Hierarchical causal models help understand cause and effect in nested data.
problem Learning cause and effect from nested hierarchical data.
method Extend structural causal models and causal graphical models with inner plates, develop graphical identification technique and estimation methods.
result Hierarchical data can enable causal identification even when non-hierarchical data cannot.
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.
Boxhead dataset tests autoencoder disentanglement in hierarchical data.
problem Evaluate disentanglement in hierarchical data.
method Introduced Boxhead dataset with hierarchically structured factors, evaluated autoencoder models.
result Hierarchical models outperform single-layer VAEs in disentangling factors.
Interactive steering improves hierarchical clustering for diverse user needs.
problem Existing hierarchical clustering methods fail to meet diverse user needs.
method Knowledge-driven and data-driven constraints, interactive steering through a visual interface.
result Facilitates the building of customized clustering trees efficiently and effectively.
t-NEB clusters high-dimensional data hierarchically with density paths.
problem Hierarchical clustering struggles with high-dimensional data.
method t-NEB uses density estimation, maximum density paths, and probabilistic merging.
result t-NEB yields state-of-the-art clustering performance on high-dimensional data.
There has been a surge in the number of large and flat data sets - data sets containing a large number of features and a relatively small number of observations - due to the growing ability to collect and store information in medical research and other fields. Hierarchical clustering is a widely used clustering tool. I…
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…
Bayesian Hierarchical Invariant Prediction refines ICP for better scalability and prior integration.
problem Improving computational scalability and invariance testing for causal inference.
method Bayesian Hierarchical structure to test invariance under heterogeneous data.
result Demonstrated improved scalability and potential as an alternative to ICP.
Hierarchical beta process has found interesting applications in recent years. In this paper we present a modified hierarchical beta process prior with applications to hierarchical modeling of multiple data sources. The novel use of the prior over a hierarchical factor model allows factors to be shared across different …
A hierarchical clustering algorithm for data clouds without structure assumptions.
problem Exploring data clouds without making structure assumptions.
method Hierarchical topological clustering algorithm that infers persistence of outliers and clusters of arbitrary shape from data hierarchy.
result The algorithm can provide meaningful clusters in complex datasets.
The study improves prediction regions for hierarchical data using a projection step.
problem Improving prediction regions for hierarchical multivariate data.
method Integrating a projection step in the split conformal prediction (SCP) procedure to reduce prediction regions.
result The resulting prediction regions are globally smaller under both joint and component-wise coverage objectives.
Inspired by the hierarchical hidden Markov models (HHMM), we present the hierarchical semi-Markov conditional random field (HSCRF), a generalisation of embedded undirectedMarkov chains tomodel complex hierarchical, nestedMarkov processes. It is parameterised in a discriminative framework and has polynomial time algorit…
Hierarchical-CPI improves variable importance measurement for medical data.
problem Limited interpretability of complex medical models.
method Hierarchical-CPI measures conditional variable importance with statistical control, handling correlated data.
result Hierarchical-CPI outperforms existing methods in medical datasets.
Method preserves order in hierarchical clustering of ordered data.
problem Order preserving hierarchical clustering of directed acyclic graphs.
method Combination of classical hierarchical clustering and ultrametric fitting.
result Optimal clustering preserves both cluster quality and order.
Many tasks such as retrieval and recommendations can significantly benefit from structuring the data, commonly in a hierarchical way. To achieve this through annotations of high dimensional data such as images or natural text can be significantly labor intensive. We propose an approach for uncovering the hierarchical s…
Diffusion models reveal latent hierarchical structure in data.
problem Quantitative measurement of data's hierarchical structure.
method Forward-backward experiments in diffusion models.
result Changes in latent variables manifest as correlated chunks in data.
Hyperbolic space outperforms Euclidean in learning hierarchical data.
problem Learning hierarchical data in Euclidean space requires exponentially many samples.
method Established geometric obstruction in Euclidean space and showed hyperbolic space's advantage.
result Hyperbolic space enables learning with O(mRlogm) samples, matching information-theoretic optimum. Hierarchical randomized smoothing improves model robustness for complex data.
problem Certifying robustness on complex data (e.g. images, graphs) is challenging.
method Add random noise to a randomly selected subset of entities in a hierarchical manner.
result Hierarchical randomized smoothing yields stronger robustness guarantees with high accuracy.
New clustering method recovers hidden tree structure from data.
problem Recovering hidden hierarchical structure in data.
method Maximum average dot product for merging clusters in hierarchical clustering.
result The algorithm produces a tree that accurately represents the underlying generative hierarchical structure.
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…
New hierarchical tensor decomposition model for complex data.
problem Lack of natural generalization of hierarchical NMF to tensors.
method Proposes a new hierarchical nonnegative tensor decomposition (HNTF) model.
result Model more naturally illuminates topic hierarchy.
Tree-SNE combines t-SNE and hierarchical clustering for data visualization.
problem Data visualization and clustering in complex datasets.
method Stacked one-dimensional t-SNE embeddings and alpha-clustering.
result Effective hierarchical clustering and visualization of various datasets.
Kernel methods can learn hierarchical polynomials efficiently.
problem Learning hierarchical structure from data.
method Iteratively reweighting kernel machines using derivatives.
result Efficient learning of hierarchical polynomials.
Hierarchical models are versatile tools for joint modeling of data sets arising from different, but related, sources. Fully Bayesian inference may, however, become computationally prohibitive if the source-specific data models are complex, or if the number of sources is very large. To facilitate computation, we propose…
Paper proposes a Renyi entropy-based method for tuning hierarchical topic models.
problem Tuning hierarchical topic models, especially determining the number of topics at each level, is challenging.
method The paper introduces a Renyi entropy-based metric for quality assessment and a practical tuning concept.
result The proposed method can estimate the number of topics for two hierarchical levels in hARTM model.
Exact hierarchical clustering algorithms for data analysis.
problem Finding meaningful structures in data like phylogenetic trees.
method Novel dynamic-programming algorithms based on a trellis data structure.
result Exact computation of partition function, maximum likelihood hierarchy, and marginal probabilities.
Unified theory for neural scaling laws in hierarchically compositional data.
problem Understanding neural scaling laws in hierarchically compositional data.
method Probabilistic context-free grammars and power-law distributed production rules.
result Unified learning curve behavior for classification and next-token prediction tasks.
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…
Diffusion models generalize better with hierarchical data structure and regularization.
problem Understanding generalization in diffusion models with finite data.
method Analyzing diffusion models through data covariance spectra and developing a theoretical framework based on linear neural networks.
result Generalization in diffusion models improves with hierarchical data structure and regularization.
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.
Two new Hie-TAN and Hie-TAN-Lite algorithms improve TAN for hierarchical feature spaces.
problem Learning dependencies in hierarchical feature spaces.
method Exploits hierarchical parent-child relationships as constraints to learn a dependency tree.
result Hie-TAN-Lite outperforms Hie-TAN and other methods in predictive accuracy.
Combines geometry and topology for analyzing hierarchical datasets.
problem Analyzing complex, hierarchical datasets with irregular structures.
method Combines manifold learning and topological data analysis.
result Superior classification results compared to state-of-the-art methods.
Hierarchical structure is ubiquitous in data across many domains. There are many hierarchical clustering methods, frequently used by domain experts, which strive to discover this structure. However, most of these methods limit discoverable hierarchies to those with binary branching structure. This limitation, while com…
The paper extends fairness to hierarchical clustering, finding efficient algorithms with minimal loss.
problem Ensuring fairness in hierarchical clustering where data is recursively partitioned.
method Extending fairness to hierarchical clustering, developing simple, efficient algorithms for various objectives.
result Simple, efficient algorithms for fair hierarchical clustering with only a negligible loss in objective.
Unsupervised method learns hierarchical graph representations without labels.
problem Lack of hierarchical graph representations and need for labeled data in GNNs.
method Maximizes mutual information between local and global graph representations.
result Comparable performance to supervised methods on graph classification benchmarks.
Discriminative classifier for compositional data using hierarchical mixture of Generalized Dirichlet models.
problem Classifying compositional data, especially in spam detection and color space identification.
method Hierarchical mixture of discriminative Generalized Dirichlet classifiers, using variational approximation for parameter learning.
result First time a variational upper-bound for Generalized Dirichlet mixture is proposed in literature.
Paper uses HGNN to predict stock types from relationships and temporal data.
problem Predicting stock types from complex market data.
method Integrates stock relationships and temporal data using HGNN.
result Effective prediction of stock types with HGNN model.
BoRA finetunes multi-task LLMs by sharing information through hierarchical priors.
problem Limited data for some tasks in multi-task LLMs.
method Bayesian hierarchical low-rank adaption.
result BoRA outperforms individual and unified model approaches.
We analyze large, multi-dimensional, sparse counting data sets, finding unsupervised groups to provide unique insights into genetic data. We create gene and biological pathway groups based on patients' variants to find common risk factors for four common types of cancer (breast, lung, prostate, and colorectal) and auti…
Formalizes concepts as latent variables in hierarchical models for high-dimensional data.
problem Lack of formalization and theoretical insights for learning discrete concepts from high-dimensional data.
method Formalizes concepts as latent causal variables in a hierarchical model, formulates conditions for concept identification.
result Conditions for identifying latent hierarchical models in unsupervised data, handling complex structures and high-dimensional data.
Paper learns latent and hierarchical structures in CDMs from data.
problem Jointly learning latent and hierarchical structures in CDMs from observed data.
method Penalized likelihood approach for selecting attributes and estimating structures; EM and latent structure recovery algorithms.
result Good performance demonstrated by simulation and real data applications.
BL learns interpretable optimization structures from data.
problem Learning interpretable optimization structures from data.
method BL parameterizes a compositional utility function from intrinsically interpretable modular blocks.
result BL supports architectures from single to hierarchical compositions, modeling hierarchical optimization structures.
A new method generates graphs with hierarchical structures.
problem Generating graphs with natural hierarchical structures.
method Recursively generates community structures at multiple resolutions, parallel generation of all sub-structures.
result Improves generative performance on multiple graph datasets.
Diffusion models learn hierarchical composition rules from data.
problem How many samples do generative models need to learn hierarchical composition rules?
method Theoretical and empirical investigation of diffusion models on probabilistic context-free grammars.
result Diffusion models learn hierarchical composition rules with sample complexity scaling polynomially with context size.
Unified Bayesian framework for PTA data analysis tackles hierarchical model issues.
problem Hierarchical Bayesian modeling challenges in PTA data analysis.
method Reparameterization strategy using Normalizing Flows (NFs) and i-nessai nested sampler.
result Improved statistical robustness and computational efficiency in PTA analysis.
Paper proposes a new hierarchical attention mechanism for multi-scale data.
problem Challenges in applying neural attention to multi-scale, multi-modal data.
method Developed a mathematical framework for multi-modal, multi-scale data and derived optimal neural attention mechanics.
result Proposed hierarchical attention mechanism improves transformer performance in multi-scale, multi-modal settings.
SCHA-VAE generates novel data from limited examples using hierarchical context aggregation.
problem Generating data from a novel distribution with limited examples.
method Hierarchical context aggregation with attention-based point to set-level aggregation.
result Hierarchical approach better captures intrinsic variability in small data.
New method explains classifiers trained on raw hierarchical data.
problem Lack of interpretability in classifiers trained on raw structured data.
method Treating classifiers as subset selection problems, generating interpretable explanations efficiently.
result Computational efficiency and higher-quality explanations compared to existing methods.