Study on quaternionic contact structures with integrable complementary distribution.
problem Characterize quaternionic contact structures with integrable complementary distributions.
method Analyze positive definite quaternionic contact (4n+3)-manifolds, focusing on the integrable complementary distribution and its relationship with Sasaki and 3-Sasaki structures. result Identify a new class of quaternionic contact structures with integrable complementary distributions that are not isomorphic to su(2). The paper proves integral formulas for manifolds with multiple orthogonal distributions.
problem Understanding geometric properties of manifolds with multiple orthogonal distributions.
method Develops integral formulas for Riemannian manifolds with k>2 orthogonal complementary distributions. result Generalizes known formulas for k=2 and applies to manifold splitting and immersions. We obtain integral formulas for a metric-affine space equipped with two complementary orthogonal distributions. The integrand depends on the Ricci and mixed scalar curvatures and invariants of the second fundamental forms and integrability tensors of the distributions. The formulas under some conditions yield splitting…
Our results concern geometry of a manifold endowed with a pair of complementary orthogonal distributions (plane fields) and a time-dependent Riemannian metric. The work begins with formulae concerning deformations of geometric quantities as the Riemannian metric varies conformally along one of the distributions. Then w…
Proposes a method for multi-view clustering that integrates consistent and complementary graph regularizers.
problem Multi-view clustering where views have both consistent and complementary information.
method Consistent and complementary graph-regularized multi-view subspace clustering (GRMSC).
result The proposed method outperforms state-of-the-art methods on benchmark datasets.
Quantum states model sequences, revealing complementary system information.
problem Modeling sequences using classical probability distributions.
method Quantum state with entanglement, DMRG algorithm for organizing reduced densities.
result Estimate of generalization error for tensor network model.
Walczak formula is a very nice tool for understanding the geometry of a Riemannian manifold equipped with two orthogonal complementary distributions. Svensson [7] has shown that this formula simplifies to a Bochner type formula when we are dealing with Kähler manifolds and holomorphic (integrable) distributions. Here, …
Generative-discriminative method improves label prediction and instance generation.
problem Difficulty in obtaining high-quality labeled instances.
method Generative-discriminative complementary learning method using CC-GAN.
result Improves accuracy in predicting ordinary labels and generating high-quality instances.
Identifies LA-groups via VB-group structure and complementary actions.
problem Understanding the structure and integrability of LA-groups.
method Identifies LA-groups via VB-group structure and complementary actions up to homotopy.
result Establishes an equivalence between LA-groups and LA-matched pairs.
Audited Conformal Prediction improves conditional coverage in pretrained models under distribution shift.
problem Uncertainty quantification for pretrained models under unknown distribution shift
method Leverages a small labeled dataset to train an audit model for marginal coverage, integrates outputs into conformal prediction framework
result Significantly higher conditional coverage than existing approaches
Study curvature of orthogonal distributions on manifolds.
problem Understanding curvature of orthogonal distributions on manifolds.
method Derived Euler-Lagrange equations for a functional of Riemannian metrics.
result Examples of critical metrics for specific distributions.
Properties of pairs of product conjugate connections are stated with a special view towards the integrability of the given almost product structure. We define the analogous in product geometry of the structural and the virtual tensors from the Hermitian geometry and express the product conjugate connections in terms of…
ct-SNE extracts hidden structure from labeled data.
problem Insufficient 2D visualization of high-dimensional data.
method Conditional t-SNE discounts prior information from labels.
result Extracts complementary structure not captured by t-SNE alone.
Paper proposes a method to adapt classifiers using complementary labels instead of true labels.
problem Training classifiers with true labels from the source domain is costly and sometimes impossible.
method Proposes a novel setting with complementary labels and a complementary label adversarial network (CLARINET).
result CLARINET significantly outperforms baselines on handwritten digits and object recognition tasks.
Framework learns item representations from text data for complementary and similar items.
problem Generating accurate complementary item recommendations from textual data.
method Quadruplet network learning framework for latent space representation of items.
result Items are placed closer together in latent space for similar and complementary items compared to non-complementary items.
Novel method uses Gaussian process to estimate particle sizes from scattering data.
problem Estimating particle size distributions from noisy optical scattering measurements.
method Constrained Gaussian process regression with normalization constraints.
result Accurately reconstructs particle size distributions from noisy data.
The paper explores formulas and applications for mixed scalar curvature in multi-product manifolds.
problem Integral and variation formulas for mixed scalar curvature in multi-product manifolds.
method Generalizes results from pseudo-Riemannian almost product manifolds to multi-product structures.
result Generalizes formulas for mixed scalar curvature in multi-product manifolds.
Proposes a multi-view architecture for drug-target interaction prediction.
problem Representing compound-target pairs in deep learning models.
method Integrates differentiable and predefined molecular descriptors using an adversarial multi-view architecture.
result Demonstrates potential of the proposed approach on clinically relevant datasets.
This research tackles sample complexity in causal graph recovery with temporal heterogeneity.
problem Recovering a unique causal graph from observational data with temporal heterogeneity.
method Integrates time-series dynamics and multi-environment heterogeneity to constrain the problem, enabling a rigorous analysis of statistical limits.
result Unified necessary identifiability conditions and explicit information-theoretic bounds quantify the sample complexity under different noise distributions.
Clarinet uses complementary labels to train classifiers with less source data.
problem Training classifiers with true-label data from source domain is costly.
method Proposes CLARINET to train classifiers with complementary-label source data and unlabeled target data.
result CLARINET significantly outperforms baselines in unsupervised domain adaptation.
UREs lead to overfitting in complex models, especially in complementary label learning.
problem Overfitting in weakly supervised learning with complementary labels.
method Proposed a surrogate complementary loss (SCL) framework to reduce gradient variance.
result SCL mitigates overfitting and improves URE-based methods.
A new method integrates multi-label and multi-view features for image classification.
problem Combining multi-label and multi-view information for effective image classification.
method Introduces MV3MR, a method that exploits the complementary property of different features and discovers intrinsic local geometry. result MV3MR outperforms existing methods on PASCAL VOC' 07 and MIR Flickr datasets. Framework transfers complementary operating conditions to train anomaly detectors.
problem Training anomaly detectors on changing operating conditions requires comprehensive data, which is hard to obtain.
method Proposes unsupervised transfer learning to align and combine data from different units.
result Demonstrates improved anomaly detection in changing operating conditions.
Bayesian Complementary Kernelized Learning models complex spatiotemporal data.
problem Modeling complex, nonstationary, and nonseparable spatiotemporal data.
method Integrates kernelized low-rank tensor factorization and short-range spatiotemporal Gaussian Processes.
result BCKL offers superior performance in providing accurate posterior mean and high-quality uncertainty estimates.
Sig-PCA integrates model outputs and observations to correct model biases.
problem Improving model accuracy and reliability by correcting biases and numerical approximations.
method Sig-PCA framework that combines summary statistics from model outputs with localized observations via a neural network.
result Corrects model outputs to align closely with observational data, preserving essential statistical information.
The various scalar curvatures on an almost Hermitian manifold are studied, in particular with respect to conformal variations. We show several integrability theorems, which state that two of these can only agree in the Kähler case. Our main question is the existence of almost Kähler metrics with conformally constant Ch…
A new method improves density ratio estimation efficiency and accuracy.
problem Density ratio estimation trade-off between quality and efficiency.
method One-step Score-based Density Ratio Estimation (OS-DRE) combining analytic and solver-free approach.
result OS-DRE offers a favorable balance between estimation quality and inference efficiency.
In this paper, we show that the recent integration of statistical models with deep recurrent neural networks provides a new way of formulating volatility (the degree of variation of time series) models that have been widely used in time series analysis and prediction in finance. The model comprises a pair of complement…
Framework uses experience replay to prevent deep networks from forgetting past tasks.
problem Deep networks forget past tasks after learning new ones in sequential multitask learning.
method Generative model that couples current task with past learned tasks through a discriminative embedding space.
result Framework learns a shared abstract distribution across all tasks, preventing catastrophic forgetting.
Combining self-training and contrastive learning improves performance under distribution shift.
problem Improving performance under distribution shift using unlabeled data.
method Combining self-training and contrastive learning techniques.
result Combined method achieves 3-8% higher accuracy than either approach independently.
We introduce the notion of cofoliation on a stack. A cofoliation is a change of the differentiable structure which amounts to giving a full representable smooth epimorphism. Cofoliations are uniquely determined by their associated Lie algebroids. Cofoliations on stacks arise from flat connections on groupoids. Connecti…
New method uses SHapley Additive Explanations to identify anomaly detectors with complementary behaviors.
problem Challenges in unsupervised anomaly detection due to diverse data distributions and lack of labels.
method Characterize anomaly detectors using SHapley Additive Explanations to measure feature importance and similarity.
result Detectors with similar explanations produce correlated anomaly scores, while those with divergent explanations are complementary.
We show that any self-complementary graph with n vertices contains a K⌊2n+1⌋ minor. We derive topological properties of self-complementary graphs.
Proposes a new framework for learning from labeled and unlabeled data.
problem Learning from unlabeled and multi-label samples with arbitrary loss functions.
method Multi-complementary and unlabeled learning framework.
result Effective estimation of classification risk with optimal convergence rate.
Proposes dual product embedding for complementary product representation learning.
problem Detecting complementary relationships from noisy and sparse customer purchase activities.
method Knowledge-aware dual product embedding with multi-task learning and user bias terms.
result Complementary relationships are captured more accurately than simple similarity.
Unified model integrates text and time series for financial forecasting.
problem Challenges in integrating complementary modalities for improved forecasting.
method Modality-specific experts and cross-modal alignment framework.
result State-of-the-art performance on financial forecasting task.
Proposes a method for multi-view clustering that considers local structures and feature weights.
problem Challenges in effectively exploiting complementary information across multiple views.
method Simultaneously assigns weights to different features and captures local information in view-specific feature spaces.
result Achieves state-of-the-art performance on benchmark datasets.
In this work, we find an equation that relates the Ricci curvature of a riemannian manifold M and the second fundamental forms of two orthogonal foliations of complementary dimensions, F and F⊥, defined on M. Using this equation, we show a sufficient condition for the manifold M to be …
In this paper, we study the classification problem in which we have access to easily obtainable surrogate for true labels, namely complementary labels, which specify classes that observations do \textbf{not} belong to. Let Y and Yˉ be the true and complementary labels, respectively. We first model the annotati…
Model learns and generalizes new concepts efficiently from few labeled instances.
problem Efficient continual learning of new concepts in AI.
method Develops a computational model inspired by learning theories, using embedding space and generative distribution.
result Model efficiently expands learned concepts to new domains using few labeled samples.
Combines BC and GAIL for efficient imitation learning.
problem Efficient imitation learning without reward signals.
method Integrates Behavior Cloning and Generative Adversarial Imitation Learning.
result Combination leads to stable and sample-efficient learning.
Paper bridges ordinary-label and complementary-label learning frameworks.
problem Combining complementary-label learning with ordinary-label learning.
method Integrates loss functions for one-versus-all and pairwise classification.
result Derives classification risk and error bound for additivity and duality loss functions.
Random subsurfaces of hyperbolic surfaces equidistribute to ribbon graphs.
problem Distribution of shapes of complementary subsurfaces in moduli space.
method Study of shapes of complementary subsurfaces in moduli space as boundary lengths go to infinity.
result Random subsurfaces look like random ribbon graphs.
LA-Courant algebroids link double Lie bialgebroids via Manin triples.
problem Establishing a mathematical framework for double Lie bialgebroids.
method Verification of Manin triple framework for double Lie bialgebroids using LA-Courant algebroids.
result LA-Courant algebroids provide a correspondence with double Lie bialgebroids.
The paper proposes a method to integrate prior information into penalized regression.
problem Improving predictive performance in high-dimensional tasks with prior information.
method Integrating multiple sources of prior information into penalized regression.
result The method improves predictive performance, as shown by simulations and applications.
A new method interpolates between sampling and variational inference using stochastic mixtures.
problem Combining the strengths of sampling and variational inference methods.
method Develops a framework using stochastic mixtures of simple component distributions to interpolate between sampling and variational inference.
result Improves on both sampling and variational inference methods by reducing bias and variance.
Distributions of Monge type are a class of strongly regular bracket-generating distributions introduced by I. Anderson, Zh. Nie and P. Nurowski. Their symbol algebras prolong to simple graded Lie algebras, thus allowing one to associate a parabolic geometry to any given Monge distribution. This article is devoted to th…
In this note we study the Seifert rational homology spheres with two complementary legs, i.e. with a pair of invariants whose fractions add up to one. We give a complete classification of the Seifert manifolds with 3 exceptional fibers and two complementary legs which bound rational homology balls. The result translate…