We introduce a new family of minmax rank aggregation problems under two distance measures, the Kendall τ and the Spearman footrule. As the problems are NP-hard, we proceed to describe a number of constant-approximation algorithms for solving them. We conclude with illustrative applications of the aggregation methods on…
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48 results for “aggregation of distances”
IDA adapts to non-iid data in federated learning for medical imaging.
problem Statistical heterogeneity in federated learning data, especially in medical imaging.
method IDA (Inverse Distance Aggregation) is a novel adaptive weighting approach for clients based on meta-information.
result IDA outperforms Federated Averaging in handling unbalanced and non-iid data in federated learning.
Data aggregation improves HAC for resource-constrained systems.
problem Resource constraints in embedded systems limit HAC's applicability.
method Data aggregation with BETULA algorithm reduces memory and runtime requirements.
result HAC can be applied to large datasets on resource-constrained systems.
Sharp bounds found on expert error in binary advice aggregation.
problem Aggregating binary advice from conditionally independent experts.
method Sharp upper and lower bounds on optimal error probability in asymmetric case.
result Sharp bounds recover and sharpen known results in symmetric case.
A new procedure aggregates models to predict data from multiple clusters.
problem Predicting data from multiple clusters with different underlying models.
method Three-step procedure: clustering, model fitting, and aggregation.
result The method outperforms existing models in various prediction problems.
We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any time spot follows a Gaussian mixture distribution, a fact exploited to softly matc…
Probabilistic graphical models are graphical representations of probability distributions. Graphical models have applications in many fields including biology, social sciences, linguistic, neuroscience. In this paper, we propose directed acyclic graphs (DAGs) learning via bootstrap aggregating. The proposed procedure i…
Paper introduces WWAggr for ensemble CPD, improving accuracy and decision threshold selection.
problem Challenges in detecting abrupt distribution shifts in high-dimensional data streams.
method Introduces WWAggr, a novel task-specific ensemble aggregation method based on Wasserstein distance.
result Demonstrates WWAggr outperforms standard aggregation techniques and decision threshold selection.
We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any time position follows a Gaussian mixture distribution, a fact exploited to softly …
Distance metric learning is successful in discovering intrinsic relations in data. However, most algorithms are computationally demanding when the problem size becomes large. In this paper, we propose a discriminative metric learning algorithm, and develop a distributed scheme learning metrics on moderate-sized subsets…
Given a finite family of functions, the goal of model selection aggregation is to construct a procedure that mimics the function from this family that is the closest to an unknown regression function. More precisely, we consider a general regression model with fixed design and measure the distance between functions by …
The paper extends mixability theory to function-valued forecasts, proving various loss functions are mixable.
problem Efficient aggregation of functional and probabilistic forecasts in online prediction games.
method Adapting mixable and exponentially concave loss functions to function-valued forecasts.
result Various loss functions used for probabilistic forecasting are mixable (exp-concave).
Energy distance measures feature heterogeneity in federated learning.
problem Heterogeneity across data sources hinders model aggregation in federated learning.
method Introduced Taylor approximations of energy distance for efficient computation.
result Taylor approximations accurately capture feature discrepancies, improving convergence.
We propose regression networks for the problem of few-shot classification, where a classifier must generalize to new classes not seen in the training set, given only a small number of examples of each class. In high dimensional embedding spaces the direction of data generally contains richer information than magnitude.…
We solve the multi-criteria benchmarking problem by formalizing it as a social choice problem and identifying conditions for meaningful rankings.
problem Aggregating multiple metrics into a single ranking for models in benchmarking problems.
method Formalizing multi-criteria benchmarking as a social choice problem and identifying sufficient conditions for meaningful rankings.
result We prove that meaningful multi-criteria benchmarking becomes possible under certain preference conditions (single-peaked, group-separable, distance-restricted).
We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a current best guess for the distribution, called reference measure, is available. We w…
Collaborative filtering, a widely-used recommendation technique, predicts a user's preference by aggregating the ratings from similar users. As a result, these measures cannot fully utilize the rating information and are not suitable for real world sparse data. To solve these issues, we propose a novel user distance me…
Extends DAMs to Gaussian distributions for efficient pattern storage and retrieval.
problem Limited storage capacity and retrieval methods for non-vector pattern representations.
method Introduces a log-sum-exp energy function over Gaussian distributions, using optimal transport maps for retrieval dynamics.
result Proves exponential storage capacity and provides quantitative retrieval guarantees.
Optimal transport offers an alternative to maximum likelihood for learning generative autoencoding models. We show that minimizing the p-Wasserstein distance between the generator and the true data distribution is equivalent to the unconstrained min-min optimization of the p-Wasserstein distance between the encoder agg…
Boosts kernel two-sample test power with multiple kernels.
problem Detecting differences between two distributions over metric spaces.
method Combining MMD estimates over multiple kernels using Mahalanobis distance.
result More powerful in detecting a wide range of alternatives in finite samples.
New method estimates SW distance using CDFs for scalable data parallelism.
problem Estimating SW distance efficiently for large datasets.
method Estimators based on CDFs of projected measures, avoiding sorting.
result Efficient estimation for large datasets and federated learning.
Study tail risk aggregation under dependence uncertainty.
problem Risk aggregation under dependence uncertainty and hidden dependence.
method Introduce hidden dependence, show compatibility with small perturbations, quantify portfolio risk.
result Small deviations in dependence structure can lead to significant risk underestimation.
This paper improves MDS visualization by adjusting Wasserstein distances for heavy-tailed data.
problem Enhancing Multidimensional Scaling (MDS) for better pattern recognition with heavy-tailed distributions.
method Introduces Max-D-SW, a metric adjustment of Max-Sliced Wasserstein distance that aggregates over orthonormal bases.
result Max-D-SW provides a clear numerical advantage in MDS outcomes, especially for heavy-tailed distributions.
Structural Classification of Locally Stationary Time Series Based on Second-order Characteristicsstat.ME
Efficient method classifies locally stationary time series based on second-order characteristics.
problem Classifying locally stationary time series for various applications.
method Autoregressive approximation, ensemble aggregation, distance-based threshold.
result Zero misclassification error rate asymptotically for mildly differing second-order characteristics.
DFMR improves robustness of learning finite mixture models in distributed settings.
problem Learning finite mixture models in distributed settings with Byzantine failures.
method DFMR leverages pairwise L2 distances to filter and retain local estimates, ensuring robust aggregation.
result DFMR achieves optimal convergence rate and asymptotic equivalence to global maximum likelihood estimate.
Study shows improper learning can outperform proper learning in misspecified models.
problem Misspecification in probabilistic prediction models.
method Investigates the performance of proper and improper learning strategies in misspecified models.
result Improper learning can achieve lower regret compared to proper learning, especially in high-dimensional settings.
We propose unsupervised representation learning and feature extraction from dendrograms. The commonly used Minimax distance measures correspond to building a dendrogram with single linkage criterion, with defining specific forms of a level function and a distance function over that. Therefore, we extend this method to …
Optimal Transport Graph Neural Networks (OT-GNN) improves graph embeddings by using optimal transport.
problem Graph Neural Networks (GNN) often lose structural or semantic information when aggregating node embeddings.
method Combines optimal transport (OT) with parametric graph models to compute graph embeddings from Wasserstein distances between node embeddings and prototype point clouds.
result OT-GNN outperforms popular methods on molecular property prediction tasks and produces smoother graph representations.
Boosting framework for vector-valued prediction with geometric stability.
problem Lack of a general theoretical understanding of aggregation for structured prediction.
method Identifies -stability property and proposes a boosting framework based on exponential reweighting and geometric-median aggregation.
result Obtains exponential decay of empirical divergence error under weak learner condition and -stability.
Here we prove the existence of a new type of the world-sheet string singularities - the cusps that are stable during the finite time. These singularities make the emission of the captured massive quantum particle possible in the frames of the author's model suggested earlier. In aggregate, we have a new mechanism of qu…
Robust VB framework for large datasets with outliers.
problem Handling outliers and contamination in large datasets.
method Divide and conquer approach with geometric median aggregation.
result VM-Posterior distribution preserves contraction properties.
Learning nonlinear dynamics from diffusion data is a challenging problem since the individuals observed may be different at different time points, generally following an aggregate behaviour. Existing work cannot handle the tasks well since they model such dynamics either directly on observations or enforce the availabi…
Enhanced travel time prediction using deep neural networks and road network information.
problem Improving travel time estimation using deep learning models.
method Proposes incorporating road network information into deep learning models for travel time prediction.
result Improved travel time prediction, especially with limited training data.
The paper bounds solutions to complex optimization problems with uncertain data.
problem Distributionally robust optimization problems with multivariate uncertainty sets.
method Conditions and bounds derived for multivariate and univariate Wasserstein distances, Bregman-Wasserstein divergences, and signed Choquet integrals.
result Computable lower and upper bounds for DRO problems, derived from scalar-valued aggregation functions and Wasserstein distances.
A new k-means algorithm using cover trees accelerates clustering.
problem Efficiently clustering large datasets with k-means.
method Combining cover trees with upper and lower bounds.
result Significantly reduces distance computations and improves clustering performance.
Paper proposes a supervised similarity framework for corporate bonds using RF proximities.
problem Challenges in measuring similarity for corporate bonds due to noisy data and lack of ground truth.
method Proposes a supervised similarity framework using Random Forest for corporate bonds, introducing a novel metric to evaluate similarities.
result Random Forest outperforms other methods in evaluating similarities for corporate bonds.
Paper introduces ITD for detecting distributional changes in decentralized learning environments.
problem Detecting distributional changes in decentralized learning environments with data privacy and heterogeneity concerns.
method Introduces Integrated Transportation Distance (ITD) for two-sample testing in federated learning.
result ITD effectively aggregates information across distributed clients, detecting subtle distributional shifts.
Simplifies GNN models by selecting important features for node classification.
problem Challenges in analyzing and selecting important features in GNN models.
method Decoupling feature aggregation and depth, using softmax and L2-normalization.
result FSGNN achieves comparable or higher accuracy than state-of-the-art GNN models.
CDOT optimizes transport between domains preserving both feature and geometric structure.
problem Optimizing transport between heterogeneous domains with preserved feature and geometric structure.
method CDOT uses operator-based regularization to align distance structures, proving pseudometric properties.
result CDOT improves robustness to local geometric variations and is provably convex.
Improves joint distribution learning for high-dimensional datasets with complex correlations.
problem Conditional independence assumption limitations in VAE decoders for high-dimensional datasets.
method Cramer-Wold distance regularization and two-step learning method for flexible prior modeling.
result Effective joint distributional learning for high-dimensional datasets with multiple categorical variables.
A new method clusters complex networks using topological and geometric structure.
problem Clustering complex networks with intricate topology.
method Centroid-based clustering strategy using Wasserstein distance and barycenter for persistence barcodes.
result Demonstrated effectiveness on simulated and real-world networks.
Graphon autoencoder generates graphs with arbitrary sizes using Chebyshev filters.
problem Generating graphs with arbitrary sizes and arbitrary structures.
method Induces graphons from observed graphs, uses Chebyshev filters for latent representation, and learns encoder and decoder to minimize Wasserstein distance.
result Graphon autoencoder provides a new paradigm for graph generation with good generalizability and transferability.
CLASSIX is a fast and explainable clustering method that sorts data and merges groups.
problem Clustering of data with various shapes and dimensions.
method Greedy aggregation followed by cluster merging with scalar parameters.
result CLASSIX performs competitively with state-of-the-art algorithms and provides intuitive explanations.
Performance metrics (error measures) are vital components of the evaluation frameworks in various fields. The intention of this study was to overview of a variety of performance metrics and approaches to their classification. The main goal of the study was to develop a typology that will help to improve our knowledge a…
A new graph kernel uses LCS and Wasserstein distance for better graph comparisons.
problem Graph learning methods can be limited by information from distant vertices and path length constraints.
method Proposes a Graph Kernel based on LCS similarity and Wasserstein distance in a novel metric space.
result The new kernel emphasizes comparisons between similar paths and reduces information loss.
Recent studies have highlighted that deep neural networks (DNNs) are vulnerable to adversarial examples. In this paper, we improve the robustness of DNNs by utilizing techniques of Distance Metric Learning. Specifically, we incorporate Triplet Loss, one of the most popular Distance Metric Learning methods, into the fra…
Most graph kernels are an instance of the class of -Convolution kernels, which measure the similarity of objects by comparing their substructures. Despite their empirical success, most graph kernels use a naive aggregation of the final set of substructures, usually a sum or average, thereby potentially dis…
Introduces CHL, a new loss function for continuous similarity learning.
problem Binary similarity learning limitations.
method CHL is a novel loss function that generalizes histogram loss to continuous similarities.
result CHL solves a wider range of tasks including similarity learning, representation learning, and data visualization.