Related papers: Concentration inequalities and cut-off phenomena f…
We follow the time sequence of binary elastic collisions in a small collection of hard-core particles. Intervals between the collisions are characterized by the numbers of collisions of different pairs in a given time. It was shown…
We consider a version of D. Price's model for the growth of a bibliographic network, where in each iteration a constant number of citations is randomly allocated according to a weighted combination of accidental (uniformly distributed) and…
In this paper we consider a well-known generalization of the Barab\'asi and Albert preferential attachment model - the Buckley-Osthus model. Buckley and Osthus proved that in this model the degree sequence has a power law distribution. As a…
In practice, optimization models are often prone to unavoidable inaccuracies due to dubious assumptions and corrupted data. Traditionally, this placed special emphasis on risk-based and robust formulations, and their focus on…
Randomness in scientific estimation is generally assumed to arise from unmeasured or uncontrolled factors. However, when combining subjective probability estimates, heterogeneity stemming from people's cognitive or information diversity is…
These are lecture notes written at the University of Zurich during spring 2014 and spring 2015. The first part of the notes gives an introduction to probability theory. It explains the notion of random events and random variables,…
In this paper we test the composite hypothesis that lifetimes follow an exponential distribution based on observed randomly right censored data. Testing this hypothesis is complicated by the presence of this censoring, due to the fact that…
Background: Pairwise and network meta-analyses using fixed effect and random effects models are commonly applied to synthesise evidence from randomised controlled trials. The models differ in their assumptions and the interpretation of the…
Classification is an important statistical learning tool. In real application, besides high prediction accuracy, it is often desirable to estimate class conditional probabilities for new observations. For traditional problems where the…
The classic model of computable randomness considers martingales that take real or rational values. Recent work by Bienvenu et al. (2012) and Teutsch (2014) shows that fundamental features of the classic model change when the martingales…
The Matthew effect describes the phenomenon that in societies the rich tend to get richer and the potent even more powerful. It is closely related to the concept of preferential attachment in network science, where the more connected nodes…
Statistical analysis is an important tool to distinguish systematic from chance findings. Current statistical analyses rely on distributional assumptions reflecting the structure of some underlying model, which if not met lead to problems…
We generalize the stochastic revealed preference methodology of McFadden and Richter (1990) for finite choice sets to settings with limited consideration. Our approach is nonparametric and requires partial choice set variation. We impose a…
In most countries, basic research is supported by research councils that select, after peer review, the individuals or teams that are to receive funding. Unfortunately, the number of grants these research councils can allocate is not…
Despite the central role of self-assembled groups in animal and human societies, statistical tools to explain their composition are limited. We introduce a statistical framework for cross-sectional observations of groups with exclusive…
Random matrix theory is a useful tool in the study of the physics of multiple scattering systems, often striking a balance between computation speed and physical rigour. Propagation of waves through thick disordered media, as arises in for…
Recently we discovered (cond-mat/0212043) that the majority of scientific citations are copied from the lists of references used in other papers. Here we show that a model, in which a scientist picks three random papers, cites them,and also…
Some statements have one well-defined continuation (e.g., "the Eiffel Tower is in [Paris]"), whereas others have a natural distribution over multiple options (e.g., "the weighted coin flip was [Heads/Tails].") We argue that language model…
A fundamental tool in network information theory is the covering lemma, which lower bounds the probability that there exists a pair of random variables, among a give number of independently generated candidates, falling within a given set.…
We show a Talagrand-type concentration inequality for Multi-Task Learning (MTL), using which we establish sharp excess risk bounds for MTL in terms of distribution- and data-dependent versions of the Local Rademacher Complexity (LRC). We…