Learning from pairwise measurements naturally arises from many applications, suchasrankaggregation,ordinalembedding,andcrowdsourcing.

We provide numerical experiments to corroborate our theory.

The paper considers a family of statistical models for pairwise measurements, in which we observe scores that come from triplets of the form (user, item1, item2). The problem is to estimate the underlying score function of user-item pair, which is assumed to be low-rank, and the observation to be generated by a natural exponential family. The authors address the problem from a novel angle as a semiparametric estimation problem, which avoids the need to specify the log-partition function in the natural exponential family. A penalized contrastive estimator is derived and its consistency and error bound are analyzed. Numerical simulation supports the rate established in the bound.

Given a set of hidden variables with an a-priori Markov structure, we derive an online algorithm which approximately updates the posterior as pairwise measurements between the hidden variables become available. The update is performed using Assumed Density Filtering: to incorporate each pairwise measurement, we compute the optimal Markov structure which represents the true posterior and use it as a prior for incorporating the next measurement. We demonstrate the resulting algorithm by cal- culating globally consistent trajectories of a robot as it navigates along a 2D trajectory. To update a trajectory of length t, the update takes O(t). When all conditional distributions are linear-Gaussian, the algorithm can be thought of as a Kalman Filter which simplifies the state covariance matrix after incorporating each measurement.

Learning from pairwise measurements naturally arises from many applications, such as rank aggregation, ordinal embedding, and crowdsourcing. However, most existing models and algorithms are susceptible to potential model misspecification. In this paper, we study a semiparametric model where the pairwise measurements follow a natural exponential family distribution with an unknown base measure. Such a semiparametric model includes various popular parametric models, such as the Bradley-Terry-Luce model and the paired cardinal model, as special cases. To estimate this semiparametric model without specifying the base measure, we propose a data augmentation technique to create virtual examples, which enables us to define a contrastive estimator.

Given a measurement graph $G= (V,E)$ and an unknown signal $r \in \mathbb{R}^n$, we investigate algorithms for recovering $r$ from pairwise measurements of the form $r_i - r_j$; $\{i,j\} \in E$. This problem arises in a variety of applications, such as ranking teams in sports data and time synchronization of distributed networks. Framed in the context of ranking, the task is to recover the ranking of $n$ teams (induced by $r$) given a small subset of noisy pairwise rank offsets. We propose a simple SVD-based algorithmic pipeline for both the problem of time synchronization and ranking. We provide a detailed theoretical analysis in terms of robustness against both sampling sparsity and noise perturbations with outliers, using results from matrix perturbation and random matrix theory. Our theoretical findings are complemented by a detailed set of numerical experiments on both synthetic and real data, showcasing the competitiveness of our proposed algorithms with other state-of-the-art methods.

Learning from pairwise measurements naturally arises from many applications, such as rank aggregation, ordinal embedding, and crowdsourcing. However, most existing models and algorithms are susceptible to potential model misspecification. In this paper, we study a semiparametric model where the pairwise measurements follow a natural exponential family distribution with an unknown base measure. Such a semiparametric model includes various popular parametric models, such as the Bradley-Terry-Luce model and the paired cardinal model, as special cases. To estimate this semiparametric model without specifying the base measure, we propose a data augmentation technique to create virtual examples, which enables us to define a contrastive estimator. In particular, we prove that such a contrastive estimator is invariant to model misspecification within the natural exponential family, and moreover, attains the optimal statistical rate of convergence up to a logarithmic factor. We provide numerical experiments to corroborate our theory.

Learning from pairwise measurements naturally arises from many applications, such as rank aggregation, ordinal embedding, and crowdsourcing. However, most existing models and algorithms are susceptible to potential model misspecification. In this paper, we study a semiparametric model where the pairwise measurements follow a natural exponential family distribution with an unknown base measure. Such a semiparametric model includes various popular parametric models, such as the Bradley-Terry-Luce model and the paired cardinal model, as special cases. To estimate this semiparametric model without specifying the base measure, we propose a data augmentation technique to create virtual examples, which enables us to define a contrastive estimator. In particular, we prove that such a contrastive estimator is invariant to model misspecification within the natural exponential family, and moreover, attains the optimal statistical rate of convergence up to a logarithmic factor. We provide numerical experiments to corroborate our theory.

In many settings, such as protein interactions and gene regulatory networks, collections ofauthor-recipient email, and social networks, the data consist of pairwise measurements, e.g., presence or absence of links between pairs of objects. Analyzing such data with probabilistic models requires nonstandard assumptions, since the usual independence or exchangeability assumptions no longer hold. In this paper, we introduce a class of latent variable models for pairwise measurements: mixedmembership stochastic blockmodels. Models in this class combine a global model of dense patches of connectivity (blockmodel) with a local model to instantiate node-specific variability in the connections (mixed membership). We develop a general variational inference algorithm for fast approximate posterior inference.We demonstrate the advantages of mixed membership stochastic blockmodel with applications to social networks and protein interaction networks.

Given a set of hidden variables with an a-priori Markov structure, we derive an online algorithm which approximately updates the posterior as pairwise measurements between the hidden variables become available. The update is performed using Assumed Density Filtering: to incorporate each pairwise measurement, we compute the optimal Markov structure which represents the true posterior and use it as a prior for incorporating the next measurement. We demonstrate the resulting algorithm by calculating globallyconsistent trajectories of a robot as it navigates along a 2D trajectory. To update a trajectory of length t, the update takes O(t). When all conditional distributions are linear-Gaussian, the algorithm can be thought of as a Kalman Filter which simplifies the state covariance matrix after incorporating each measurement.