HIP-GP improves GP inference for inter-domain observations with millions of inducing points.
problem Inference for Gaussian Processes across different domains.
method Hierarchical inducing point Gaussian process with grid structure and stationary kernel assumption.
result Improved approximation accuracy through increased number of inducing points.
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.
Sparse GPs improved with nearest neighbor inducing variables.
problem Sparse GPs struggle with large numbers of inducing variables.
method Introduced a hierarchical prior for inducing variables and used nearest neighbor information for sparsity.
result Significant computational gains compared to standard sparse GPs.
A new framework for verifying robustness of neural networks.
problem Verifying the robustness of neural networks against adversarial attacks.
method LayerCert framework exploiting the nested hyperplane arrangement structure of ReLU networks.
result LayerCert reduces the number and size of convex programs needed for robustness verification.
Importance weighted variational inference (Burda et al., 2015) uses multiple i.i.d. samples to have a tighter variational lower bound. We believe a joint proposal has the potential of reducing the number of redundant samples, and introduce a hierarchical structure to induce correlation. The hope is that the proposals w…
Existing methods for sparse channel estimation typically provide an estimate computed as the solution maximizing an objective function defined as the sum of the log-likelihood function and a penalization term proportional to the l1-norm of the parameter of interest. However, other penalization terms have proven to have…
Compression and computational efficiency in deep learning have become a problem of great significance. In this work, we argue that the most principled and effective way to attack this problem is by adopting a Bayesian point of view, where through sparsity inducing priors we prune large parts of the network. We introduc…
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.
A new hierarchical clustering method selects representative points from sub-minimum-spanning-trees.
problem Selecting representative points for hierarchical clustering to improve robustness and reliability.
method Identify representative points using reciprocal nearest data points in sub-minimum-spanning-trees.
result The proposed algorithm outperforms other methods in accuracy and efficiency.
Proposes a method to improve hierarchical clustering using set-level structural priors.
problem Lack of supervision for non-leaf structure in hierarchical clustering.
method Introduces set-level structural priors for semi-supervised hyperbolic hierarchical clustering.
result Improves label consistency and similarity-based tree quality over baselines.
Deep Gaussian Processes (DGP) are hierarchical generalizations of Gaussian Processes (GP) that have proven to work effectively on a multiple supervised regression tasks. They combine the well calibrated uncertainty estimates of GPs with the great flexibility of multilayer models. In DGPs, given the inputs, the outputs …
This paper proposes to learn hierarchical compositional AND-OR model for interpretable image synthesis by sparsifying the generator network. The proposed method adopts the scene-objects-parts-subparts-primitives hierarchy in image representation. A scene has different types (i.e., OR) each of which consists of a number…
Paper develops a new objective for hierarchical clustering in Euclidean space.
problem Hierarchical clustering in Euclidean space with dissimilarity scores.
method Develops a new global objective and connects it to bisecting k-means.
result Optimal 2-means solution approximates the new objective, proving bisecting k-means optimizes a natural global objective.
We prove a geometric model for HHS hierarchies as CAT(0) cube complexes.
problem Modeling hierarchically hyperbolic spaces as cube complexes.
method Prove quasi-median quasi-isometry between hulls and cubical models.
result Hierarchical boundaries are locally modeled by CAT(0) cube complexes.
A new drug embedding method using hierarchical drug relations and chemical structures.
problem Learning accurate drug representations from chemical structures and hierarchies.
method Semi-supervised drug embedding using VAE in hyperbolic space.
result The method accurately places drugs in a hierarchy and predicts side-effects.
The Baire metric induces an ultrametric on a dataset and is of linear computational complexity, contrasted with the standard quadratic time agglomerative hierarchical clustering algorithm. In this work we evaluate empirically this new approach to hierarchical clustering. We compare hierarchical clustering based on the …
Generates infinite-depth hierarchical clusters from few examples.
problem Inadequate finite-sample clustering methods for fine-scale hierarchical structures.
method Classification fields generated by a local refinement rule, approximated by predictors.
result Learned predictors can approximate infinite-depth hierarchical structures.
The paper introduces a method to probabilistically select inducing points in sparse Gaussian processes.
problem The challenge is selecting the optimal number of inducing points in sparse Gaussian processes.
method A point process prior is applied to the inducing points, and the posterior is approximated using stochastic variational inference.
result The model learns which and how many inducing points to use, leading to fewer inducing points being preferred as they become less informative.
HALO learns to prune neural networks by adaptively shrinking weights.
problem Sparsity and model size in deep neural networks.
method Bayesian hierarchical models and trainable parameters for adaptive sparsification.
result HALO learns to create highly sparse networks with significant performance gains.
LION generates high-quality 3D shapes using hierarchical latent diffusion models.
problem Creating high-quality 3D shapes for digital artists.
method Hierarchical Latent Point Diffusion Model (LION) with a global shape latent and point-structured latent space.
result LION achieves state-of-the-art generation performance on ShapeNet benchmarks.
Proposes HypCSE for enhanced hierarchical clustering.
problem Challenges in existing hierarchical clustering methods.
method Hyperbolic Continuous Structural Entropy (HypCSE) neural networks.
result Superior performance on seven datasets.
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.
OMERF extends random forest for hierarchical data and ordinal responses.
problem Analyzing hierarchical data and ordinal responses using tree-based methods.
method Ordinal Mixed-Effects Random Forest (OMERF) that preserves flexibility and hierarchical structure.
result OMERF identifies discriminating student characteristics and estimates school effects.
Hierarchical Federated Learning bounds generalize using Wasserstein distance.
problem Bounding generalization error in Federated Learning with hierarchical sampling.
method Introduced a hierarchical sampling framework and derived generalization bounds using Wasserstein distance.
result Recover and strictly imply existing CMI bounds for bounded losses.
For supervised and unsupervised learning, positive definite kernels allow to use large and potentially infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done through the penalization of predictor functions by Euclidean or Hilbertian norms. In …
Separable Bregman divergences induce Riemannian metric spaces that are isometric to the Euclidean space after monotone embeddings. We investigate fixed rate quantization and its codebook Voronoi diagrams, and report on experimental performances of partition-based, hierarchical, and soft clustering algorithms with respe…
The development of algorithms for hierarchical clustering has been hampered by a shortage of precise objective functions. To help address this situation, we introduce a simple cost function on hierarchies over a set of points, given pairwise similarities between those points. We show that this criterion behaves sensibl…
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.
A new method selects inducing points to optimize high-throughput Bayesian optimisation.
problem Current inducing point selection methods sacrifice high-fidelity modeling of promising regions.
method Information-theoretic criterion to select inducing points maximizing global and maximum value uncertainties.
result Surrogate models support high-precision high-throughput Bayesian optimisation.
The recently developed variational autoencoders (VAEs) have proved to be an effective confluence of the rich representational power of neural networks with Bayesian methods. However, most work on VAEs use a rather simple prior over the latent variables such as standard normal distribution, thereby restricting its appli…
Local GP approach improves simulation efficiency for large datasets.
problem High computational cost of traditional Gaussian processes for large-scale simulations.
method Hybridizes global and local GP approximations with strategic placement of inducing points.
result Local inducing points enhance accuracy and computational efficiency.
We develop a normative framework for hierarchical model-based policy optimization based on applying second-order methods in the space of all possible state-action paths. The resulting natural path gradient performs policy updates in a manner which is sensitive to the long-range correlational structure of the induced st…
Efficiently trains deep Gaussian processes on large datasets.
problem Large-scale data and multi-scale features in function approximation.
method Combines variational learning with MCMC for efficient and accurate training.
result Highly efficient and accurate deep GP training on large-scale data.
Proposes a hierarchical model for learning discrete Bayesian networks with shrinkage.
problem Learning discrete Bayesian networks with high-order interactions and cell probabilities.
method Hierarchical Dirichlet shrinkage model with Metropolis-adjusted Langevin algorithm for sampling.
result Efficiently learns graph structure and selects between DAGs from sparse count data.
This paper fortifies the recently introduced hierarchical-optimization recursive least squares (HO-RLS) against outliers which contaminate infrequently linear-regression models. Outliers are modeled as nuisance variables and are estimated together with the linear filter/system variables via a sparsity-inducing (non-)co…
Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly focus on designing graph convolution operations. The graph pooling (or downsampli…
Study investigates induced geometry on surfaces in 3D contact manifolds.
problem Understanding the metric structure on surfaces embedded in 3D contact sub-Riemannian manifolds.
method Defined a coefficient to characterize characteristic points and identified global conditions for finite induced distance.
result Proved induced distance finite for certain surfaces with isolated characteristic points.
Unified framework for hierarchical image classification with epistemic uncertainty.
problem Overconfident predictions and lack of logical consistency in deep learning models.
method Neurosymbolic approach with epistemic deep learning, using focal set reasoning and differentiable fuzzy logic.
result Maintains accuracy on par with transformer baselines while providing more calibrated and interpretable predictions.
PointGMM learns hGMMs from point clouds for 3D shape representation.
problem Lack of shape priors and non-local information in point cloud representations.
method Neural network that learns hierarchical Gaussian mixture models (hGMMs) for 3D shapes.
result Generative model learns meaningful latent space for interpolations and novel shape synthesis.
We examine how the structure of the world trade network has been shaped by globalization and recessions over the last 40 years. We show that by treating the world trade network as an evolving system, theory predicts the trade network is more sensitive to evolutionary shocks and recovers more slowly from them now than i…
We introduce Grinch, a new algorithm for large-scale, non-greedy hierarchical clustering with general linkage functions that compute arbitrary similarity between two point sets. The key components of Grinch are its rotate and graft subroutines that efficiently reconfigure the hierarchy as new points arrive, supporting …
Method cleans covariance matrices for better statistical inference.
problem Reducing estimation noise in covariance matrices for better statistical inference.
method Robust yet flexible hierarchical ansatz with bootstrap procedure.
result Lower realized risk in global minimum variance portfolios.
Develops a hierarchical model for analyzing longitudinal data on manifolds.
problem Correlation between intra-subject measurements in nonlinear manifolds.
method Geodesic hierarchical models extended to Bézier spline trends.
result Validated on osteoarthritis data, improving disease progression classification.
Hierarchical clustering uses OWA operators to generalize linkage methods and avoid dendrogram inversions.
problem Avoiding unaesthetic inversions in hierarchical clustering dendrograms.
method OWA-based linkages combined with the Lance-Williams formula and conditions on weight generators.
result Conditions for weight generators to produce dendrograms without inversions.
Tangles improve clustering in various datasets.
problem Clustering diverse datasets efficiently and accurately.
method Tangles aggregate cuts to identify dense structures, leading to soft cluster characterization.
result Tangle framework generates hierarchical soft dendrograms for cluster exploration.
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. MHVAE learns cross-modality inference inspired by human cognition.
problem Cross-modality inference in multimodal data.
method Hierarchical multimodal generative model with modality-specific and joint-modality distributions.
result MHVAE performs on par with state-of-the-art models on multimodal datasets.
New method for deep learning hierarchies like sequences and graphs.
problem Lack of formalism for dealing with hierarchical structures in deep learning.
method Express equivariant maps for hierarchies using combinations of building block symmetries.
result Demonstrates effectiveness on semantic segmentation of point-cloud data.