As datasets capturing human choices grow in richness and scale -- particularly in online domains -- there is an increasing need for choice models that escape traditional choice-theoretic axioms such as regularity, stochastic transitivity, and Luce's choice axiom. In this work we introduce the Pairwise Choice Markov Cha…
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48 results for “Luce axioms”
Bayesian model eliminates feedback loops in personalization systems.
problem Feedback loops in user choice systems based on limited exposure.
method Bayesian choice model based on Luce axioms, fair and efficient.
result Low regret in learning to present, accurate preference estimates with minimal interactions.
Paper connects Plackett-Luce and Cox models for preference estimation.
problem Estimating preferences from annotated data.
method Connects Plackett-Luce model to Cox Proportional Hazards model.
result Implications of the connection between the two models.
Understanding how users navigate in a network is of high interest in many applications. We consider a setting where only aggregate node-level traffic is observed and tackle the task of learning edge transition probabilities. We cast it as a preference learning problem, and we study a model where choices follow Luce's a…
The aggregation of k-ary preferences is a historical and important problem, since it has many real-world applications, such as peer grading, presidential elections and restaurant ranking. Meanwhile, variants of Plackett-Luce model has been applied to aggregate k-ary preferences. However, there are two urgent issues sti…
Researchers show mixtures of ranking models are generally identifiable.
problem Understanding when and how parameters of mixtures of ranking models can be uniquely determined.
method Algebraic geometry framework applied to verify the number of solutions in polynomial systems.
result Popular mixtures of ranking models with two components are generically identifiable.
Paper tackles non-identifiability of mixture models in partial order datasets.
problem Non-identifiability of mixture models in datasets with partial orders.
method Proved non-identifiability conditions and proposed GMM algorithms.
result GMM algorithms for learning mixtures of two Plackett-Luce models are consistent.
The paper analyzes RLHF with human feedback and provides convergence results for MLE and pessimistic MLE.
problem Improving RLHF with human feedback from pairwise or -wise comparisons.
method Theoretical framework for RLHF with convergence analysis of MLE and pessimistic MLE.
result MLE fails but pessimistic MLE provides improved policies under certain coverage assumptions.
Proposes variance reduction for optimizing permutation models.
problem High variance in gradient estimates for discrete latent variables.
method Control variates for the Plackett-Luce distribution.
result Optimization of black-box functions over permutations using SGD.
Algorithm selects k arms from context-dependent options using Plackett-Luce model.
problem Selecting k arms from context-dependent options with Plackett-Luce feedback.
method Proposes CPPL algorithm inspired by UCB, evaluated on synthetic and real data.
result Demonstrates effectiveness of CPPL algorithm in online algorithm selection.
The purpose of this note is introduce a new axiom (called the Descent Axiom) in the theory of -spin cohomological field theories. This axiom explains the origin of gravitational descendants in this theory. Furthermore, the Descent Axiom immediately implies the Vanishing Axiom, explicating the latter (which has no a …
This paper optimizes slate decision systems for large action spaces.
problem Optimizing large-scale decision systems with arbitrary reward functions.
method A policy optimization framework with a novel relaxation of decision functions.
result Demonstrates the effectiveness of the proposed method on large action spaces.
PLD distills knowledge using choice-theoretic Plackett-Luce model.
problem Model compression and knowledge transfer between large and small networks.
method PLD uses a weighted list-wise ranking loss based on the Plackett-Luce model.
result PLD achieves consistent gains across diverse architectures and distillation methods.
We consider PAC-learning a good item from -subsetwise feedback information sampled from a Plackett-Luce probability model, with instance-dependent sample complexity performance. In the setting where subsets of a fixed size can be tested and top-ranked feedback is made available to the learner, we give an algorithm w…
Criterions for constancy of the holomorphic sectional curvature and the antiholomorphic sectional curvature are proved for almost Hermitian manifolds. It is shown, that an almost Hermitian manifold satisfying the axiom of antiholomorphic planes or the axiom of antiholomorphic spheres is a real or a complex space form.
The paper improves spectral ranking methods for diverse comparison graphs.
problem Estimating preference scores from multiway comparisons with heterogeneous sizes.
method Develops a two-step spectral method for estimating preference scores and their uncertainties.
result The two-step spectral method achieves the same asymptotic efficiency as the Maximum Likelihood Estimator (MLE).
New RLHF approach mitigates bias in aligning LLMs with human preferences.
problem Algorithmic bias in RLHF leading to preference collapse.
method Preference Matching (PM) RLHF, using PM regularizer and conditional variant.
result 29% to 41% improvement in alignment with human preferences.
Here, an axiom of spheres in Finsler geometry is proposed and it is proved that if a Finslerian manifold satisfies the axiom of spheres then it is of constant flag curvature.
Elo ratings learn model parameters quickly using Markov chains.
problem Ranking players in online settings.
method Bradley--Terry--Luce model and Markov chain theory.
result Elo learns model parameters at a competitive rate.
A Morse complex for Axiom A flows on smooth manifolds.
problem Constructing a finite-dimensional cohomological complex for Axiom A flows.
method Defining anisotropic Sobolev spaces and spectral projectors.
result The cohomology of the constructed complex is isomorphic to De Rham cohomology.
Study Vassiliev invariants and periodic orbits of Axiom A flows.
problem Calculating Vassiliev invariants and writhe for periodic orbits of Axiom A flows.
method Asymptotic analysis of Vassiliev invariants and writhe.
result Obtained asymptotics for Vassiliev invariants and writhe of periodic orbits.
The axiom of θ-holomorphic 2-planes is introduced. It is proved, that if an almost Hermitian manifold satisfies this axiom for a fixed θ, 0< θ< π/2, then it is a real space form.
Paper quantifies uncertainty in pairwise comparison models.
problem Uncertainty quantification in sparse Bradley-Terry-Luce models.
method Unified proof strategy for MLE and spectral estimator.
result Sharp and uniform non-asymptotic expansions for estimators.
New algorithm learns human preferences from few comparisons efficiently.
problem Learning human preferences from limited comparison feedback.
method Formulated as D-optimal design for Plackett-Luce model, solved using randomized Frank-Wolfe algorithm.
result Proposed algorithm efficiently solves D-optimal design problem for Plackett-Luce objective.
We propose a novel and flexible rank-breaking-then-composite-marginal-likelihood (RBCML) framework for learning random utility models (RUMs), which include the Plackett-Luce model. We characterize conditions for the objective function of RBCML to be strictly log-concave by proving that strict log-concavity is preserved…
Treating a conjecture, P^#P != NP, on the separation of complexity classes as an axiom, an implication is found in three manifold topology with little obvious connection to complexity theory. This is reminiscent of Harvey Friedman's work on finitistic interpretations of large cardinal axioms.
CRS model improves ranking data modeling with theoretical guarantees.
problem Lack of rich, multimodal models for ranking data.
method Contextual Repeated Selection (CRS) model for multimodal ranking data.
result CRS model significantly outperforms existing methods in various ranking contexts.
It is known, that if a 2m-dimensional Kahler manifold satisfies the axiom of holomorphic 2n-spheres (1<n<m) or the axiom of antiholomorphic n-spheres (2<n), it is of constant holomorphic sectional curvature. In this paper the same result is obtained under weaker assumptions.
The notion of Courant algebroid was introduced by Liu, Weinstein and Xu in 1997. Its definition consists of five axioms and an assumption for a derivation. It is shown that two of the axioms and the assumption for the derivation follow from the rest of the axioms.
New method reduces variance in estimating PL model expectations.
problem High variance in Monte Carlo estimates of PL model expectations.
method Combining Gumbel top-k trick with quasi-Monte Carlo sampling.
result More sample-efficient estimators of PL model expectations.
Random utility theory models an agent's preferences on alternatives by drawing a real-valued score on each alternative (typically independently) from a parameterized distribution, and then ranking the alternatives according to scores. A special case that has received significant attention is the Plackett-Luce model, fo…
Efficiently calculates PL model likelihood for partitioned preference data.
problem Computational infeasibility of calculating PL model likelihood for partitioned preference data.
method Random utility model formulation and efficient numerical integration approach.
result Proposed method outperforms existing LTR baselines and scales to real-world tasks.
We studied the axiom of anti-invariant 2-spheres and the axiom of co-holomorphic -spheres. We proved that a nearly Kählerian manifold satisfying the axiom of anti-invariant 2-spheres is a space of constant holomorphic sectional curvature. We also showed that an almost Hermitian manifold of dimension $2m\geq…
Hierarchical Partial-Order Models for Ranking
problem Rank aggregation combining ordered lists
method Hierarchical partial-order models
result Bayesian inference for latent poset hierarchy
New axioms justify ES without NRC, linking it to mean-ES portfolio selection.
problem Economic axioms for portfolio risk assessment and mean-ES portfolio selection.
method Introducing concentration aversion as an alternative to NRC, establishing axiomatic foundations.
result Concentration aversion uniquely characterizes the family of ES and provides new formulas.
The famous theorems of Cartan, related to the axiom of -planes, and Leung-Nomizu about the axiom of -spheres were extended to Kähler geometry by several authors. In this paper we replace the strong notions of totally geodesic submanifolds (-planes) and extrinsic spheres (-spheres) by a wider class of specia…
Paper proposes efficient and accurate initialization and EM algorithm for PL mixture models.
problem Initialization issues and combinatorial complexity in PL likelihood maximization.
method Initialization algorithm and EM algorithm for true log-likelihood maximization.
result Proposed algorithm provides accurate initial estimates and efficiently maximizes true log-likelihood.
Solves clustering contradictions by high-dimensional embedding with wide gaps.
problem Kleinberg's clustering axioms are contradictory.
method Embedding in high-dimensional space with wide gaps between clusters.
result Handles clustering contradictions by design.
Shapley values criticized for feature selection, leading to new insights.
problem Using Shapley values for feature selection is problematic.
method Introduced and critiqued Shapley values as feature selection tools, using counterexamples and simulations.
result Shapley values may not always align with feature selection goals.
It is proved, that if an almost Hermitian manifold satisfies the axiom of coholomorphic spheres, it is conformal flat.
We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.
Study examines how machine learning attribution methods reflect risk in finance.
problem Ensuring machine learning attribution methods accurately reflect underlying risks in finance.
method Examined Shapley value and Integrated Gradients, and derived axioms from asset pricing domain knowledge.
result Neither Shapley value nor Integrated Gradients can satisfy all axioms for reflecting risks accurately.
The second author previously discussed how classical complexity separation conjectures, we call them "axioms", have implications in three manifold topology: polynomial length stings of operations which preserve certain Jones polynomial evaluations cannot produce exponential simplifications of link diagrams. In this pap…
Caratheodory's axiom limits arbitrage in resource-limited systems.
problem Non-arbitrage constraints in resource-limited financial systems.
method Preserving Caratheodory's axiom in resource-limited systems.
result Exponential family is the necessary geometric structure for both thermodynamics and finance.
Kleinberg introduced three natural clustering properties, or axioms, and showed they cannot be simultaneously satisfied by any clustering algorithm. We present a new clustering property, Monotonic Consistency, which avoids the well-known problematic behaviour of Kleinberg's Consistency axiom, and the impossibility resu…
In this paper we propose a Bayesian nonparametric model for clustering partial ranking data. We start by developing a Bayesian nonparametric extension of the popular Plackett-Luce choice model that can handle an infinite number of choice items. Our framework is based on the theory of random atomic measures, with the pr…
Axioms for Automated Market Makers: A Mathematical Framework in FinTech and Decentralized Financeq-fin.MF
The paper establishes axioms for AMMs to ensure fair pricing and fee structures.
problem Ensuring fair and efficient pricing in decentralized finance (DeFi) AMMs.
method Formulating axioms on utility functions to characterize swap sizes and pricing oracles.
result Most existing AMMs satisfy the proposed axioms, and a new AMM is proposed with desirable properties.
New method uses rank-conditioned Horvitz-Thompson estimation for unbiased sample reuse in Plackett-Luce best-of-K objective.
problem Estimating the expected maximum reward in Plackett-Luce draws without replacement.
method Rank-conditioned Horvitz-Thompson estimation with joint-score REINFORCE for unbiased sample reuse.
result Unbiased estimation of the Plackett-Luce best-of-K objective with finite second moment guarantees.