423 research outputs found
Continuous-time Mallows processes
No full textIn this article, we introduce \textit{Mallows processes}, defined to be
continuous-time c\`adl\`ag processes with Mallows distributed marginals. We
show that such processes exist and that they can be restricted to have certain
natural properties. In particular, we prove that there exists \textit{regular}
Mallows processes, defined to have their inversions numbers
be independent
increasing stochastic processes with jumps of size . We further show that
there exists a unique Markov process which is a regular Mallows process.
Finally, we study properties of regular Mallows processes and show various
results on the structure of these objects. Among others, we prove that the
graph structure related to regular Mallows processes looks like an
\textit{expanded hypercube} where we stacked hypercubes on the dimension
; we also prove that the first jumping times of regular Mallows
processes converge to a Poisson point process.Comment: 23 pages, 1 figur
An R package for permutations, Mallows and Generalized Mallows models
No full text[EN]Probability models on permutations associate a probability value to each of the permutations on n items. This paper considers two popular probability models, the Mallows model and the Generalized Mallows model. We describe methods for making inference, sampling and learning such distributions, some of which are novel in the literature. This paper also describes operations for permutations, with special attention in those related with the Kendall and Cayley distances and the random generation of permutations. These operations are of key importance for the efficient computation of the operations on distributions. These algorithms are implemented in the associated R package. Moreover, the internal code is written in C++
An R package for permutations, Mallows and Generalized Mallows models
No full text[EN]Probability models on permutations associate a probability value to each of the permutations on n items. This paper considers two popular probability models, the Mallows model and the Generalized Mallows model. We describe methods for making inference, sampling and learning such distributions, some of which are novel in the literature. This paper also describes operations for permutations, with special attention in those related with the Kendall and Cayley distances and the random generation of permutations. These operations are of key importance for the efficient computation of the operations on distributions. These algorithms are implemented in the associated R package. Moreover, the internal code is written in C++
Clustered Mallows Model
No full textRankings are a type of preference elicitation that arise in experiments where
assessors arrange items, for example, in decreasing order of utility. Orderings
of n items labelled {1,...,n} denoted are permutations that reflect strict
preferences. For a number of reasons, strict preferences can be unrealistic
assumptions for real data. For example, when items share common traits it may
be reasonable to attribute them equal ranks. Also, there can be different
importance attributions to decisions that form the ranking. In a situation
with, for example, a large number of items, an assessor may wish to rank at top
a certain number items; to rank other items at the bottom and to express
indifference to all others. In addition, when aggregating opinions, a judging
body might be decisive about some parts of the rank but ambiguous for others.
In this paper we extend the well-known Mallows (Mallows, 1957) model (MM) to
accommodate item indifference, a phenomenon that can be in place for a variety
of reasons, such as those above mentioned.The underlying grouping of similar
items motivates the proposed Clustered Mallows Model (CMM). The CMM can be
interpreted as a Mallows distribution for tied ranks where ties are learned
from the data. The CMM provides the flexibility to combine strict and
indifferent relations, achieving a simpler and robust representation of rank
collections in the form of ordered clusters. Bayesian inference for the CMM is
in the class of doubly-intractable problems since the model's normalisation
constant is not available in closed form. We overcome this challenge by
sampling from the posterior with a version of the exchange algorithm
\citep{murray2006}. Real data analysis of food preferences and results of
Formula 1 races are presented, illustrating the CMM in practical situations.Comment: Paper submitted for publicatio
A Central Limit Theorem on Two-Sided Descents of Mallows Distributed Elements of Finite Coxeter Groups
No full textThe Mallows distribution is a non-uniform distribution, first introduced over
permutations to study non-ranked data, in which permutations are weighted
according to their length. It can be generalized to any Coxeter group, and we
study the distribution of where is a
Mallows distributed element of a finite irreducible Coxeter group. We show that
the asymptotic behavior of this statistic is Guassian. The proof uses a
size-bias coupling with Stein's method.Comment: 49 pages, 1 figure. arXiv admin note: text overlap with
arXiv:2005.09802 by other author
PEMILIHAN VARIABEL PADA REGRESI LINIER DENGAN METODE STATISTIK C,MALLOWS
No full textTulisan ini bertujuan untuk mengetahui keidentikan statisik Tp yang didefinisikan Tp WI' -K + 2p dengan statistik Cp Mallows yang didefinisikan
Cp =n + 2p dengan K menyatakan jumlah parameter pada model penuh dan
p menyatakan j umlah parameter pada submodel (model yang telah disederhanakan). Pada estimasi kuadrat terkecil, kedua metode ini akan identik dengan nilai CI- P dan nilai Tp :s; p
A geometric interpretation of Mallows' C-p statistic and an alternative plot in variable selection
No full textMallows' C-p plot is a useful tool for variable selection in linear regression. Though not as popular as the C-p plot, Spjotvoll's F-p and P-p plots are also used in the variable selection procedure. The C-p, F-p and P-p plots are useful in their own right. If the interest is the direct measure of the amount of bias of the submodels and a distributional assumption is not made about the error term, a C-p or F-p plot is used. If a formal testing procedure is to be performed, then a P-p plot is employed. A geometrical approach is used in order to propose an alternative plot that unifies all the information in these three plots, and that has some advantages over them. A Mathematica package has been written to implement the approach. (c) 2007 Elsevier B.V. All rights reserved
A Bayesian Mallows Approach to Non-Transitive Pair Comparison Data: How Human are Sounds?
No full textInternational audienceWe are interested in learning how listeners perceive sounds as having human origins. An experiment was performed with a series of electronically synthesized sounds, and listeners were asked to compare them in pairs. We propose a Bayesian probabilistic method to learn individual preferences from non-transitive pairwise comparison data, as happens when one (or more) individual preferences in the data contradicts what is implied by the others. We build a Bayesian Mallows model in order to handle non-transitive data, with a latent layer of uncertainty which captures the generation of preference misreporting. We then develop a mixture extension of the Mallows model, able to learn individual preferences in a heterogeneous population. The results of our analysis of the musicology experiment are of interest to electroacoustic composers and sound designers, and to the audio industry in general, whose aim is to understand how computer generated sounds can be produced in order to sound more human
Bayesian Preference Learning with the Mallows Model
No full textIn our modern society, with the bourgeoning of e-commerce and online streaming platforms, customers are overwhelmed by the choices. One important approach to solve this problem is recommender systems. Recommender systems learn customers' preferences based on their past interactions with the website/platform, as well as the interactions data of other customers, to eventually provide a list of recommendations that is relevant to the customer.
In this work, the author studied the use of statistical models to learn customers' preferences, with a focus on the Bayesian Mallows Model. The author provided a new approach to learn personal preferences and make personalised recommendations from clicking data. Through experimentation, it was illustrated that the proposed method achieved good balance between recommending items that are closely related to what the customers previously interacted with, while not overlooking the issue of recommendation diversity: that is, recommending the items that are interesting, novel and surprising to the customer. The author also provided a new approach to achieve more computationally efficient preference learning
Linear programming bounds for doubly-even self-dual codes
No full textUsing a variant of linear programming method we
derive a new upper bound on the minimum distance d of doubly-even self-dual codes of length n. Asymptotically, for n growing, it gives d/n <=166315 + o(1), thus improving on the Mallows–
Odlyzko–Sloane bound of 1/6. To establish this, we prove that in any doubly even-self-dual code the distance distribution is asymptotically upper-bounded by the corresponding normalized binomial distribution in a certain interval
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