相关论文: Influence in product spaces

Wisdom of crowds refers to the phenomenon that the aggregate prediction or forecast of a group of individuals can be surprisingly more accurate than most individuals in the group, and sometimes - than any of the individuals comprising it.…

For centuries, it has been widely believed that the influence of a small coalition of voters is negligible in a large election. Consequently, there is a large body of literature on characterizing the likelihood for an election to be…

We study the spread of influence in a social network based on the Linear Threshold model. We derive an analytical expression for evaluating the expected size of the eventual influenced set for a given initial set, using the probability of…

Although copulas are used and defined for various infinite-dimensional objects (e.g. Gaussian processes and Markov processes), there is no prevalent notion of a copula that unifies these concepts. We propose a unified approach and define…

Robust model fitting is a fundamental problem in computer vision: used to pre-process raw data in the presence of outliers. Maximisation of Consensus (MaxCon) is one of the most popular robust criteria and widely used. Recently (Tennakoon…

We present a measure-theoretic condition for a property to hold ``almost everywhere'' on an infinite-dimensional vector space, with particular emphasis on function spaces such as $C^k$ and $L^p$. Like the concept of ``Lebesgue almost…

Recent work has attempted to directly approximate the `function-space' or predictive posterior distribution of Bayesian models, without approximating the posterior distribution over the parameters. This is appealing in e.g. Bayesian neural…

Phase plays a crucial role in many quantum effects including interference. Phase is normally defined in terms of complex numbers that appear when representing quantum states as complex vectors. Here we give an operational definition whereby…

We define the information threshold as the point of maximum curvature in the prior vs. posterior Bayesian curve, both of which are described as a function of the true positive and negative rates of the classification system in question. The…

Quantum inequalities are lower bounds for local averages of quantum observables that have positive classical counterparts, such as the energy density or the Wick square. We establish such inequalities in general (possibly interacting)…

We introduce a new Stata package called summclust that summarizes the cluster structure of the dataset for linear regression models with clustered disturbances. The key unit of observation for such a model is the cluster. We therefore…

The Pinsker inequality lower bounds the Kullback--Leibler divergence $D_{\textrm{KL}}$ in terms of total variation and provides a canonical way to convert $D_{\textrm{KL}}$ control into $\lVert \cdot \rVert_1$-control. Motivated by…

We analyze statistical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. We study particle dynamics with discrete time. We show that a quantum-like interference pattern could appear as a statistical…

Causal spaces have recently been introduced as a measure-theoretic framework to encode the notion of causality. While it has some advantages over established frameworks, such as structural causal models, the theory is so far only developed…

We survey the current state of affairs in the study of thresholds and sharp thresholds in random structures on the occasion of the recent proof of the Kahn--Kalai Conjecture by Park and Pham and the fairly recent proof of the satisfiability…

The Subspace Theorem due to Schmidt (1972) is a broad generalisation of Roth's Theorem in Diophantine Approximation (1955) which, in the same way as the latter, suffers a notorious lack of effectivity. This problem is tackled from a…

This essay considers a simple model of observers that are influenced by the world around them. Consistent quantification of information about such influences results in a great deal of familiar physics. The end result is a new perspective…

We introduce a product in all complex normed vector spaces, which generalizes the inner product of complex inner product spaces. Naturally the question occurs whether the Cauchy-Schwarz inequality is fulfilled. We provide a positive answer.…

The original Hegselmann-Krause (HK) model comprises a set of $n$ agents characterized by their opinion, a number in $[0,1]$. Agent $i$ updates its opinion $x_i$ via taking the average opinion of its neighbors whose opinion differs by at…

Plausibility measures are structures for reasoning in the face of uncertainty that generalize probabilities, unifying them with weaker structures like possibility measures and comparative probability relations. So far, the theory of…