Related papers: On the identifiability of mixtures of ranking mode…
We propose a novel combinatorial inference framework to conduct general uncertainty quantification in ranking problems. We consider the widely adopted Bradley-Terry-Luce (BTL) model, where each item is assigned a positive preference score…
In this paper we address the identifiability and efficient learning problems of finite mixtures of Plackett-Luce models for rank data. We prove that for any $k\geq 2$, the mixture of $k$ Plackett-Luce models for no more than $2k-1$…
Mixtures of ranking models have been widely used for heterogeneous preferences. However, learning a mixture model is highly nontrivial, especially when the dataset consists of partial orders. In such cases, the parameter of the model may…
Rankings and ratings are commonly used to express preferences but provide distinct and complementary information. Rankings give ordinal and scale-free comparisons but lack granularity; ratings provide cardinal and granular assessments but…
Phylogenetic mixture models are statistical models of character evolution allowing for heterogeneity. Each of the classes in some unknown partition of the characters may evolve by different processes, or even along different trees. The…
Recent work has shown that finite mixture models with $m$ components are identifiable, while making no assumptions on the mixture components, so long as one has access to groups of samples of size $2m-1$ which are known to come from the…
Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is…
This work concerns learning probabilistic models for ranking data in a heterogeneous population. The specific problem we study is learning the parameters of a Mallows Mixture Model. Despite being widely studied, current heuristics for this…
In this paper, we consider mixtures of multinomial logistic models (MNL), which are known to $\epsilon$-approximate any random utility model. Despite its long history and broad use, rigorous results are only available for learning a uniform…
In this paper, we consider mixtures of two Mallows models for top-$k$ rankings, both with the same location parameter but with different scale parameters, i.e., a mixture of concentric Mallows models. This situation arises when we have a…
Mixture models have been widely used in modeling of continuous observations. For the possibility to estimate the parameters of a mixture model consistently on the basis of observations from the mixture, identifiability is a necessary…
While hidden class models of various types arise in many statistical applications, it is often difficult to establish the identifiability of their parameters. Focusing on models in which there is some structure of independence of some of…
Phylogenetic data arising on two possibly different tree topologies might be mixed through several biological mechanisms, including incomplete lineage sorting or horizontal gene transfer in the case of different topologies, or simply…
I present here a simple proof that, under general regularity conditions, the standard parametrization of generalized linear mixed model is identifiable. The proof is based on the assumptions of generalized linear mixed models on the first…
The problem of identifiability of finite mixtures of finite product measures is studied. A mixture model with $K$ mixture components and $L$ observed variables is considered, where each variable takes its value in a finite set with…
A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable -- that is, whether parameter values can be inferred from noiseless data -- directly from the combinatorics…
The Bradley-Terry-Luce (BTL) model is a classic and very popular statistical approach for eliciting a global ranking among a collection of items using pairwise comparison data. In applications in which the comparison outcomes are observed…
Linear compartmental models are a widely used tool for analyzing systems arising in biology, medicine, and more. In such settings, it is essential to know whether model parameters can be recovered from experimental data. This is the…
Mixtures of Mallows models are a popular generative model for ranking data coming from a heterogeneous population. They have a variety of applications including social choice, recommendation systems and natural language processing. Here we…
Identifiability of phylogenetic models is a necessary condition to ensure that the model parameters can be uniquely determined from data. Mixture models are phylogenetic models where the probability distributions in the model are convex…