In classification problems, especially those that categorize data into a large number of classes, the classes often naturally follow a hierarchical structure. That is, some classes are likely to share similar structures and features. Those characteristics can be captured by considering a hierarchical relationship among…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
Trend · papers per month
48 results for “hierarchical class structure”
New combinatorial structure for hierarchically hyperbolic spaces.
problem Constructing new hierarchically hyperbolic spaces.
method Combinatorial hierarchical hyperbolicity criterion to construct and clarify HHS structures.
result HHSs admit a combinatorial structure, clarifying the application of the combinatorial HHS criterion.
Paper proposes integrating hierarchical class structure into prototypical network supervision.
problem Improving classification accuracy in tasks with hierarchical class structures.
method Integrates hierarchical class structure (metric) into prototypical network supervision.
result Consistent improvement of error rate weighted by the cost matrix compared to traditional methods.
This work improves metric learning models by incorporating class hierarchies.
problem Class hierarchies are often ignored in classification-based metric learning models.
method Trained softmax classifier and metric learning models with predefined class hierarchies.
result ProxyDR model performs better in hierarchical inference and hierarchy-informed performance.
HCC extends conformal prediction to handle class hierarchies, improving prediction reliability.
problem Uncertainty quantification in classification models with class hierarchy considerations.
method Formulates HCC as a constrained optimization problem, ensuring coverage guarantees with a smaller subset of candidate solutions.
result HCC produces more reliable prediction sets by leveraging class hierarchy information.
Reduces high granularity and dimensionality in hierarchical categorical variables.
problem Overfitting and estimation issues in predictive models due to high granularity and dimensionality.
method Entity embedding and top-down clustering algorithm to reduce granularity and dimensionality.
result The reduced hierarchy improves model fit and complexity balance.
We propose a method to visualize class similarity in large-scale classifiers.
problem Analyzing hierarchical structures and relationships in large-scale classification.
method Compute class similarity based on prediction scores and visualize the class similarity matrix.
result Visualizing class similarity matrices reveals hierarchical structures and relationships.
Hierarchically hyperbolic spaces (HHSs) are a large class of spaces that provide a unified framework for studying the mapping class group, right-angled Artin and Coxeter groups, and many 3--manifold groups. We investigate strongly quasiconvex subsets in this class and characterize them in terms of their contracting pro…
Paper investigates methods to improve classification by inducing a hierarchy from flat labels.
problem Improving classification performance on datasets lacking a natural hierarchy.
method The approach involves clustering conditional distributions and using a hierarchical classifier with the induced hierarchy.
result The methods can discover latent hierarchies and improve accuracy in various applications.
A novel unsupervised domain adaptation method using hierarchical optimal transport.
problem Unsupervised domain adaptation between source and target domains.
method Hierarchical optimal transport, leveraging class labels for structure formation in the source domain and learning probability measures in the target domain.
result The proposed HOT-DA method outperforms state-of-the-art approaches on various datasets.
Hierarchically hyperbolic spaces provide a common framework for studying mapping class groups of finite type surfaces, Teichmüller space, right-angled Artin groups, and many other cubical groups. Given such a space , we build a bordificationcompatible with the hierarchically hyperbolic structure. If $\mathc…
Proves deep networks can learn hierarchical structures efficiently.
problem Understanding how deep networks learn hierarchical structures in data.
method Random Hierarchy Models, gradient-based methods, layerwise training.
result Proves deep networks can efficiently learn hierarchical structures.
Hierarchical CNNs improve diagnosis of GI diseases from histopathological images.
problem Diagnosing GI diseases from histopathological images is challenging due to heterogeneity and shared features.
method Embedded a class hierarchy into a VGGNet to address the hierarchical structure of GI diseases.
result The hierarchical model achieved better results than a flat model for multi-category diagnosis of GI disorders.
Due to myriads of classes, designing accurate and efficient classifiers becomes very challenging for multi-class classification. Recent research has shown that class structure learning can greatly facilitate multi-class learning. In this paper, we propose a novel method to learn the class structure for multi-class clas…
New bicombings found for mapping class groups and Teichmüller spaces.
problem Finding efficient ways to navigate mapping class groups and Teichmüller spaces.
method Explained bicombings via stable cubical intervals in hierarchically hyperbolic spaces.
result Hierarchical hulls are quasi-isometric to finite CAT(0) cube complexes.
Efficient Path Prediction for Semi-Supervised and Weakly Supervised Hierarchical Text Classificationcs.LG
Hierarchical text classification has many real-world applications. However, labeling a large number of documents is costly. In practice, we can use semi-supervised learning or weakly supervised learning (e.g., dataless classification) to reduce the labeling cost. In this paper, we propose a path cost-sensitive learning…
A simple guide to understanding hierarchical causality in complex systems.
problem Understanding hierarchical causality in complex systems.
method Formalizing hierarchical causality in terms of actors and agents, with three key structures.
result The system requires three additional structures: causation classes, aggregation operators, and discrete event-time maps.
Large-scale classification of data where classes are structurally organized in a hierarchy is an important area of research. Top-down approaches that exploit the hierarchy during the learning and prediction phase are efficient for large scale hierarchical classification. However, accuracy of top-down approaches is poor…
Injectivity, cubical approximations and equivariant wall structures beyond CAT(0) cube complexesmath.GR
Survey discusses new ideas in geometric group theory and their applications.
problem Understanding geodesic metric spaces and their equivariant wall structures.
method Introduces and highlights the impact of injective metric spaces and cubical approximation theorem.
result Rich equivariant wall structures in various geodesic metric spaces.
We give several sufficient conditions for uniform exponential growth in the setting of virtually torsion-free hierarchically hyperbolic groups. For example, any hierarchically hyperbolic group that is also acylindrically hyperbolic has uniform exponential growth. In addition, we provide a quasi-isometric characterizati…
Diffusion models reveal a phase transition in reconstructing high-level features.
problem Understanding the hierarchical structure of natural data.
method Study of hierarchical generative models of data using diffusion models.
result The backward diffusion process shows a phase transition at a threshold time, where high-level features suddenly drop in reconstructibility.
Loss assigns examples to classes and superclasses in hierarchical data.
problem Learning from hierarchical classification problems with known class hierarchy.
method Introduces a loss function that considers the hierarchy of classes, aiming for consistent classification across different granularities.
result Improves accuracy and reduces coarse errors in classification compared to cross-entropy loss.
Hierarchical graph clustering is a common technique to reveal the multi-scale structure of complex networks. We propose a novel metric for assessing the quality of a hierarchical clustering. This metric reflects the ability to reconstruct the graph from the dendrogram, which encodes the hierarchy. The optimal represent…
The geometry of genericity in mapping class groups and Teichmüller spaces via CAT(0) cube complexesmath.GT
Develops geometric foundations for sublinear Morse boundaries in mapping class groups and Teichmüller spaces.
problem Capturing generic directions in mapping class groups and Teichmüller spaces.
method Develops tools for modeling hulls of median rays in hierarchically hyperbolic spaces via CAT(0) cube complexes.
result Sublinear Morse boundaries are visibility spaces and admit continuous equivariant injections into the boundary of the curve graph.
We show that many graphs naturally associated to a connected, compact, orientable surface are hierarchically hyperbolic spaces in the sense of Behrstock, Hagen and Sisto. They also automatically have the coarse median property defined by Bowditch. Consequences for such graphs include a distance formula analogous to Mas…
Introduces hierarchical hyperbolic spaces for non-experts.
problem Understanding hierarchical hyperbolic spaces for non-experts.
method No specific method mentioned; aimed at non-experts.
result Introduces hierarchical hyperbolic spaces for non-experts.
Bottom-up algorithms outperform top-down in hierarchical community detection at intermediate levels.
problem Finding the optimal hierarchical community structure in networks.
method A bottom-up algorithm for hierarchical clustering of networks.
result Bottom-up algorithms achieve the information-theoretic threshold for exact recovery at intermediate levels of the hierarchy.
Over the past decade, Deep Convolutional Neural Networks (DCNNs) have shown remarkable performance in most computer vision tasks. These tasks traditionally use a fixed dataset, and the model, once trained, is deployed as is. Adding new information to such a model presents a challenge due to complex training issues, suc…
Three-layer neural networks learn hierarchical polynomial functions efficiently.
problem Learning hierarchical polynomial functions with three-layer neural networks.
method Layerwise gradient descent on square loss, focusing on feature learning.
result Achieves optimal sample complexity for learning hierarchical polynomials.
Tree-based variational inference improves PLN model for hierarchical count data.
problem Limited applicability of PLN model in ecosystems due to lack of hierarchical tree structures.
method Introduced PLN-Tree model integrating structured variational inference techniques.
result Enhanced generative improvements and practical interpretability in microbiome modeling.
We prove that all hierarchically hyperbolic spaces have finite asymptotic dimension and obtain strong bounds on these dimensions. One application of this result is to obtain the sharpest known bound on the asymptotic dimension of the mapping class group of a finite type surface: improving the bound from exponential to …
Sharp theory of neural network scaling laws for hierarchical targets.
problem Learning hierarchical multi-index models in neural networks.
method Sharp information-theoretic scaling laws derived for two-layer neural networks.
result Optimal rates achieved by a simple spectral estimator.
Neural NMF discovers hierarchical topics in multilayer data.
problem Detecting latent hierarchical structure in multilayer data.
method Recursive application of nonnegative matrix factorization (NMF) in layers with backpropagation optimization.
result Neural NMF outperforms other hierarchical NMF methods in synthetic and real-world datasets.
Efficient algorithm for evaluating hierarchical classification methods at multiple operating points.
problem Evaluating hierarchical classification methods at multiple operating points.
method Efficient algorithm to produce operating characteristic curves for any method that assigns scores to every class in the hierarchy.
result Top-down classifiers are dominated by a naive flat softmax classifier across the entire operating range.
New framework for domain adaptation using hierarchical optimal transport.
problem Improving domain adaptation when source and target data distributions differ.
method Proposes a new theoretical framework and hierarchical Wasserstein distance.
result Provides more explicit generalization bounds and aligns specific structures for successful adaptation.
Classifies 3-manifold groups with equivariant hierarchically hyperbolic structures.
problem Classifying 3-manifold groups with equivariant hierarchically hyperbolic structures.
method Construction of suitable quasimorphisms on Seifert pieces to construct actions on quasi-lines.
result 3-manifold groups admit equivariant hierarchically hyperbolic structures.
The study shows how quotients of mapping class groups are hierarchically hyperbolic.
problem Understanding the hierarchical hyperbolicity of mapping class groups and their quotients.
method A combinatorial criterion for hierarchical hyperbolicity applied to mapping class groups.
result Quotients of mapping class groups by large powers of Dehn twists are hierarchically hyperbolic.
The cooperative hierarchical structure is a common and significant data structure observed in, or adopted by, many research areas, such as: text mining (author-paper-word) and multi-label classification (label-instance-feature). Renowned Bayesian approaches for cooperative hierarchical structure modeling are mostly bas…
A Bayesian Nonparametric Perspective on Mahalanobis Distance for Out of Distribution Detectionstat.ML
Bayesian nonparametric models improve OOD detection, especially with complex covariance structures.
problem Improving out-of-distribution detection methods, especially in complex scenarios.
method Proposes Bayesian nonparametric mixture models with hierarchical priors that generalize the Mahalanobis distance score.
result Bayesian nonparametric methods outperform existing OOD methods, especially in complex scenarios.
Variable selection for models including interactions between explanatory variables often needs to obey certain hierarchical constraints. The weak or strong structural hierarchy requires that the existence of an interaction term implies at least one or both associated main effects to be present in the model. Lately, thi…
Kropholler's class of groups is the smallest class of groups which contains all finite groups and is closed under the following operator: whenever admits a finite-dimensional contractible -CW-complex in which all stabilizer groups are in the class, then is itself in the class. Kropholler's class admits a hie…
Deep neural networks have achieved impressive success in large-scale visual object recognition tasks with a predefined set of classes. However, recognizing objects of novel classes unseen during training still remains challenging. The problem of detecting such novel classes has been addressed in the literature, but mos…
New groups are hyperbolic and rigid in mapping class groups.
problem Understanding the structure of Veech groups in mapping class groups.
method Showed that Veech groups are hierarchically hyperbolic and quasi-isometrically rigid.
result Veech groups are hierarchically hyperbolic and quasi-isometrically rigid.
Typically, Softmax is used in the final layer of a neural network to get a probability distribution for output classes. But the main problem with Softmax is that it is computationally expensive for large scale data sets with large number of possible outputs. To approximate class probability efficiently on such large sc…
Hierarchical clustering is a class of algorithms that seeks to build a hierarchy of clusters. It has been the dominant approach to constructing embedded classification schemes since it outputs dendrograms, which capture the hierarchical relationship among members at all levels of granularity, simultaneously. Being gree…
Paper introduces hierarchical softmax for global hierarchical classification tasks.
problem Improving classification accuracy in tasks with class hierarchies.
method Global hierarchical neural networks using hierarchical softmax.
result Hierarchical softmax outperforms regular softmax in multiple datasets.
Stable cubulations and bicombings in mapping class groups and Teichmüller spaces.
problem Understanding geometric structures in mapping class groups and Teichmüller spaces.
method Proving stably approximated by CAT(0) cube complexes, applying to broader colorable hierarchically hyperbolic spaces and groups.
result Stable cubulations and bicombings in mapping class groups and Teichmüller spaces, with stable coarse barycenters.
The staircase property aids deep learning by guiding hierarchical feature learning.
problem Understanding how hierarchical structure influences deep learning performance.
method Defined and proved the staircase property for Boolean hypercube functions, and showed its learnability by layerwise stochastic coordinate descent.
result Staircase functions can be learned in polynomial time using layerwise stochastic coordinate descent on regular neural networks.