arXiv subjects

Srikanta Tirthapura

Publications and source records attributed to Srikanta Tirthapura.

At least 19 recordsLinked to original sources

arXiv2020

DriftSurf: A Risk-competitive Learning Algorithm under Concept Drift

When learning from streaming data, a change in the data distribution, also known as concept drift, can render a previously-learned model inaccurate and require training a new model. We present an adaptive learning algorithm that extends previous drift-detection-based methods by incorporating drift detection into a broader stable-state/reactive-state process. The advantage of our approach is that we can use aggressive drift detection in the stable state to achieve a high detection rate, but mitigate the false positive rate of standalone drift detection via a reactive state that reacts quickly to true drifts while eliminating most false positives. The algorithm is generic in its base learner and can be applied across a variety of supervised learning problems. Our theoretical analysis shows that the risk of the algorithm is competitive to an algorithm with oracle knowledge of when (abrupt) drifts occur. Experiments on synthetic and real datasets with concept drifts confirm our theoretical analysis.

cs.LG↗

arXiv2020

Shared-Memory Parallel Maximal Clique Enumeration from Static and Dynamic Graphs

Maximal Clique Enumeration (MCE) is a fundamental graph mining problem, and is useful as a primitive in identifying dense structures in a graph. Due to the high computational cost of MCE, parallel methods are imperative for dealing with large graphs. We present shared-memory parallel algorithms for MCE, with the following properties: (1) the parallel algorithms are provably work-efficient relative to a state-of-the-art sequential algorithm (2) the algorithms have a provably small parallel depth, showing they can scale to a large number of processors, and (3) our implementations on a multicore machine show good speedup and scaling behavior with increasing number of cores, and are substantially faster than prior shared-memory parallel algorithms for MCE; for instance, on certain input graphs, while prior works either ran out of memory or did not complete in 5 hours, our implementation finished within a minute using 32 cores. We also present work-efficient parallel algorithms for maintaining the set of all maximal cliques in a dynamic graph that is changing through the addition of edges.

cs.DC↗

arXiv2019

Random Sampling for Group-By Queries

Random sampling has been widely used in approximate query processing on large databases, due to its potential to significantly reduce resource usage and response times, at the cost of a small approximation error. We consider random sampling for answering the ubiquitous class of group-by queries, which first group data according to one or more attributes, and then aggregate within each group after filtering through a predicate. The challenge with group-by queries is that a sampling method cannot focus on optimizing the quality of a single answer (e.g. the mean of selected data), but must simultaneously optimize the quality of a set of answers (one per group). We present CVOPT, a query- and data-driven sampling framework for a set of group-by queries. To evaluate the quality of a sample, CVOPT defines a metric based on the norm (e.g. $\ell_2$ or $\ell_\infty$) of the coefficients of variation (CVs) of different answers, and constructs a stratified sample that provably optimizes the metric. CVOPT can handle group-by queries on data where groups have vastly different statistical characteristics, such as frequencies, means, or variances. CVOPT jointly optimizes for multiple aggregations and multiple group-by clauses, and provides a way to prioritize specific groups or aggregates. It can be tuned to cases when partial information about a query workload is known, such as a data warehouse where queries are scheduled to run periodically. Our experimental results show that CVOPT outperforms current state-of-the-art on sample quality and estimation accuracy for group-by queries. On a set of queries on two real-world data sets, CVOPT yields relative errors that are 5x smaller than competing approaches, under the same space budget.

cs.DB↗

arXiv2019

FLEET: Butterfly Estimation from a Bipartite Graph Stream

We consider space-efficient single-pass estimation of the number of butterflies, a fundamental bipartite graph motif, from a massive bipartite graph stream where each edge represents a connection between entities in two different partitions. We present a space lower bound for any streaming algorithm that can estimate the number of butterflies accurately, as well as FLEET, a suite of algorithms for accurately estimating the number of butterflies in the graph stream. Estimates returned by the algorithms come with provable guarantees on the approximation error, and experiments show good tradeoffs between the space used and the accuracy of approximation. We also present space-efficient algorithms for estimating the number of butterflies within a sliding window of the most recent elements in the stream. While there is a significant body of work on counting subgraphs such as triangles in a unipartite graph stream, our work seems to be one of the few to tackle the case of bipartite graph streams.

cs.DS↗

arXiv2019

Parallel Streaming Random Sampling

This paper investigates parallel random sampling from a potentially-unending data stream whose elements are revealed in a series of element sequences (minibatches). While sampling from a stream was extensively studied sequentially, not much has been explored in the parallel context, with prior parallel random-sampling algorithms focusing on the static batch model. We present parallel algorithms for minibatch-stream sampling in two settings: (1) sliding window, which draws samples from a prespecified number of most-recently observed elements, and (2) infinite window, which draws samples from all the elements received. Our algorithms are computationally and memory efficient: their work matches the fastest sequential counterpart, their parallel depth is small (polylogarithmic), and their memory usage matches the best known.

cs.DS↗

arXiv2019

Weighted Reservoir Sampling from Distributed Streams

We consider message-efficient continuous random sampling from a distributed stream, where the probability of inclusion of an item in the sample is proportional to a weight associated with the item. The unweighted version, where all weights are equal, is well studied, and admits tight upper and lower bounds on message complexity. For weighted sampling with replacement, there is a simple reduction to unweighted sampling with replacement. However, in many applications the stream has only a few heavy items which may dominate a random sample when chosen with replacement. Weighted sampling \textit{without replacement} (weighted SWOR) eludes this issue, since such heavy items can be sampled at most once. In this work, we present the first message-optimal algorithm for weighted SWOR from a distributed stream. Our algorithm also has optimal space and time complexity. As an application of our algorithm for weighted SWOR, we derive the first distributed streaming algorithms for tracking \textit{heavy hitters with residual error}. Here the goal is to identify stream items that contribute significantly to the residual stream, once the heaviest items are removed. Residual heavy hitters generalize the notion of $\ell_1$ heavy hitters and are important in streams that have a skewed distribution of weights. In addition to the upper bound, we also provide a lower bound on the message complexity that is nearly tight up to a $\log(1/ε)$ factor. Finally, we use our weighted sampling algorithm to improve the message complexity of distributed $L_1$ tracking, also known as count tracking, which is a widely studied problem in distributed streaming. We also derive a tight message lower bound, which closes the message complexity of this fundamental problem.

cs.DS↗

arXiv2019

Optimal Random Sampling from Distributed Streams Revisited

We give an improved algorithm for drawing a random sample from a large data stream when the input elements are distributed across multiple sites which communicate via a central coordinator. At any point in time the set of elements held by the coordinator represent a uniform random sample from the set of all the elements observed so far. When compared with prior work, our algorithms asymptotically improve the total number of messages sent in the system as well as the computation required of the coordinator. We also present a matching lower bound, showing that our protocol sends the optimal number of messages up to a constant factor with large probability. As a byproduct, we obtain an improved algorithm for finding the heavy hitters across multiple distributed sites.

cs.DC↗

arXiv2018

Streaming k-Means Clustering with Fast Queries

We present methods for k-means clustering on a stream with a focus on providing fast responses to clustering queries. Compared to the current state-of-the-art, our methods provide substantial improvement in the query time for cluster centers while retaining the desirable properties of provably small approximation error and low space usage. Our algorithms rely on a novel idea of "coreset caching" that systematically reuses coresets (summaries of data) computed for recent queries in answering the current clustering query. We present both theoretical analysis and detailed experiments demonstrating their correctness and efficiency

cs.DS↗

arXiv2018

Enumerating Top-k Quasi-Cliques

Quasi-cliques are dense incomplete subgraphs of a graph that generalize the notion of cliques. Enumerating quasi-cliques from a graph is a robust way to detect densely connected structures with applications to bio-informatics and social network analysis. However, enumerating quasi-cliques in a graph is a challenging problem, even harder than the problem of enumerating cliques. We consider the enumeration of top-k degree-based quasi-cliques, and make the following contributions: (1) We show that even the problem of detecting if a given quasi-clique is maximal (i.e. not contained within another quasi-clique) is NP-hard (2) We present a novel heuristic algorithm KernelQC to enumerate the k largest quasi-cliques in a graph. Our method is based on identifying kernels of extremely dense subgraphs within a graph, following by growing subgraphs around these kernels, to arrive at quasi-cliques with the required densities (3) Experimental results show that our algorithm accurately enumerates quasi-cliques from a graph, is much faster than current state-of-the-art methods for quasi-clique enumeration (often more than three orders of magnitude faster), and can scale to larger graphs than current methods.

cs.DS↗

arXiv2018

Shared-Memory Parallel Maximal Clique Enumeration

We present shared-memory parallel methods for Maximal Clique Enumeration (MCE) from a graph. MCE is a fundamental and well-studied graph analytics task, and is a widely used primitive for identifying dense structures in a graph. Due to its computationally intensive nature, parallel methods are imperative for dealing with large graphs. However, surprisingly, there do not yet exist scalable and parallel methods for MCE on a shared-memory parallel machine. In this work, we present efficient shared-memory parallel algorithms for MCE, with the following properties: (1) the parallel algorithms are provably work-efficient relative to a state-of-the-art sequential algorithm (2) the algorithms have a provably small parallel depth, showing that they can scale to a large number of processors, and (3) our implementations on a multicore machine shows a good speedup and scaling behavior with increasing number of cores, and are substantially faster than prior shared-memory parallel algorithms for MCE.

cs.DS↗

arXiv2018

Onion Curve: A Space Filling Curve with Near-Optimal Clustering

Space filling curves (SFCs) are widely used in the design of indexes for spatial and temporal data. Clustering is a key metric for an SFC, that measures how well the curve preserves locality in moving from higher dimensions to a single dimension. We present the {\em onion curve}, an SFC whose clustering performance is provably close to optimal for the cube and near-cube shaped query sets, irrespective of the side length of the query. We show that in contrast, the clustering performance of the widely used Hilbert curve can be far from optimal, even for cube-shaped queries. Since the clustering performance of an SFC is critical to the efficiency of multi-dimensional indexes based on the SFC, the onion curve can deliver improved performance for data structures involving multi-dimensional data.

cs.CG↗

arXiv2018

Incremental Maintenance of Maximal Cliques in a Dynamic Graph

We consider the maintenance of the set of all maximal cliques in a dynamic graph that is changing through the addition or deletion of edges. We present nearly tight bounds on the magnitude of change in the set of maximal cliques, as well as the first change-sensitive algorithms for clique maintenance, whose runtime is proportional to the magnitude of the change in the set of maximal cliques. We present experimental results showing these algorithms are efficient in practice and are faster than prior work by two to three orders of magnitude.

cs.DS↗

arXiv2018

Butterfly Counting in Bipartite Networks

We consider the problem of counting motifs in bipartite affiliation networks, such as author-paper, user-product, and actor-movie relations. We focus on counting the number of occurrences of a "butterfly", a complete $2 \times 2$ biclique, the simplest cohesive higher-order structure in a bipartite graph. Our main contribution is a suite of randomized algorithms that can quickly approximate the number of butterflies in a graph with a provable guarantee on accuracy. An experimental evaluation on large real-world networks shows that our algorithms return accurate estimates within a few seconds, even for networks with trillions of butterflies and hundreds of millions of edges.

cs.DM↗

arXiv2018

Variance-Optimal Offline and Streaming Stratified Random Sampling

Stratified random sampling (SRS) is a fundamental sampling technique that provides accurate estimates for aggregate queries using a small size sample, and has been used widely for approximate query processing. A key question in SRS is how to partition a target sample size among different strata. While Neyman allocation provides a solution that minimizes the variance of an estimate using this sample, it works under the assumption that each stratum is abundant, i.e., has a large number of data points to choose from. This assumption may not hold in general: one or more strata may be bounded, and may not contain a large number of data points, even though the total data size may be large. We first present VOILA, an offline method for allocating sample sizes to strata in a variance-optimal manner, even for the case when one or more strata may be bounded. We next consider SRS on streaming data that are continuously arriving. We show a lower bound, that any streaming algorithm for SRS must have (in the worst case) a variance that is Ω(r) factor away from the optimal, where r is the number of strata. We present S-VOILA, a practical streaming algorithm for SRS that is locally variance-optimal in its allocation of sample sizes to different strata. Our result from experiments on real and synthetic data show that VOILA can have significantly (1.4 to 50.0 times) smaller variance than Neyman allocation. The streaming algorithm S-VOILA results in a variance that is typically close to VOILA, which was given the entire input beforehand.

cs.DB↗

arXiv2017

Learning Graphical Models from a Distributed Stream

A current challenge for data management systems is to support the construction and maintenance of machine learning models over data that is large, multi-dimensional, and evolving. While systems that could support these tasks are emerging, the need to scale to distributed, streaming data requires new models and algorithms. In this setting, as well as computational scalability and model accuracy, we also need to minimize the amount of communication between distributed processors, which is the chief component of latency. We study Bayesian networks, the workhorse of graphical models, and present a communication-efficient method for continuously learning and maintaining a Bayesian network model over data that is arriving as a distributed stream partitioned across multiple processors. We show a strategy for maintaining model parameters that leads to an exponential reduction in communication when compared with baseline approaches to maintain the exact MLE (maximum likelihood estimation). Meanwhile, our strategy provides similar prediction errors for the target distribution and for classification tasks.

cs.AI↗

arXiv2017

A Change-Sensitive Algorithm for Maintaining Maximal Bicliques in a Dynamic Bipartite Graph

We consider the maintenance of maximal bicliques from a dynamic bipartite graph that changes over time due to the addition or deletion of edges. When the set of edges in a graph changes, we are interested in knowing the change in the set of maximal bicliques (the "change"), rather than in knowing the set of maximal bicliques that remain unaffected. The challenge in an efficient algorithm is to enumerate the change without explicitly enumerating the set of all maximal bicliques. In this work, we present (1) near-tight bounds on the magnitude of change in the set of maximal bicliques of a graph, due to a change in the edge set (2) a "change-sensitive" algorithm for enumerating the change in the set of maximal bicliques, whose time complexity is proportional to the magnitude of change that actually occurred in the set of maximal bicliques in the graph. To our knowledge, these are the first algorithms for enumerating maximal bicliques in a dynamic graph, with such provable performance guarantees. Our algorithms are easy to implement, and experimental results show that their performance exceeds that of current baseline implementations by orders of magnitude.

cs.DS↗

arXiv2016

Work-Efficient Parallel and Incremental Graph Connectivity

On an evolving graph that is continuously updated by a high-velocity stream of edges, how can one efficiently maintain if two vertices are connected? This is the connectivity problem, a fundamental and widely studied problem on graphs. We present the first shared-memory parallel algorithm for incremental graph connectivity that is both provably work-efficient and has polylogarithmic parallel depth. We also present a simpler algorithm with slightly worse theoretical properties, but which is easier to implement and has good practical performance. Our experiments show a throughput of hundreds of millions of edges per second on a $20$-core machine.

cs.DS↗

arXiv2014

Mining Maximal Cliques from an Uncertain Graph

We consider mining dense substructures (maximal cliques) from an uncertain graph, which is a probability distribution on a set of deterministic graphs. For parameter 0 < α < 1, we present a precise definition of an α-maximal clique in an uncertain graph. We present matching upper and lower bounds on the number of α-maximal cliques possible within an uncertain graph. We present an algorithm to enumerate α-maximal cliques in an uncertain graph whose worst-case runtime is near-optimal, and an experimental evaluation showing the practical utility of the algorithm.

cs.DS↗