Related papers: Replica analysis of a preferential urn model
We consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles. A new particle can either form a new cluster (with probability q) or join an already existing cluster with a…
Prototypal analysis is introduced to overcome two shortcomings of archetypal analysis: its sensitivity to outliers and its non-locality, which reduces its applicability as a learning tool. Same as archetypal analysis, prototypal analysis…
The aim of this paper is twofold. First, three theoretical principles are formalized: randomization, overrepresentation and restriction. We develop these principles and give a rationale for their use in choosing the sampling design in a…
The paper provides a survey of results related to the "$\kappa$-generalized distribution", a statistical model for the size distribution of income and wealth. Topics include, among others, discussion of basic analytical properties,…
It is well known that the probability distribution of high-frequency financial returns is characterized by a leptokurtic, heavy-tailed shape. This behavior undermines the typical assumption of Gaussian log-returns behind the standard…
The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…
Density Ratio Estimation has attracted attention from the machine learning community due to its ability to compare the underlying distributions of two datasets. However, in some applications, we want to compare distributions of random…
Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for…
We study wealth rank correlations in a simple model of macro-economy. To quantify rank correlations between wealth rankings at different times, we use Kendall's $\tau$ and Spearman's $\rho$, Goodman--Kruskal's $\gamma$, and the lists'…
With ever-increasing available data, predicting individuals' preferences and helping them locate the most relevant information has become a pressing need. Understanding and predicting preferences is also important from a fundamental point…
There has been increasing concern within the machine learning community that we are in a reproducibility crisis. As many have begun to work on this problem, all work we are aware of treat the issue of reproducibility as an intrinsic binary…
Beta regression models are a suitable choice for continuous response variables on the unity interval. Random effects add further flexibility to the models and accommodate data structures such as hierarchical, repeated measures and…
This paper is dedicated to a robust ordinal method for learning the preferences of a decision maker between subsets. The decision model, derived from Fishburn and LaValle (1996) and whose parameters we learn, is general enough to be…
By the methods of multitype branching processes in random environment counted by random characteristics we study the tail distribution of busy periods and some other characteristics of the branching type polling systems in which the service…
Inference-time algorithms are an emerging paradigm in which pre-trained models are used as subroutines to solve downstream tasks. Such algorithms have been proposed for tasks ranging from inverse problems and guided image generation to…
We study the learning problem of revealed preference in a stochastic setting: a learner observes the utility-maximizing actions of a set of agents whose utility follows some unknown distribution, and the learner aims to infer the…
With the advent of structured data in the form of social networks, genetic circuits and protein interaction networks, statistical analysis of networks has gained popularity over recent years. Stochastic block model constitutes a classical…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
In numerous predictive scenarios, the predictive model affects the sampling distribution; for example, job applicants often meticulously craft their resumes to navigate through a screening systems. Such shifts in distribution are…
One of the most used priors in Bayesian clustering is the Dirichlet prior. It can be expressed as a Chinese Restaurant Process. This process allows nonparametric estimation of the number of clusters when partitioning datasets. Its key…