Related papers: Constructions for Clumps Statistics
A composite likelihood is a non-genuine likelihood function that allows to make inference on limited aspects of a model, such as marginal or conditional distributions. Composite likelihoods are not proper likelihoods and need therefore…
Goulden and Jackson introduced a very powerful method to study the distributions of certain consecutive patterns in permutations, words, and other combinatorial objects which is now called the cluster method. There are a number of natural…
Clustering attempts to partition data instances into several distinctive groups, while the similarities among data belonging to the common partition can be principally reserved. Furthermore, incomplete data frequently occurs in many…
The Conway-Maxwell-Poisson (CMP) distribution is a natural two-parameter generalisation of the Poisson distribution which has received some attention in the statistics literature in recent years by offering flexible generalisations of some…
Using Chen-Stein method in combination with size-biased couplings, we obtain the multivariate Poisson approximation in terms of the Wasserstein distance. As applications, we study the multivariate Poisson approximation of the distribution…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
A sequence of geometric random variables of length $n$ is a sequence of $n$ independent and identically distributed geometric random variables ($\Gamma_1, \Gamma_2, \dots, \Gamma_n$) where $\mathbb{P}(\Gamma_j=i)=pq^{i-1}$ for…
As is the case of many signals produced by complex systems, language presents a statistical structure that is balanced between order and disorder. Here we review and extend recent results from quantitative characterisations of the degree of…
Statistical methods for reconstructing networks from repeated measurements typically assume that all measurements are generated from the same underlying network structure. This need not be the case, however. People's social networks might…
Compression of integer sets and sequences has been extensively studied for settings where elements follow a uniform probability distribution. In addition, methods exist that exploit clustering of elements in order to achieve higher…
Optimal quantization for mixed distributions has emerged as a compelling area of study. In this work, we have focused on a mixed distribution formed from two uniform distributions with partially overlapping supports. For this class of…
A computational theory for clustering and a semi-supervised clustering algorithm is presented. Clustering is defined to be the obtainment of groupings of data such that each group contains no anomalies with respect to a chosen grouping…
Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…
Inflection graphs are highly complex networks representing relationships between inflectional forms of words in human languages. For so-called synthetic languages, such as Latin or Polish, they have particularly interesting structure due to…
Fix two words over the binary alphabet $\{0,1\}$, and generate iid Bernoulli$(p)$ bits until one of the words occurs in sequence. This setup, commonly known as Penney's ante, was popularized by Conway, who found (in unpublished work) a…
Collective human behaviors are analyzed using the time series of word appearances in blogs. As expected, we confirm that the number of fluctuations is approximated by a Poisson distribution for very-low-frequency words. A non-trivial…
Additive composition (Foltz et al, 1998; Landauer and Dumais, 1997; Mitchell and Lapata, 2010) is a widely used method for computing meanings of phrases, which takes the average of vector representations of the constituent words. In this…
In this paper we consider the normalized lengths of the factors of some factorizations of random words. First, for the \emph{Lyndon factorization} of finite random words with $n$ independent letters drawn from a finite or infinite totally…
The paper advocates the use of a statistical tool dedicated to the exploration of data samples populated by several sources of events. This new technique, called sPlot, is able to unfold the contributions of the different sources to the…
Lambda calculus is the basis of functional programming and higher order proof assistants. However, little is known about combinatorial properties of lambda terms, in particular, about their asymptotic distribution and random generation.…