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In this paper, we consider sparse networks consisting of a finite number of non-overlapping communities, i.e. disjoint clusters, so that there is higher density within clusters than across clusters. Both the intra- and inter-cluster edge…
This paper addresses a fundamental problem in random variate generation: given access to a random source that emits a stream of independent fair bits, what is the most accurate and entropy-efficient algorithm for sampling from a discrete…
For nonparametric regression in the streaming setting, where data constantly flow in and require real-time analysis, a main challenge is that data are cleared from the computer system once processed due to limited computer memory and…
We study streaming algorithms for the interval selection problem: finding a maximum cardinality subset of disjoint intervals on the line. A deterministic 2-approximation streaming algorithm for this problem is developed, together with an…
The Hierarchical Heavy Hitters problem extends the notion of frequent items to data arranged in a hierarchy. This problem has applications to network traffic monitoring, anomaly detection, and DDoS detection. We present a new streaming…
In this paper, we investigate the quantization of the output of a binary input discrete memoryless channel that maximizing the mutual information between the input and the quantized output under an entropy-constrained of the quantized…
We study the problem of computing the \textsc{Maxima} of a set of $n$ $d$-dimensional points. For dimensions 2 and 3, there are algorithms to solve the problem with order-oblivious instance-optimal running time. However, in higher…
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…
We consider the problem of estimating an upper bound on the capacity of a memoryless channel with unknown channel law and continuous output alphabet. A novel data-driven algorithm is proposed that exploits the dual representation of…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
In this work, we consider the problem of online (real-time, single-shot) estimation of static or slow-varying parameters along quantum trajectories in quantum dynamical systems. Based on the measurement signal of a continuously-monitored…
The problem of communicating sensor measurements over shared networks is prevalent in many modern large-scale distributed systems such as cyber-physical systems, wireless sensor networks, and the internet of things. Due to bandwidth…
Deep within the networks of distributed systems, one often finds anomalies that affect their efficiency and performance. These anomalies are difficult to detect because the distributed systems may not have sufficient sensors to monitor the…
Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good…
In the first of these two papers we demonstrated that assuming streams delineate orbits can lead to order one errors in potential parameters for realistic Galactic potentials. Motivated by the need for an improvement on orbit-fitting, we…
This paper introduces a method for calculating the quantum relative entropy of channels, an essential quantity in quantum channel discrimination and resource theories of quantum channels. By building on recent developments in the…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
Motivated by cloud computing, a number of recent works have studied annotated data streams and variants thereof. In this setting, a computationally weak verifier (cloud user), lacking the resources to store and manipulate his massive input…
This thesis derives, tests and applies two linear projection algorithms for machine learning under non-stationarity. The first finds a direction in a linear space upon which a data set is maximally non-stationary. The second aims to…
One of the most popular approaches to multi-target tracking is tracking-by-detection. Current min-cost flow algorithms which solve the data association problem optimally have three main drawbacks: they are computationally expensive, they…