Improved decision tree for big data classification.
problem Classification of large datasets.
method Divide and conquer strategy with decision tree segmentation and leaf level classifier.
result Models are interpretable and as accurate as ensemble methods.
The study finds that certain curved manifolds can be mapped to symmetric spaces.
problem Understanding singular Riemannian foliations in positively curved manifolds.
method Generalizing fixed point homogeneous actions to singular Riemannian foliations.
result Positively curved manifolds with point leaf maximal SRF's are diffeo/homeomorphic to compact rank one symmetric spaces.
A new type of random forest improves robustness against noisy data.
problem Noise in test samples damages random forest performance.
method Introduces denoising autoencoders into random forests to identify and correct incorrect decisions.
result Improves estimation accuracy by considering multiple traversal paths for incorrect nodes.
Poisson homogeneous spaces for Poisson groupoids are classfied in terms of Dirac structures for the corresponding Lie bialgebroids. Applications include Drinfel'd's classification in the case of Poisson groups and a description of leaf spaces of foliations as homogeneous spaces of pair groupoids.
We study the foliation space of complex and invariant (by torsion of intrinsic Hermitian connection) umbilic distribution on an isometric immersion from a nearly Kähler manifold M into the Euclidean space. Under suitable conditions this leaf space is nearly Kähler and M can be decomposed into a product of this leaf…
DiPriMe forests use private medians to create balanced tree splits for privacy-protected data.
problem Privacy concerns in training random forests due to multiple data queries.
method Proposes DiPriMe forests, which use a private median to generate balanced splits, ensuring differential privacy.
result DiPriMe forests achieve high utility while maintaining differential privacy, as shown both theoretically and empirically.
A foliation on a Riemannian manifold is hyperpolar if it admits a flat section, that is, a connected closed flat submanifold that intersects each leaf of the foliation orthogonally. In this article we classify the hyperpolar homogeneous foliations on every Riemannian symmetric space of noncompact type.
A hierarchical routing mixture of experts model for complex regression tasks.
problem Complex data distribution in regression tasks.
method Binary tree-structured hierarchical routing mixture of experts (HRME) model with classifiers and simple regression models.
result Effective prediction with simple leaf experts in multimodal data.
The paper explores CR structures and their leaf spaces in semi-Riemannian manifolds.
problem Classifying CR structures and their leaf spaces.
method Using unit tangent bundles and dynamical Legendrian contact structures.
result New examples of 2-nondegenerate CR structures are provided.
Bi-directional Curriculum Learning improves graph anomaly detection by considering both homogeneity and heterogeneity.
problem Existing graph anomaly detection methods often ignore the different contributions of nodes to training.
method Introduces Bi-directional Curriculum Learning (BCL) to optimize GAD methods by considering both homogeneity and heterogeneity of nodes.
result Extensive experiments show that BCL significantly improves the performance of GAD anomaly detection models.
Regular neighborhoods of singular submanifolds are isotopic to bundle morphisms.
problem Isotoping regular neighborhoods of singular submanifolds to bundle morphisms.
method Leaf preserving isotopy and homogeneity assumptions on foliations.
result Every leaf preserving diffeomorphism of a regular neighborhood is isotopic to a bundle morphism.
Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly trained with backpropagation, like a neural network. Even though this continuity …
For i = 1,2, let Gamma_i be a lattice in a simply connected, solvable Lie group G_i, and let X_i be a connected Lie subgroup of G_i. The double cosets Gamma_igX_i provide a foliation F_i of the homogeneous space Gamma_i\G_i. Let f be a continuous map from Gamma_1\G_1 to Gamma_2\G_2 whose restriction to each leaf of F_1…
We show that a simply connected Riemannian homogeneous space M which admits a totally geodesic hypersurface F is isometric to either (a) the Riemannian product of a space of constant curvature and a homogeneous space, or (b) the warped product of the Euclidean space and a homogeneous space, or (c) the twisted product o…
Steerable neural ODEs on homogeneous spaces for equivariant feature dynamics.
problem Learning continuous-time equivariant dynamics of vector-valued features on homogeneous spaces.
method Introduces steerable neural ordinary differential equations on homogeneous spaces, interpreting features as sections of associated vector bundles over M. result Steerable NODEs are G-equivariant when the flow and connection are G-invariant, and they incorporate existing models. In many statistical learning problems, the target functions to be optimized are highly non-convex in various model spaces and thus are difficult to analyze. In this paper, we compute \emph{Energy Landscape Maps} (ELMs) which characterize and visualize an energy function with a tree structure, in which each leaf node re…
Study recovers tree structure in noisy MRFs with support size 3 or more.
problem Learning tree-structured MRFs with symmetric noise.
method Characterized recoverability based on joint PMF, provided algorithm for recovery.
result Structure of leaf clusters can be partially or fully identifiable.
USNRT uses tree-structured learning to improve uncertainty quantification of variance networks.
problem Improving uncertainty quantification of variance networks.
method Tree-structured local neural network model that partitions feature space into regions for training region-specific neural networks to predict mean and variance.
result USNRT shows superior performance in estimating uncertainty with variances on UCI datasets compared to recent methods.
PINE embeds graph nodes flexibly, capturing any neighbor dependency.
problem Learning flexible node representations from graph neighborhoods.
method PINE uses partial permutation invariant set functions to capture any possible neighbor dependencies.
result PINE outperforms state-of-the-art methods on various graph learning tasks.
Network Lens identifies node behaviors in heterogeneous networks with high accuracy.
problem Identifying different behaviors in various parts of large heterogeneous networks.
method Zoom into network using different-sized lenses to capture local structure, weight signatures to predict node labels.
result Achieved a peak accuracy of ~42% on two networks with ~100,000 and ~1,000,000 nodes, significantly better than random.
JSRT improves regression tree performance by incorporating global node information.
problem Regression tree performance relies on local node means, ignoring global node information.
method Proposes JSRT by integrating global mean information from different nodes.
result Demonstrates superior performance and efficiency compared to other regression tree methods.
EM algorithm converges to global max in latent Gaussian tree models.
problem Optimizing log-likelihood in latent Gaussian tree models.
method Analyzed the optimization landscape and convergence of EM algorithm.
result EM algorithm converges to global maximum in latent Gaussian tree models.
A foliation F on a Riemannian manifold M is homogeneous if its leaves coincide with the orbits of an isometric action on M. A foliation F is polar if it admits a section, that is, a connected closed totally geodesic submanifold of M which intersects each leaf of F, and intersects orthogonally at each point of intersect…
DAG-FM discovers causal relationships from heterogeneous data.
problem Challenges in causal discovery from heterogeneous causal mechanisms.
method DAG-FM uses two specialized Transformer-based sub-modules and a robust tabular interaction block to model complex row-column interactions.
result DAG-FM achieves state-of-the-art performance on synthetic and real-world datasets.
Totally geodesic dual leaves on curved manifolds are also curved.
problem Characterizing dual leaves of nonnegatively curved polar manifolds.
method Proving dual leaves are totally geodesic and closed, and inducing a Riemannian submersion.
result Dual leaves of nonnegatively curved polar manifolds are themselves nonnegatively curved and totally geodesic.
In this article we study isometric immersions of nearly Kähler manifolds into a space form (specially Euclidean space) and show that every nearly Kähler submanifold of a space form has a totally umbilic foliation whose leafs are 6-dimensional nearly Kähler manifolds. Moreover using this foliation we show that there is …
GP-CNAS uses genetic programming to automatically design CNN architectures.
problem Designing optimal CNN architectures is laborious and error-prone.
method GP-CNAS uses a tree-based representation of CNNs and dynamic crossover operators to search for optimal architectures.
result GP-CNAS finds optimal CNN architectures with balanced depth and width in limited trials.
A tree-based dictionary learning model is developed for joint analysis of imagery and associated text. The dictionary learning may be applied directly to the imagery from patches, or to general feature vectors extracted from patches or superpixels (using any existing method for image feature extraction). Each image is …
Atlas dataset categorizes clothing products with high accuracy.
problem Lack of real-world datasets for e-commerce clothing product categorization.
method Collected and labeled a dataset of 186,150 images, established a benchmark for image classification and sequence models.
result Benchmark model achieved a micro f-score of 0.92.
Method identifies root causes of anomalies in causal processes.
problem Identifying root causes of anomalies in causal processes.
method Noisy functional causal model, Bayesian learning, gradient-based attribution.
result Proposes efficient method to compute anomaly attribution scores.
New algorithm speeds up causal discovery for network data.
problem Scalability issues in score-matching for temporal network data.
method Developed a new parent-finding subroutine for DAGs, improving score matching efficiency.
result Efficiency-lifted score matching for both i.i.d. and temporal data on networks.
A new algorithm improves sample complexity for thresholding in Monte Carlo Tree Search.
problem Determining if the root node value of a tree is at least a given threshold.
method Developed a δ-correct sequential sampling algorithm based on the Track-and-Stop strategy.
result Ratio-based modification of D-Tracking strategy reduces sample complexity and computational cost.
GHNet improves graph learning by balancing homogeneity and heterogeneity.
problem Over-smoothing in GCN leads to similar node representations.
method GHNet uses gating units to balance homogeneity and heterogeneity in feature propagation.
result GHNet achieves larger receptive fields without over-smoothing.
We prove the "End Curve Theorem," which states that a normal surface singularity (X,o) with rational homology sphere link Σ is a splice-quotient singularity if and only if it has an end curve function for each leaf of a good resolution tree. An "end-curve function" is an analytic function $(X,o)\to (\C,0)$ whose ze…
Model counts interactions in dynamic networks using Poisson processes and clusters.
problem Counting interactions in dynamic networks with unknown cluster structure.
method Developed a model using non-homogeneous Poisson processes and block modeling. Truncated to discrete time for tractability. Used an exact integrated classification likelihood criterion for estimation.
result Estimates cluster memberships and number of clusters simultaneously.
The study integrates Banach manifolds into H-manifolds, integrating Lie algebras into H-groups.
problem Integrating Banach manifolds and Lie algebras into H-manifolds and H-groups.
method Investigating quotients of Banach manifolds with free actions of pseudogroups of local diffeomorphisms.
result Every real Banach-Lie algebra can be integrated to an H-group.
ProHOC detects OOD samples in class hierarchies, predicting them to correct internal nodes.
problem Binary OOD detection ignores semantic relationships between OOD and ID classes.
method Probabilistic hierarchical model using multi-depth networks trained for ID classification.
result ProHOC effectively classifies OOD samples to their correct internal nodes in class hierarchies.
Develops new approach to recover CR structures from their Levi foliations.
problem Recovering CR structures from their Levi foliations for nonregular symbols.
method Reduction to dynamical Legendrian contact structure on leaf space.
result New geometric interpretation of CR prolongation conditions.
Given a non-compact, simply connected homogeneous three-manifold X and a sequence {Ωn}n of isoperimetric domains in X with volumes tending to infinity, we prove that as n→∞: 1. The radii of the Ωn tend to infinity. 2. The ratios $\{Area} (\partial Ω_n)/\{Vol}(Ω_n)$ converge to the Cheeger consta…
Paper tackles robust estimation of tree-structured Ising models without side information.
problem Learning tree-structured Ising models with flipped signs of variables.
method Proves unidentifiability, proposes an algorithm with logarithmic sample complexity and polynomial run-time complexity.
result Empirically demonstrates robustness of proposed algorithm in the flipped signs setting.
Bayesian nonparametric method for hierarchical clustering.
problem Hierarchical non-overlapping clustering of a dataset.
method Combining nCRP and HDP for complex latent mixture features.
result Solid empirical results compared to existing algorithms.
A simple banking network model is proposed which features multiple waves of bank defaults and is analytically solvable in the limiting case of an infinitely large homogeneous network. The model is a collection of nodes representing individual banks; associated with each node is a balance sheet consisting of assets and …
In this paper, we investigate the mean curvature flows starting from all non-minimal leaves of the isoparametric foliation given by a certain kind of solvable group action on a symmetric space of non-compact type. We prove that the mean curvature flow starting from each non-minimal leaf of the foliation exists in infin…
Study controls bifurcations in Eulerian flows with multiple Hopf singularities.
problem Bifurcation analysis and control of nonlinear Eulerian flows with non-resonant n-tuple Hopf singularities.
method Analysis of CW complex bifurcations of flow-invariant Clifford hypertori, using leaf-bifurcation varieties.
result Tertiary toral CW complex bifurcates from and persists outside a secondary toral CW complex.
Riemannian manifolds can be realized as leaf spaces of matchbox manifolds.
problem Realizing Riemannian manifolds as leaf spaces of matchbox manifolds.
method Graph coloring techniques to prove realization of manifolds as leaves.
result Any repetitive Riemannian manifold of bounded geometry can be realized as a leaf of a minimal Riemannian matchbox manifold without holonomy.
We study the geometry of the leaf closure space of regular and singular Riemannian foliations. We give conditions which assure that this leaf space is a singular symplectic or Kähler space.
Active-LATHE boosts error exponent for learning homogeneous trees.
problem Learning homogeneous trees from i.i.d. data with active sampling.
method Design and analysis of Active Learning Algorithm for Trees with Homogeneous Edge (Active-LATHE).
result Active-LATHE boosts the error exponent by at least 40% for ρ≥0.8. We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Unlike many existing methods, the observed …