Related papers: Influences in Mixing Measures
Influence functions offer a principled way to trace model predictions back to training data, but their use in deep learning is hampered by the need to invert a large, ill-conditioned Hessian matrix. Approximations such as Generalised…
We examine two aspects of the mathematical basis for two-tier voting systems, such as that of the Council of the European Union. These aspects concern the use of square-root weights and the choice of quota. Square-root weights originate in…
We study the mathematical properties of probabilistic processes in which the independent actions of $n$ players (`causes') can influence the outcome of each player (`effects'). In such a setting, each pair of outcomes will generally be…
We show that the correlations in stochastic outputs of time-distributed weak measurements can be used to study the dynamics of an individual quantum object, with a proof-of-principle setup based on small Faraday rotation caused by a single…
Much of interesting complex biological behaviour arises from collective properties. Important information about collective behaviour lies in the time and space structure of fluctuations around average properties, and two-point correlation…
Estimators based on influence functions (IFs) have been shown to be effective in many settings, especially when combined with machine learning techniques. By focusing on estimating a specific target of interest (e.g., the average effect of…
In this paper we study the volatility and its probability distribution function for the cumulative production based on the experience curve hypothesis. This work presents a generalization of the study of volatility in [1], which addressed…
Recommendation systems have received considerable attention recently. However, most research has been focused on improving the performance of collaborative filtering (CF) techniques. Social networks, indispensably, provide us extra…
This paper considers convolution equations that arise from problems such as measurement error and non-parametric regression with errors in variables with independence conditions. The equations are examined in spaces of generalized functions…
The analysis of practical probabilistic models on the computer demands a convenient representation for the available knowledge and an efficient algorithm to perform inference. An appealing representation is the influence diagram, a network…
Complex systems are often modeled as Boolean networks in attempts to capture their logical structure and reveal its dynamical consequences. Approximating the dynamics of continuous variables by discrete values and Boolean logic gates may,…
In this paper, we apply Devroye inequality to study various statistical estimators and fluctuations of observables for processes. Most of these observables are suggested by dynamical systems. These applications concern the co-variance…
How to estimate heterogeneity, e.g. the effect of some variable differing across observations, is a key question in political science. Methods for doing so make simplifying assumptions about the underlying nature of the heterogeneity to…
Preferences of individuals are distributions of elements generated by generalized functions. Models of economic decision-making derived from such distributions are consistent with results of physiological experiments, and explain any…
Large-scale black-box models have become ubiquitous across numerous applications. Understanding the influence of individual training data sources on predictions made by these models is crucial for improving their trustworthiness. Current…
The development of state-of-the-art systems in different applied areas of machine learning (ML) is driven by benchmarks, which have shaped the paradigm of evaluating generalisation capabilities from multiple perspectives. Although the…
The global dynamics of event cascades are often governed by the local dynamics of peer influence. However, detecting social influence from observational data is challenging due to confounds like homophily and practical issues like missing…
This paper surveys mathematical models, structural results and algorithms in controlled sensing with social learning in social networks. Part 1, namely Bayesian Social Learning with Controlled Sensing addresses the following questions: How…
Being able to correctly aggregate the beliefs of many people into a single belief is a problem fundamental to many important social, economic and political processes such as policy making, market pricing and voting. Although there exist…
We present a model of voting behaviour based on a version of aggregated overdispersed multinomial distributions; relative to a similar model by \citet{BP86}, our model is based on more realistic assumptions and free from certain…