We develop efficient methods to approximate maximum entropy distributions for pairwise moments.
problem Intractability of calculating exact maximum entropy distributions.
method Design distributions that approximate maximum entropy distributions while maintaining comparable entropy.
result Approximation guarantees for log-partition functions comparable to low-temperature limits.
New algorithm learns permutations mixtures with optimal sample complexity.
problem Learning mixtures of permutations in high-dimensional settings.
method Combining groups of pairwise comparisons and combinatorial method of moments.
result Optimal sample complexity proportional to log(n) for high-dimensional data.
Exact simulation of correlated binary outcomes using PMF constraints and linear programming.
problem Simulating dependent Bernoulli outcomes with specific means and correlations.
method Formulate the problem over the joint Bernoulli PMF, impose constraints, and solve as a linear program. Use convex-hull characterization and truncated-moment completion scheme for feasibility and simulation.
result Exact simulation framework for correlated binary outcomes, providing a convex-hull characterization and truncated-moment completion scheme.
The Johnson-Lindenstrauss Lemma allows for the projection of n points in p−dimensional Euclidean space onto a k−dimensional Euclidean space, with k≥3ε2−2ε324lnn, so that the pairwise distances are preserved within a factor of 1±ε. Here, working directly with the distributions of the …
Exact pairwise ranking is achievable but not possible under noisy comparisons.
problem Recovering the exact rank of items from noisy pairwise comparisons.
method Information-theoretic upper and lower bounds using the SST model and combinatorial arguments.
result Sharp information-theoretic bounds match in the parametric limit and outperform previous methods.
Paper shows robustness of kernel-based pairwise learning without strict assumptions.
problem Statistical robustness of kernel-based pairwise learning under minimal conditions.
method No assumptions on input and output spaces; derives influence function and robustness.
result Qualitative robustness of kernel-based estimator established.
Bayesian approach optimizes crowdsourced ranking with limited budget.
problem Efficiently collect high-quality pairwise comparisons for accurate ranking.
method Bayesian Markov decision process for dynamic item and worker selection.
result Proposed policy achieves high ranking accuracy with lower labeling cost.
Spectral learning extends matrix methods to tensors for better latent variable modeling.
problem Limitations of matrix-based spectral methods in capturing non-Gaussian data.
method Extend spectral decomposition to tensor-based methods for higher-order moments.
result Tensor decomposition can identify latent effects missed by matrix methods.
New method uses geometric moments for accurate machine learning potentials.
problem Creating high-dimensional potential energy surfaces efficiently.
method Feed-forward neural networks with invariant local molecular descriptors based on geometric moments.
result Accuracy comparable to established models, high efficiency.
The problem of classifying Einstein solvmanifolds, or equivalently, Ricci soliton nilmanifolds, is known to be equivalent to a question on the variety of n-dimensional complex nilpotent Lie algebra laws. Namely, one has to determine which GL(n)-orbits in this variety have a critical point of the squared norm of the mom…
GEM-T generates synthetic tabular data by fitting moments, outperforming neural networks.
problem Generating synthetic tabular data from limited or sensitive real-world data.
method Generative Entropy Maximization (MaxEnt) for tables, capturing nth-order interactions.
result GEM-T matches or exceeds deep neural network approaches in 23 out of 34 datasets.
Polynomial-time algorithm for clustering mixtures with separation Δ=Ω(√(log k)).
problem Clustering mixtures of mean-separated Gaussians in high dimensions.
method Polynomial-time algorithm using implicit moment estimation.
result Achieves almost optimal clustering guarantee with separation Δ=Ω(√(log k)).
The study finds dense clusters of solutions in a simple neural network model, providing bounds for their existence.
problem Exploring the existence of minimizers in a simple neural network model with binary weights.
method Formulating the learning problem as a constraint satisfaction problem and computing moment bounds for the existence of solutions.
result First rigorous steps toward proving the existence of dense clusters of solutions in certain parameter regimes.
Financial markets are a classical example of complex systems as they comprise many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns. Spin glass models have been applied and gave some valuable results but at the price…
We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. We define the Gaussian fractional Bethe free energy in terms of the moment parameters of the approximate marginals, derive a lower and an upper bound on the fractional Beth…
We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. As an extension of Welling and Teh (2001), we define the Gaussian fractional Bethe free energy in terms of the moment parameters of the approximate marginals and derive an …
New model reduces bias in crowdsourced pairwise comparisons.
problem Crowdsourced pairwise comparisons are biased due to perceptual factors.
method factorBT model accounts for irrelevant factors affecting worker answers.
result factorBT produces more accurate rankings than previous models.
Sparse random projections simplify complex choice models.
problem Estimating models with large choice sets.
method Sparse random projections followed by cyclic monotonicity moment inequalities.
result The method works well in simulations and real data applications.
Geometric framework for consistent pairwise comparisons reduces inconsistency.
problem Inconsistency in pairwise comparisons matrices.
method Generalized pairwise comparison matrices to Lie group G, provided necessary and sufficient consistency criteria, and proposed geometric interpretation. result Found a geometric interpretation and basic criteria for finding nearest consistent matrices.
Torus graphs analyze multivariate phase coupling among brain signals.
problem Identifying coordinated phase changes across multiple brain regions.
method Torus graphs based on full exponential family with pairwise interactions.
result Torus graphs accurately identify conditional associations in multivariate phase data.
Paper introduces differential pairwise privacy for secure metric learning.
problem Securely measuring similarities of individuals given sensitive pairwise data.
method Develops differential pairwise privacy (DPP) to protect sensitive pairwise data.
result Achieves pairwise data privacy without significant performance loss.
Paper studies SGD stability and optimization error in pairwise learning.
problem Stability and optimization error of SGD for pairwise learning.
method Established stability and optimization error trade-offs for SGD in convex, strongly convex, and non-convex settings.
result Lower bounds for SGD optimization error and excess expected risk.
Cross-entropy loss linked to metric learning, outperforming complex pairwise losses.
problem Improving metric learning performance without complex optimization schemes.
method Theoretical analysis linking cross-entropy to pairwise losses, showing cross-entropy as an upper bound and equivalent to mutual information maximization.
result Minimizing cross-entropy is equivalent to maximizing mutual information, leading to state-of-the-art performance.
ROVAE uses noisy pairwise comparisons to disentangle factors in VAEs.
problem Disentangling factors in VAEs requires an inductive bias.
method Robust Ordinal VAE (ROVAE) incorporates noisy pairwise ordinal comparisons to disentangle factors.
result ROVAE outperforms existing methods and is more robust to noisy comparisons.
Develops a statistical framework to measure uncertainty in model rankings based on human preferences.
problem Uncertainty in model rankings based on human preferences due to mismatch between human and model preferences.
method Statistical framework using pairwise comparisons by humans and models to provide rank-sets for each model.
result Rank-sets constructed using only pairwise comparisons by strong models often do not cover the true ranking of human preferences.
Improves labeling quality in machine learning with pairwise feedback.
problem Scalability and quality of labeled datasets in machine learning.
method Incorporates pairwise feedback into the programmatic creation of labeled datasets.
result Even a small number of pairwise feedback sources can substantially improve label quality.
As one of the most important types of (weaker) supervised information in machine learning and pattern recognition, pairwise constraint, which specifies whether a pair of data points occur together, has recently received significant attention, especially the problem of pairwise constraint propagation. At least two reaso…
A method for classification using pairwise similarities and unlabeled data.
problem Handling pairwise similarities and unlabeled data for classification.
method Empirical risk minimization approach to create an unbiased risk estimator.
result Derives an unbiased risk estimator for handling both similarities and unlabeled data.
Paper proposes Pcomp classification for binary classification with pairwise confidence comparisons.
problem Lack of pointwise labels due to privacy, confidentiality, or security reasons.
method Developed Pcomp classification, derived an unbiased risk estimator (URE), and improved it using correction functions and consistency regularization.
result Demonstrated the effectiveness of Pcomp classification methods.
Optimal binary autoencoder learns from pairwise correlations.
problem Learning binary autoencoders efficiently.
method Formulates binary autoencoder as biconvex optimization problem using pairwise correlations. Finds optimal decoder through convex optimization.
result Optimal binary autoencoder reconstructs inputs with worst-case optimal loss.
Study on pairwise counter-monotonicity, a type of negative dependence.
problem Understanding and quantifying extremal negative dependence structures.
method Established stochastic representation and invariance property; showed implications and connections.
result Pairwise counter-monotonicity implies negative association and joint mix dependence.
This study considers a model of the income distribution of agents whose pairwise interaction is asymmetric and price-invariant. Asymmetric transactions are typical for chain-trading groups who arrange their business such that commodities move from senior to junior partners and money moves in the opposite direction. The…
This paper examines the problem of ranking a collection of objects using pairwise comparisons (rankings of two objects). In general, the ranking of n objects can be identified by standard sorting methods using nlog2n pairwise comparisons. We are interested in natural situations in which relationships among the o…
Conditions for curves on a torus with specific pairwise intersections.
problem Finding curves on a torus with prescribed pairwise intersections.
method Necessary and sufficient conditions for curves on a torus with given pairwise intersections.
result Necessary and sufficient conditions for the existence of curves on a torus with specific pairwise intersections.
Analyzes GJR-GARCH moments for efficient predictive distributions.
problem Estimating moments of GARCH processes for accurate predictions.
method Derives analytic expressions for GJR-GARCH moments and their limits.
result Analytic moments provide excellent approximate predictive distributions.
Enhances matrix completion with pairwise penalties for latent features.
problem Improving prediction performance in matrix completion.
method Proposes a general optimization framework with non-/convex pairwise penalty functions and develops an efficient algorithm.
result The proposed framework outperforms standard matrix completion methods, especially in scenarios with latent subgroup structures.
New method improves neural network classification accuracy and confidence.
problem Improving neural network classification accuracy and confidence.
method Pairwise coupling of convolutional neural networks.
result Bayes covariant method provides higher accuracy and better sureness predictions.
EM converges for mixtures of many linear regressions with SNR > Ω(k).
problem Convergence of EM algorithm for mixtures of linear regressions.
method Analysis of EM algorithm convergence for mixtures of linear regressions with arbitrary number of components.
result EM converges to true parameters with SNR > Ω(k), independent of parameter norms.
Paper characterizes and represents pairwise causal background knowledge for improved causal inference.
problem Improving causal inference by handling pairwise causal constraints.
method Graphical characterization, direct causal clause (DCC), unified representation, MPDAG, polynomial-time algorithms.
result Pairwise causal background knowledge uniquely decomposes into MPDAG and DCCs, improving causal effect identification.
Paper establishes statistical inference for pairwise comparison models.
problem Statistical inference for pairwise comparison models when the number of subjects diverges.
method Identifies Fisher information matrix as a weighted graph Laplacian for asymptotic normality.
result Near-optimal asymptotic normality result for maximum likelihood estimator.
Proposes a novel tensor-based approach for multi-level link prediction.
problem Inferring potential links from observed networks.
method Tensor-based joint network embedding capturing pairwise and hyperlinks.
result Improves hyperlink and pairwise link prediction accuracy.
Enhances clustering performance by integrating tensor similarity.
problem Noise contamination and imbalance in samples or features hinder accurate clustering.
method Proposes a high-order similarity matrix from tensor similarity, which captures spatial information and complements pairwise similarity.
result The proposed IPS2 method significantly outperforms previous similarity-based methods on real-world datasets.
Pairwise fairness for ranking and regression models.
problem Ensuring fairness in ranking and regression models with protected groups and attributes.
method Developed pairwise fairness metrics for ranking and regression, using constrained optimization and robust optimization techniques.
result Efficient and effective solutions for training problems, demonstrated through experiments.
A new method calculates fractional moments using the moment-generating function.
problem Computing fractional moments from probability densities.
method Integral framework based on moment-generating function.
result Exact integral expressions for various types of moments.
Unified analysis of kernel ridge regression methods for pairwise learning.
problem Theoretical analysis of kernel-based pairwise learning methods.
method Unified review and analysis of kernel ridge regression methods.
result Kronecker kernel ridge regression unifies and explains existing methods.
Study compares weak and homotopy moment maps in multisymplectic geometry.
problem Existence and equivariance of moment maps in multisymplectic geometry.
method Comparison of weak and homotopy moment maps.
result Analysis of existence and equivariance phenomena.
S3C2 uses Siamese networks for semi-supervised clustering with pairwise constraints.
problem Semi-supervised clustering with pairwise constraints.
method S3C2 decomposes SSC into two classification tasks: first, using Siamese networks to label unlabeled pairs; second, using the labeled dataset for clustering.
result S3C2 outperforms existing SSC methods on various datasets.
Paper develops active learning for clustering unknown pairwise similarities.
problem Learning positive and negative pairwise similarities efficiently.
method Generic active learning framework for correlation clustering.
result Demonstrates effectiveness of query strategies in clustering.