323,191 research outputs found
Mallows Models for Top-k Lists
No full textThe classic Mallows model is a widely-used tool to realize distributions on permutations. Motivated by common practical situations, in this paper, we generalize Mallows to model distributions on top-k lists by using a suitable distance measure between top-k lists. Unlike many earlier works, our model is both analytically tractable and computationally efficient. We demonstrate this by studying two basic problems in this model, namely, sampling and reconstruction, from both algorithmic and experimental points of view
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
Sequential Rank and Preference Learning with the Bayesian Mallows Model
No full textThis repository contains code for reproducing all the results in the article "Sequential Rank and Preference Learning with the Bayesian Mallows Model" by Øystein Sørensen, Anja Stein, Waldir Leoncio Netto, and David S. Leslie
A Mallows model for Coxeter groups and buildings
No full textRank data is comprised of a set of complete and partial rankings which reflect preference or standing (examples of such data can be generated by voters, search engines, market survey responses, etc.). Complete rankings (viewed as bijective maps from a set of n items to n ranks) can be identified with the symmetric group S n, and this identification gives rise to a variety of analytic techniques. One such method is a probabilistic soft clustering technique based on the Mallows probability distribution for the symmetric group. This distribution relies on Kendall's tau (a distance on Sn) and is normalized by a sum over the entire space of n! rankings. It can be extended to partial rankings (which differ from complete rankings by allowing multi-way ties at varying ranks), theoretically facilitating the extension of this probabilistic method. Unfortunately, the generalization of the Mallows distribution requires the evaluation of even more complex sums, which quickly become prohibitively large. In this thesis, we present a closed form of Mallows distribution for partial rankings which allows us to extend the clustering method to accommodate arbitrary sets of rank data. In addition, our combinatorial proof of this closed form allows Mallows model and its accompanying closed forms to be generalized to several natural extensions of the symmetric group, namely the flag variety of the finite general linear group and all finite Coxeter groups
Assessing the similarity of distributions - Finite sample performance of the empirical Mallows distance
No full textThe problem of assessing similarity of two cumulative distribution functions (c.d.f.'s) has been the topic of a previous paper by the authors (Munk and Czado (1995)). Here, we developed an asymptotic test based; on a trimmed version of the Mallows distance (Mallows 1972) between two c.d.f.'s F and G. This allows to assess the similarity of two c.d.f.'s with respect to this distance at controlled type I error rate. In particular, this applies to bioequivalence testing within a purely nonparametric setting. In this paper, we investigate the finite sample behavior of this test. The effect of trimming and non equal sample size on the observed power and level is studied. Sample size driven recommendations for the choice of the trimming bounds are given in order to minimize the bias. Finally, assuming normality and homogeneous variances, we simulate the relative efficiency of the Mallows test to the (asymptotically optimal) standard equivalence t test, which reveals the Mallows test as a robust alternative to the standard equivalence t test
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
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
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
Differences in knee extensor strength in healthy-weight and obese children
No full textM. Tsiros, A. Coates, P. Howe, P. Grimshaw, J. Walkley, A. Shield, R. Mallows, A. Hills, M. Kagawa, S. Shultz, J. Buckle
Query-Based Selection of Optimal Candidates under the Mallows Model
No full textWe study the secretary problem in which rank-ordered lists are generated by
the Mallows model and the goal is to identify the highest-ranked candidate
through a sequential interview process which does not allow rejected candidates
to be revisited. The main difference between our formulation and existing
models is that, during the selection process, we are given a fixed number of
opportunities to query an infallible expert whether the current candidate is
the highest-ranked or not. If the response is positive, the selection process
terminates, otherwise, the search continues until a new potentially optimal
candidate is identified. Our optimal interview strategy, as well as the
expected number of candidates interviewed and the expected number of queries
used, can be determined through the evaluation of well-defined recurrence
relations. Specifically, if we are allowed to query times and to make a
final selection without querying (thus, making selections in total) then
the optimum scheme is characterized by thresholds that depend on the
parameter of the Mallows distribution but are independent on the
maximum number of queries.Comment: 28 pages, 2 figures, 2 table
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