Related papers: Streaming Algorithms for High-Dimensional Robust S…
Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with `Big Data' analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well…
This paper presents a novel high speed clustering scheme for high dimensional data streams. Data stream clustering has gained importance in different applications, for example, in network monitoring, intrusion detection, and real-time…
Many classical algorithms are known for computing the convex hull of a set of $n$ point in $\mathbb{R}^2$ using $O(n)$ space. For large point sets, whose size exceeds the size of the working space, these algorithms cannot be directly used.…
In this paper, we study streaming and online algorithms in the context of randomness in the input. For several problems, a random order of the input sequence---as opposed to the worst-case order---appears to be a necessary evil in order to…
In this paper, we study streaming algorithms that minimize the number of changes made to their internal state (i.e., memory contents). While the design of streaming algorithms typically focuses on minimizing space and update time, these…
Emerging applications of machine learning in numerous areas involve continuous gathering of and learning from streams of data. Real-time incorporation of streaming data into the learned models is essential for improved inference in these…
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…
A streaming algorithm to compute the spectral proper orthogonal decomposition (SPOD) of stationary random processes is presented. As new data becomes available, an incremental update of the truncated eigenbasis of the estimated…
Many well-known, real-world problems involve dynamic data which describe the relationship among the entities. Hypergraphs are powerful combinatorial structures that are frequently used to model such data. For many of today's data-centric…
In this work we present an overview of statistical learning, followed by a survey of robust streaming techniques and challenges, culminating in several rigorous results proving the relationship that we motivate and hint at throughout the…
A streaming algorithm is adversarially robust if it is guaranteed to perform correctly even in the presence of an adaptive adversary. Recently, several sophisticated frameworks for robustification of classical streaming algorithms have been…
In the adversarially robust streaming model, a stream of elements is presented to an algorithm and is allowed to depend on the output of the algorithm at earlier times during the stream. In the classic insertion-only model of data streams,…
In the real world, data streams are ubiquitous -- think of network traffic or sensor data. Mining patterns, e.g., outliers or clusters, from such data must take place in real time. This is challenging because (1) streams often have high…
In this thesis, we explore streaming algorithms for approximating constraint satisfaction problems (CSPs). The setup is roughly the following: A computer has limited memory space, sees a long "stream" of local constraints on a set of…
Robust statistics aims to compute quantities to represent data where a fraction of it may be arbitrarily corrupted. The most essential statistic is the mean, and in recent years, there has been a flurry of theoretical advancement for…
Constrained $k$-submodular maximization is a general framework that captures many discrete optimization problems such as ad allocation, influence maximization, personalized recommendation, and many others. In many of these applications,…
In large-scale applications including medical imaging, collocation differential equation solvers, and estimation with differential privacy, the underlying linear inverse problem can be reformulated as a streaming problem. In theory, the…
Many existing algorithms for streaming geometric data analysis have been plagued by exponential dependencies in the space complexity, which are undesirable for processing high-dimensional data sets. In particular, once $d\geq\log n$, there…
In this paper, we show that if the optimization function is restricted-strongly-convex (RSC) and restricted-smooth (RSM) -- a rich subclass of weakly submodular functions -- then a streaming algorithm with constant factor approximation…
Robust streaming, the study of streaming algorithms that provably work when the stream is generated by an adaptive adversary, has seen tremendous progress in recent years. However, fundamental barriers remain: the best known algorithm for…