Related papers: Approximate Majorization

We confirm a conjecture by Everett, Sinclair, and Dankelmann~[Some Centrality results new and old, J. Math. Sociology 28 (2004), 215--227] regarding the problem of maximizing closeness centralization in two-mode data, where the number of…

The p-median problem is a common model for optimal facility location. The task is to place p facilities (e.g., warehouses or schools) in a heterogeneously populated space such that the average distance from a person's home to the nearest…

Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths. Since an exact computation is prohibitive in large networks, several approximation algorithms have been…

We propose a new method for estimating the intrinsic dimension of a dataset by applying the principle of regularized maximum likelihood to the distances between close neighbors. We propose a regularization scheme which is motivated by…

The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…

We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…

One reason why standard formulations of the central limit theorems are not applicable in high-dimensional and non-stationary regimes is the lack of a suitable limit object. Instead, suitable distributional approximations can be used, where…

We prove a limit theorem for the the maximal interpoint distance (also called the diameter) for a sample of n i.i.d. points in the unit ball of dimension 2 or more. The exact form of the limit distribution and the required normalisation are…

We present a technique for constructing suitable posterior probability distributions in situations for which the sampling distribution of the data is not known. This is very useful for modern scientific data analysis in the era of "big…

Dealing with massive data is a challenging task for machine learning. An important aspect of machine learning is function approximation. In the context of massive data, some of the commonly used tools for this purpose are sparsity,…

Distribution learning finds probability density functions from a set of data samples, whereas clustering aims to group similar data points to form clusters. Although there are deep clustering methods that employ distribution learning…

The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…

We consider distributed networks, such as peer-to-peer networks, whose structure can be manipulated by adjusting the rules by which vertices enter and leave the network. We focus in particular on degree distributions and show that, with…

We consider the problem of approximating two, possibly unrelated probability distributions from a single complex-valued function $\psi$ and its Fourier transform. We show that this problem always has a solution within a specified degree of…

Cooperative geolocation has attracted significant research interests in recent years. A large number of localization algorithms rely on the availability of statistical knowledge of measurement errors, which is often difficult to obtain in…

We study the relative entropy between the empirical estimate of a discrete distribution and the true underlying distribution. If the minimum value of the probability mass function exceeds an $\alpha > 0$ (i.e. when the true underlying…

Measuring the importance of nodes in a network with a centrality measure is a core task in any network application. There are many measures available and it is speculated that many encode similar information. We give an explicit non-linear…

What does it mean to be flat? We propose to define it by measuring the maximal variation around a point, or from a dual perspective, the distance to neighboring level sets. After developing some calculus rules, we show how flat minima,…

Consider the task of generating samples from a tilted distribution of a random vector whose underlying distribution is unknown, but samples from it are available. This finds applications in fields such as finance and climate science, and in…

Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…