Telescoping Sums, Permutations, and First Occurrence Distributions

Telescoping sums very naturally lead to probability distributions on ${\mathbb Z}^+$. But are these distributions typically cosmetic and devoid of motivation? In this paper we give three examples of "first occurrence" distributions, each defined by telescoping sums, and that each arise from concrete questions about the structure of permutations.Comment: 13 page

Fine-Grain Checkpointing with In-Cache-Line Logging

Non-Volatile Memory offers the possibility of implementing high-performance, durable data structures. However, achieving performance comparable to well-designed data structures in non-persistent (transient) memory is difficult, primarily because of the cost of ensuring the order in which memory writes reach NVM. Often, this requires flushing data to NVM and waiting a full memory round-trip time. In this paper, we introduce two new techniques: Fine-Grained Checkpointing, which ensures a consistent, quickly recoverable data structure in NVM after a system failure, and In-Cache-Line Logging, an undo-logging technique that enables recovery of earlier state without requiring cache-line flushes in the normal case. We implemented these techniques in the Masstree data structure, making it persistent and demonstrating the ease of applying them to a highly optimized system and their low (5.9-15.4\%) runtime overhead cost.Comment: In 2019 Architectural Support for Programming Languages and Operating Systems (ASPLOS 19), April 13, 2019, Providence, RI, US

NetLSD: Hearing the Shape of a Graph

Comparison among graphs is ubiquitous in graph analytics. However, it is a hard task in terms of the expressiveness of the employed similarity measure and the efficiency of its computation. Ideally, graph comparison should be invariant to the order of nodes and the sizes of compared graphs, adaptive to the scale of graph patterns, and scalable. Unfortunately, these properties have not been addressed together. Graph comparisons still rely on direct approaches, graph kernels, or representation-based methods, which are all inefficient and impractical for large graph collections. In this paper, we propose the Network Laplacian Spectral Descriptor (NetLSD): the first, to our knowledge, permutation- and size-invariant, scale-adaptive, and efficiently computable graph representation method that allows for straightforward comparisons of large graphs. NetLSD extracts a compact signature that inherits the formal properties of the Laplacian spectrum, specifically its heat or wave kernel; thus, it hears the shape of a graph. Our evaluation on a variety of real-world graphs demonstrates that it outperforms previous works in both expressiveness and efficiency.Comment: KDD '18: The 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, August 19--23, 2018, London, United Kingdo

The Secure Link Prediction Problem

Link Prediction is an important and well-studied problem for social networks. Given a snapshot of a graph, the link prediction problem predicts which new interactions between members are most likely to occur in the near future. As networks grow in size, data owners are forced to store the data in remote cloud servers which reveals sensitive information about the network. The graphs are therefore stored in encrypted form. We study the link prediction problem on encrypted graphs. To the best of our knowledge, this secure link prediction problem has not been studied before. We use the number of common neighbors for prediction. We present three algorithms for the secure link prediction problem. We design prototypes of the schemes and formally prove their security. We execute our algorithms in real-life datasets.Comment: This has been accepted for publication in Advances in Mathematics of Communications (AMC) journa

Normal, Abby Normal, Prefix Normal

A prefix normal word is a binary word with the property that no substring has more 1s than the prefix of the same length. This class of words is important in the context of binary jumbled pattern matching. In this paper we present results about the number $pnw(n)$ of prefix normal words of length $n$, showing that $pnw(n) =\Omega\left(2^{n - c\sqrt{n\ln n}}\right)$ for some $c$ and $pnw(n) = O \left(\frac{2^n (\ln n)^2}{n}\right)$. We introduce efficient algorithms for testing the prefix normal property and a "mechanical algorithm" for computing prefix normal forms. We also include games which can be played with prefix normal words. In these games Alice wishes to stay normal but Bob wants to drive her "abnormal" -- we discuss which parameter settings allow Alice to succeed.Comment: Accepted at FUN '1

Programming with a Differentiable Forth Interpreter

Given that in practice training data is scarce for all but a small set of problems, a core question is how to incorporate prior knowledge into a model. In this paper, we consider the case of prior procedural knowledge for neural networks, such as knowing how a program should traverse a sequence, but not what local actions should be performed at each step. To this end, we present an end-to-end differentiable interpreter for the programming language Forth which enables programmers to write program sketches with slots that can be filled with behaviour trained from program input-output data. We can optimise this behaviour directly through gradient descent techniques on user-specified objectives, and also integrate the program into any larger neural computation graph. We show empirically that our interpreter is able to effectively leverage different levels of prior program structure and learn complex behaviours such as sequence sorting and addition. When connected to outputs of an LSTM and trained jointly, our interpreter achieves state-of-the-art accuracy for end-to-end reasoning about quantities expressed in natural language stories.Comment: 34th International Conference on Machine Learning (ICML 2017

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