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In this paper, we propose a broad and general sequential sampling scheme, which incorporates four different types of sampling procedures: i) the classic Anscombe-Chow-Robbins purely sequential sampling procedure; ii) the ordinary…
In this paper, we consider several efficient data structures for the problem of sampling from a dynamically changing discrete probability distribution, where some prior information is known on the distribution of the rates, in particular…
Irregular repetition slotted Aloha (IRSA) has shown significant advantages as a modern technique for uncoordinated random access with massive number of users due to its capability of achieving theoretically a throughput of $1$ packet per…
Generating random variates from high-dimensional distributions is often done approximately using Markov chain Monte Carlo. In certain cases, perfect simulation algorithms exist that allow one to draw exactly from the stationary…
Many real phenomena may be modelled as random closed sets in $\mathbb{R}^d$, of different Hausdorff dimensions. In many real applications, such as fiber processes and $n$-facets of random tessellations of dimension $n\leq d$ in spaces of…
We survey recent results of normal and anomalous diffusion of two types of random motions with long memory in ${\Bbb R}^d$ or ${\Bbb Z}^d$. The first class consists of random walks on ${\Bbb Z}^d$ in divergence-free random drift field,…
We study channel simulation and distributed matching, two fundamental problems with several applications to machine learning, using a recently introduced generalization of the standard rejection sampling (RS) algorithm known as Ensemble…
In this paper, we propose a compressive random access (CRA) scheme using multiple resource blocks (RBs) to support massive connections for machine type communications (MTC). The proposed CRA scheme is scalable. As a result, if the number of…
We examine diffusion-limited aggregation for a one-dimensional random walk with long jumps. We achieve upper and lower bounds on the growth rate of the aggregate as a function of the number of moments a single step of the walk has. In this…
We extend the classical preferential attachment random graph model to random simplicial complexes. At each stage of the model, we choose one of the existing $k$-simplices with probability proportional to its $k$-degree. The chosen…
This paper presents a novel sequential estimator for the direction-of-arrival and polynomial coefficients of wideband polynomial-phase signals impinging on a sensor array. Addressing the computational challenges of Maximum-likelihood…
Improving Importance Sampling estimators for rare event probabilities requires sharp approx- imations of the optimal density leading to a nearly zero-variance estimator. This paper presents a new way to handle the estimation of the…
Recently, random feature attentions (RFAs) are proposed to approximate the softmax attention in linear time and space complexity by linearizing the exponential kernel. In this paper, we first propose a novel perspective to understand the…
We analyze the list-decodability, and related notions, of random linear codes. This has been studied extensively before: there are many different parameter regimes and many different variants. Previous works have used complementary styles…
Density regression characterizes the conditional density of the response variable given the covariates, and provides much more information than the commonly used conditional mean or quantile regression. However, it is often computationally…
We consider learning problems over training sets in which both, the number of training examples and the dimension of the feature vectors, are large. To solve these problems we propose the random parallel stochastic algorithm (RAPSA). We…
In big data analysis, a simple task such as linear regression can become very challenging as the variable dimension $p$ grows. As a result, variable screening is inevitable in many scientific studies. In recent years, randomized algorithms…
A recently proposed theory for diffusion-limited aggregation (DLA), which models this system as a random branched growth process, is reviewed. Like DLA, this process is stochastic, and ensemble averaging is needed in order to define…
Constraints can be interpreted in a broad sense as any kind of explicit restriction over the parameters. While some constraints are defined directly on the parameter space, when they are instead defined by known behaviour on the model,…
The present PhD dissertation focuses on modern random access (RA) techniques. In the first part an slot- and frame-asynchronous RA scheme adopting replicas, successive interference cancellation and combining techniques is presented and its…