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Counting small subgraphs, referred to as motifs, in large graphs is a fundamental task in graph analysis, extensively studied across various contexts and computational models. In the sublinear-time regime, the relaxed problem of approximate…
Frequency estimation of elements is an important task for summarizing data streams and machine learning applications. The problem is often addressed by using streaming algorithms with sublinear space data structures. These algorithms allow…
Linear algebraic operations are ubiquitous in engineering applications, and arise often in a variety of fields including statistical signal processing and machine learning. With contemporary large datasets, to perform linear algebraic…
Sketches are commonly used in computer systems and network monitoring tools to provide efficient query executions while maintaining a compact data representation. Switches and routers maintain sketches to track statistical characteristics…
A key need in different disciplines is to perform analytics over fast-paced data streams, similar in nature to the traditional OLAP analytics in relational databases i.e., with filters and aggregates. Storing unbounded streams, however, is…
Given a random text over a finite alphabet, we study the frequencies at which fixed-length words occur as subsequences. As the data size grows, the joint distribution of word counts exhibits a rich asymptotic structure. We investigate all…
Frequency estimation is one of the most fundamental problems in streaming algorithms. Given a stream $S$ of elements from some universe $U=\{1 \ldots n\}$, the goal is to compute, in a single pass, a short sketch of $S$ so that for any…
In Statistics, log-concave density estimation is a central problem within the field of nonparametric inference under shape constraints. Despite great progress in recent years on the statistical theory of the canonical estimator, namely the…
Sketch-based algorithms for network traffic monitoring have drawn increasing interest in recent years due to their sub-linear memory efficiency and high accuracy. As the volume of network traffic grows, software-based sketch implementations…
Shape constraints yield flexible middle grounds between fully nonparametric and fully parametric approaches to modeling distributions of data. The specific assumption of log-concavity is motivated by applications across economics, survival…
Subgraph counting is a fundamental primitive in graph processing, with applications in social network analysis (e.g., estimating the clustering coefficient of a graph), database processing and other areas. The space complexity of subgraph…
Cardinality sketches are popular data structures that enhance the efficiency of working with large data sets. The sketches are randomized representations of sets that are only of logarithmic size but can support set merges and approximate…
Structured high-cardinality data arises in many domains, and poses a major challenge for both modeling and inference. Graphical models are a popular approach to modeling structured data but they are unsuitable for high-cardinality…
Data structures that allow efficient distance estimation (distance oracles, distance sketches, etc.) have been extensively studied, and are particularly well studied in centralized models and classical distributed models such as CONGEST. We…
We derive optimal statistical and computational complexity bounds for exp-concave stochastic minimization in terms of the effective dimension. For common eigendecay patterns of the population covariance matrix, this quantity is…
We study the problem of maximum likelihood estimation of densities that are log-concave and lie in the graphical model corresponding to a given undirected graph $G$. We show that the maximum likelihood estimate (MLE) is the product of the…
Subgraph counting aims to count occurrences of a template T in a given network G(V, E). It is a powerful graph analysis tool and has found real-world applications in diverse domains. Scaling subgraph counting problems is known to be memory…
Hypergraphs, which use hyperedges to capture groupwise interactions among different entities, have gained increasing attention recently for their versatility in effectively modeling real-world networks. In this paper, we study the problem…
Link prediction is a fundamental problem for graph-structured data (e.g., social networks, drug side-effect networks, etc.). Graph neural networks have offered robust solutions for this problem, specifically by learning the representation…
With the increasing prevalence of scalable file systems in the context of High Performance Computing (HPC), the importance of accurate anomaly detection on runtime logs is increasing. But as it currently stands, many state-of-the-art…