Tree Mover's Distance measures graph attributes and improves GNN performance.
problem Measuring generalization and robustness in graph neural networks.
method Introducing Tree Mover's Distance (TMD) for attributed graphs.
result TMD correlates with GNN performance under distribution shifts.
Method learns relational features for Gaifman models from knowledge bases.
problem Structure learning for Gaifman models.
method Relational tree distances to learn relational features.
result Empirical evaluation shows superiority over classical rule-learning.
A new supervised tree-Wasserstein distance improves document classification.
problem Measuring document similarity efficiently and accurately.
method Rewriting Wasserstein distance on tree metric, using contrastive loss for optimization.
result The Supervised Tree-Wasserstein (STW) distance improves document classification accuracy.
This paper approximates 1-Wasserstein distance using tree-based embedding.
problem Computational inefficiency of estimating 1-Wasserstein distance.
method L1-regularized approach to learn tree weights, using shortest path distance as a linear model.
result Tree-Wasserstein distance (TWD) approximates 1-Wasserstein distance efficiently.
Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has demonstrated that metric learning approaches can also be applied to trees, such as m…
Metric learning has the aim to improve classification accuracy by learning a distance measure which brings data points from the same class closer together and pushes data points from different classes further apart. Recent research has demonstrated that metric learning approaches can also be applied to trees, such as m…
New metric learning approach for tree data reduces computation cost.
problem Efficiently computing distances between ordered labeled trees.
method Introduced pq-grams and a differentiable weighted pq-gram distance, combined with LMNN for optimization.
result Significantly reduces computation time for tree classification problems.
The paper tightens bounds on distances between Reeb graphs.
problem Certifying quasi-universality of distances between Reeb graphs.
method Establishes tight bi-Lipschitz bounds for various distances.
result Proves strict universality of the functional contortion distance for contour trees and coincides with interleaving distance for merge trees.
A new tree-Wasserstein distance for high-dimensional data with latent feature hierarchy.
problem Finding meaningful distances between high-dimensional data samples with latent feature hierarchy.
method Proposes a new tree-Wasserstein distance (TWD) for high-dimensional data with a latent feature hierarchy, using diffusion geometry and tree decoding.
result The proposed TWD effectively recovers the latent feature hierarchy and is efficient and scalable.
Optimal transport (\OT) theory defines a powerful set of tools to compare probability distributions. \OT~suffers however from a few drawbacks, computational and statistical, which have encouraged the proposal of several regularized variants of OT in the recent literature, one of the most notable being the \textit{slice…
Locally adaptive clustering for tree delineation.
problem Tree delineation from distance data.
method Locally adaptive hierarchical cluster termination.
result Multi-scale alternative to conventional termination criteria.
This study investigates self-supervised learning with Wasserstein distance on tree structures.
problem Improving self-supervised learning methods using Wasserstein distance.
method Utilized Tree-Wasserstein distance (TWD) and Jeffrey divergence regularization for training.
result A simple combination of softmax function and Tree-Wasserstein distance outperforms cosine similarity-based methods.
The paper proposes a method to infer differentiation trees from RNA velocity data.
problem Reconstructing dynamic cellular processes from sequencing data.
method Defining varifold distances between RNA velocity curves to approximate shortest-path distances in a tree.
result The varifold distance method approximates the shortest-path distance in a tree isomorphic to the target differentiation tree.
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.
Method learns hierarchical representations of samples and features simultaneously.
problem Hierarchical structures in samples and features not considered by existing methods.
method Jointly learns hierarchical representations via Tree-Wasserstein Distance alternating between samples and features.
result Method improves performance in link prediction and node classification tasks.
PhyloVAE learns tree topologies without supervision.
problem Learning accurate tree representations from evolutionary data.
method Unsupervised learning via variational autoencoders with efficient tree generation.
result PhyloVAE generates high-resolution tree topologies efficiently.
Paper extends tree bijection for hyperbolic surfaces without requiring cusps.
problem Computing volumes and distances on hyperbolic surfaces without cusps.
method Extend tree bijection to half-tight cylinders, using Busemann function.
result Tree bijection can now be applied to surfaces without cusps.
This paper introduces a new method to cluster qualitative attribute data using tree structures.
problem Clustering qualitative attribute data, especially when values are not in Euclidean space.
method Developed a joint learning mechanism to iteratively learn trees representing qualitative values' order relationships.
result The joint learning mechanism successfully clusters qualitative attribute data, yielding accurate results.
Paper develops a new method to analyze 3D tree-like objects.
problem Analyzing complex geometrical and topological variations in 3D tree-like objects.
method Extended SRVF representation and new metric for tree-shaped 3D objects.
result Captures full elasticity and topological variations of branches.
Optimal algorithms learn Gaussian trees and polytrees from data.
problem Learning undirected Gaussian trees and polytrees from data.
method Two approaches: Chow-Liu algorithm for tree structure and modified PC algorithm for polytree structure.
result Explicit finite-sample guarantees and matching lower bounds for both approaches.
The paper improves decision tree stability for health care applications.
problem Stability of decision trees in health care applications.
method Introducing a new distance metric to determine tree stability and proposing a novel training methodology.
result On average, a 4.6% decrease in predictive power yields a 38% increase in model stability.
Width trees link link invariants and bridge number.
problem Understanding link invariants through geometric structures.
method Associate width trees to links and use their geometric properties to bound link invariants.
result Width trees uniquely realize certain link invariants under specific conditions.
Proposes a hierarchical clustering method for positive and negative dissimilarities.
problem Clustering dissimilarities, especially positive and negative.
method Hierarchical correlation clustering followed by tree preserving embedding.
result Performance on various datasets.
New algorithm solves unbalanced optimal transport on trees in quasi-linear time.
problem Efficiently solving unbalanced optimal transport problems on trees.
method Proposed an algorithm that solves a more general unbalanced optimal transport problem exactly in quasi-linear time on a tree metric.
result Solves unbalanced optimal transport on trees in quasi-linear time (less than one second for a tree with one million nodes).
A new metric for comparing measures on tree systems reduces computational burden.
problem Heavy computation in Optimal Transport problems.
method Introducing tree systems and a novel metric (Tree-Sliced Wasserstein distance on Systems of Lines, TSW-SL).
result TSW-SL performs favorably compared to Sliced Wasserstein and its variants.
We describe in this paper a geometric construction in the projective p-adic plane that gives, together with a suitable notion of p-adic convexity, some open subsets of P 2 .Q p / naturally endowed with a "Hilbert" distance and a transitive action of PGL.2; Q p / by isometries. ese open sets are natural analogues of the…
Efficiently learns tree-structured Ising models with minimal samples.
problem Learning tree-structured Ising models efficiently and accurately.
method Plug-in estimator for mutual information using the Chow-Liu algorithm.
result Proper learning of tree-structured Ising models with O(nlnn/ε2) samples. New relation on paths is not transitive.
problem Extending tree-like property to non-Lipschitz paths.
method Analyzing a fractal construction in the plane.
result The resulting relation is not an equivalence relation.
We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance between two points i and j is smaller than the distance between the points i an…
New framework estimates staged tree models using hierarchical clustering on the probability simplex.
problem Estimating staged tree models with context-specific dependencies.
method Hierarchical clustering on the probability simplex, using simplex-based divergences and linkage methods.
result Total Variation divergence with Ward.D2 linkage produces staged trees with better model fit, structure recovery, and computational efficiency.
Optimal sample complexity for contrastive learning of distances.
problem Minimum labeled tuples needed for high accuracy in learning distances.
method Analyzes sample complexity in various distance settings, proving tight bounds.
result Almost optimal bound on sample complexity for learning ℓp distances. Paper disproves symmetry of stars at infinity in a specific graph.
problem Symmetry of stars at infinity in a specific graph.
method Defined incidence geometry of stars at infinity; provided an example.
result Relation of one boundary point being included in a star of another is not symmetric.
DiFF-RF detects point-wise and collective anomalies using random partitioning trees.
problem Detecting anomalies in data, especially collective anomalies.
method Random partitioning binary trees with distance-based leaves and semi-supervised learning.
result DiFF-RF significantly outperforms isolation forest and one-class SVM.
SMERF improves distance learning with decision forests.
problem Subpar inference and prediction due to poor distances.
method Decision forest algorithm for distance learning.
result Empirically demonstrates ability to approximate arbitrary distances and identify features.
The paper monitors stock market relationships using network analysis and statistical control charts.
problem Detecting abnormal changes in the financial market network structure.
method Network construction using distance methods, hierarchical clustering, and Shewhart control charts.
result Abnormal changes in financial market relationships can be detected using statistical process control.
We study in this paper a variant of Wasserstein barycenter problem, which we refer to as tree-Wasserstein barycenter, by leveraging a specific class of ground metrics, namely tree metrics, for Wasserstein distance. Drawing on the tree structure, we propose an efficient algorithmic approach to solve the tree-Wasserstein…
Gromov-Wasserstein (GW) is a powerful tool to compare probability measures whose supports are in different metric spaces. GW suffers however from a computational drawback since it requires to solve a complex non-convex quadratic program. We consider in this work a specific family of cost metrics, namely \textit{tree me…
We provide a systematic study of the problem of finding the source of a rumor in a network. We model rumor spreading in a network with a variant of the popular SIR model and then construct an estimator for the rumor source. This estimator is based upon a novel topological quantity which we term \textbf{rumor centrality…
Ensembles of decision trees perform well on many problems, but are not interpretable. In contrast to existing approaches in interpretability that focus on explaining relationships between features and predictions, we propose an alternative approach to interpret tree ensemble classifiers by surfacing representative poin…
We generalize to tree graphs obtained by connecting path graphs an oracle result obtained for the Fused Lasso over the path graph. Moreover we show that it is possible to substitute in the oracle inequality the minimum of the distances between jumps by their harmonic mean. In doing so we prove a lower bound on the comp…
We consider the problem of estimating the evolutionary history of a set of species (phylogeny or species tree) from several genes. It is known that the evolutionary history of individual genes (gene trees) might be topologically distinct from each other and from the underlying species tree, possibly confounding phyloge…
We study the problem of learning a tree Ising model from samples such that subsequent predictions made using the model are accurate. The prediction task considered in this paper is that of predicting the values of a subset of variables given values of some other subset of variables. Virtually all previous work on graph…
Many machine learning models can be attacked with adversarial examples, i.e. inputs close to correctly classified examples that are classified incorrectly. However, most research on adversarial attacks to date is limited to vectorial data, in particular image data. In this contribution, we extend the field by introduci…
Two new methods reduce random forest latency and improve accuracy.
problem High latency and memory demands in deep random forest models.
method DiNo and RanBu convert shallow random forests into efficient predictors.
result RanBu matches or exceeds full-depth random forest accuracy with up to 95% reduction in time.
Finding an optimal assignment between two sets of objects is a fundamental problem arising in many applications, including the matching of `bag-of-words' representations in natural language processing and computer vision. Solving the assignment problem typically requires cubic time and its pairwise computation is expen…
Paper tackles NNS under uncertainty with improved algorithms.
problem Efficient nearest neighbor search with noisy distance estimates.
method Combines cover trees and multi-armed bandits for optimal performance.
result Optimal dependence on dataset size and unknown geometry achieved.
New tree structure for pseudo-Anosovs from interval maps.
problem Understanding pseudo-Anosovs from interval maps.
method Tree structure on pseudo-Anosovs using rational numbers.
result Deepened dictionary between invariants.
A bijection proves a polynomial volume for genus-0 hyperbolic surfaces with boundaries.
problem Proving the Weil-Petersson volume polynomial in boundary lengths for genus-0 surfaces.
method Generalizing a tree bijection to handle geodesic boundaries, extending spine construction.
result Explicit formula for three-point function in Weil-Petersson random surfaces.