across a large number of disks/nodes by the use of range partitioning. Such partitioning is often desirable in large-scale parallel databases, as well as in peer-to-peer (P2P) systems. As tuples are inserted and deleted, the partitions may need to be adjusted, and data moved, in order to achieve storage balance across the participant disks/nodes. We propose efficient, asymptotically optimal algorithms that ensure storage balance at all times, even against an adversarial insertion and deletion of tuples. We combine the above algorithms with distributed routing structures to architect a P2P system that supports efficient range queries, while simultaneously guaranteeing storage balance.

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Online balancing of range-partitioned data with applications to peer-to-peer systems

In a vertical representation of a market-basket database, each item is associated with a column of values representing the transactions in which it is present. The association-rule mining algorithms that have been recently proposed for this representation show performance improvements over their classical horizontal counterparts, but are either efficient only for certain database sizes, or assume particular characteristics of the database contents, or are applicable only to specific kinds of database schemas. We present here a new vertical mining algorithm called VIPER, which is general-purpose, making no special requirements of the underlying database. VIPER stores data in compressed bit-vectors called “snakes” and integrates a number of novel optimizations for efficient snake generation, intersection, counting and storage. We analyze the performance of VIPER for a range of synthetic database workloads. Our experimental results indicate significant performance gains, especially for large databases, over previously proposed vertical and horizontal mining algorithms. In fact, there are even workload regions where VIPER outperforms an optimal, but practically infeasible, horizontal mining algorithm.

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Mayank Bawa

Papers

Symphony: distributed hashing in a small world

LSH forest: self-tuning indexes for similarity search

Two Can Keep a Secret: A Distributed Architecture for Secure Database Services

Online balancing of range-partitioned data with applications to peer-to-peer systems

Turbo-charging vertical mining of large databases