The Analysis of Permutations

By R. Plackett. 1975

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Citations in the corpus

Direct Preference Optimization: Your Language Model is Secretly a Reward Model (2023, methodology): “6 uses the Bradley-Terry model, we can similarly derive expressions under the more general Plackett-Luce models [30, 21], shown in Appendix A.3.”
Offline A/B Testing for Recommender Systems (2018, methodology): “Good examples of distributions are the BradleyTerry Luce (BTL) model [3], the Placket-Luce model [4, 7, 20] or more generally Thurstonian models [26, 28].”
Learning Deep Generative Models of Graphs (2018, neutral): “In particular, in the learning to rank literature there is an extensive body of work on learning distributions over permutations, for example the Mallows model (Mallows, 1957) and the Plackett-Luce model (Plackett, 1975; Luce, 1959), which may be used here.”
Toward Continual Learning for Conversational Agents (2017, methodology): “In order to optimize the projection matrix, M , we adopt the Plackett-Luce model (Plackett, 1975).”
Stochastic Beams and Where to Find Them: The Gumbel-Top-k Trick for Sampling Sequences Without Replacement (2019, methodology): “When sampling the complete domain, this is equivalent to the Thurstonian (Thurstone, 1927) interpretation of the Plackett-Luce ranking model (Plackett, 1975; Luce, 1959) as given by Yellott (1977).”
A Nonparametric Approach to Modeling Choice with Limited Data (2009, methodology): “…(transitive) (see Mas-Colell et al. 1995) preferences over all alternatives,3 and that a particular customer will purchase her most preferred product from the offered set according to these preferences; a given customer sampled at different times may well have a distinct set of preferences.”
Preference Ranking Optimization for Human Alignment (2023, background): “When Equation 5 is fully optimized, π PRO is able to consistently generate the most preferred response (with a higher output probability) from a candidate set, thereby capturing human preferences.”
Estimating the Integrated Likelihood via Posterior Simulation Using the Harmonic Mean Identity (2006, methodology): “These probabilities can be used to give the probability of a vote (i.e. candidate ordering) using the Placket-Luce model ( Plackett, 1975) P{xi|p} = n i Y t=1 p ic(i,t) P N s=t p ic(i,s) , where c(i, 1), c(i, 2), . . . , c(i, ni) is the ordered list of the candidates selected by voter i and c(i, ni…”
MM algorithms for generalized Bradley-Terry models (2003, background): “The author does not know of another algorithm in the literature specifically for maximizing the Plackett-Luce likelihood; Plackett (1975) merely states that “the maximum of the likelihood can be determined only by numerical methods.””
Gradient Estimation with Stochastic Softmax Tricks (2020, methodology): “Previously, [57] considered U ∼ Gumbel( θ ) and [31] uses correlated Gumbel-based utilities that induce a Plackett-Luce model [51][65].”
Learning to rank for information retrieval (2009, unknown): “Many famous models have been proposed to represent permutation probability distributions, such as the Luce model [81, 95] and the Mallows model [82].”
Preference-based Online Learning with Dueling Bandits: A Survey (2018, background): “Sz¨or´enyi et al. (2015) assume the underlying probability distribution is a Plackett-Luce (PL) model (Plackett, 1975; Luce, 1959).”
Reward-rational (implicit) choice: A unifying formalism for reward learning (2020, background): “Boltzmann-rational policies are widespread in psychology [13, 14, 15], economics [16, 17, 18, 17], and AI [19, 20, 21, 22, 23] as models of human choices, actions, or inferences.”
Learning to rank: from pairwise approach to listwise approach (2007, methodology): “For example, following the work by Luce (1959), Plackett (1975) de.ned probability models on ranking lists of objects.”
Matrix estimation by Universal Singular Value Thresholding (2012, background): “Numerous extensions and applications have been proposed, for example, [3, 54, 58, 71, 72, 80, 82].”
A mixture of experts model for rank data with applications in election studies (2008, methodology): “…successfully employed to model rank data [see Gormley and Murphy (2006, 2008a)], but alternative rank data models are also available; the Plackett–Luce model for rank data [Plackett (1975)] is a special case of the Benter model in which the dampening parameter vector is constrained such that α = 1.”
Stochastic Optimization of Sorting Networks via Continuous Relaxations (2019, background): “, sn} is the vector of scores parameterizing this distribution (Plackett, 1975).”