Optimizes global optimization with random embeddings by defining a minimal low-dimensional domain.
problem Complexity in defining bounds for a low-dimensional domain under box constraints.
method Detailed study of random embedding properties, minimal low-dimensional set definition, and alternative embedding procedure.
result Enhanced performance and robustness in global optimization with random embeddings.
Paper tackles robust domain adaptation without target domain data.
problem Learning domain invariant representations without target domain data.
method Integrates deep autoencoder and causal structure learning into a unified model.
result CAE learns causal representations using only source domain data.
Deep networks can adapt to intrinsic dimensionality beyond domain constraints.
problem Approximating functions on low-dimensional manifolds with high-dimensional data.
method Two-layer compositions with ReLU activation, using dimensionality reducing feature maps.
result Near optimal approximation rates depend on the complexity of the dimensionality reducing map, not the ambient dimension.
Proposes MR-SNE for multimodal data visualization.
problem Visualizing data from multiple domains with relations across them.
method Extends t-SNE to compute augmented relations and jointly embed them in a low-dimensional space.
result Demonstrates promising performance in visualizing Flickr and Animal with Attributes 2 datasets.
New method learns low-dimensional representations of nonlinear time series without supervision.
problem Learning low-dimensional representations of nonlinear time series without supervision.
method Based on monotone variational inequality, the method learns representations by assuming sequences arise from a common domain.
result The method can learn the geometry for the entire domain and faithful representations for the dynamics of each individual sequence.
New method uses limited labeled data and multiple starts to adapt models across domains.
problem Accurate predictions in target domain with few labeled data.
method Fine-tuning from multiple adaptive starts, extending UDA methods.
result Minimax-optimal target performance with limited labeled target data.
BézierGAN generates smooth curves from low-dimensional parameters.
problem Designing smooth curves for aerodynamic and hydrodynamic shapes.
method Generative model that maps low-dimensional latent representation to Bézier curve points.
result Generates diverse and realistic curves with consistent shape variation.
Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous space. In particular, mixtures of Gaussians can be fitted to data very quickly using an accelerated EM algorithm that employs multiresolution kd-trees (Moore, 1999). In thi…
The paper introduces a method for interpretable principal component analysis of high-dimensional time series.
problem Inconsistent and difficult-to-interpret principal component estimates in high-dimensional regimes.
method Localized sparse principal component analysis of spectral density matrices in frequency domain.
result Efficient algorithm for sparse-localized estimates of principal subspaces.
The paper proposes a method to improve data analysis by considering multiple subsets of attributes (views) to enhance geometric information.
problem Distortion of distance metrics in high-dimensional data analysis.
method Partitioning attributes into multiple subsets (views) and using consensus between views to extract geometric information.
result Enhanced geometric information from multiple views improves data analysis.
CoSCA improves unsupervised domain adaptation by better aligning ambiguous target samples.
problem Missing alignment of ambiguous target samples in unsupervised domain adaptation.
method CoSCA explicitly incorporates intra- and inter-class domain discrepancy, estimating label hypotheses and optimizing a contrastive loss with MMD for better global alignment.
result CoSCA outperforms state-of-the-art approaches in producing more discriminative features.
SCTL scales causal domain adaptation without prior knowledge.
problem Domain adaptation with covariate shift and invariances across domains.
method SCTL: scalable causal discovery algorithm based on Markov blanket.
result SCTL achieves scalable and robust domain adaptation.
Embedding RL policies in RKHS for robustness and theoretical guarantees.
problem Stability and theoretical guarantees in RL policy representation.
method Low-dimensional embedding of RL policies in RKHS.
result Embedded policies maintain high return with strong theoretical guarantees.
Paper solves Gromov-Wasserstein for point clouds efficiently.
problem Quantifying similarity between two formations or shapes.
method Reformulates QAP as low-rank concave quadratic optimization problem.
result Global solution for large-scale problems with thousands of points.
This paper tackles continuous domain generalization, improving model performance across unseen domains.
problem Existing domain generalization approaches fail to capture the complex, multidimensional nature of real-world variation.
method Introduces Continuous Domain Generalization (CDG), a principled framework grounded in geometric and algebraic theories. Proposes a Neural Lie Transport Operator (NeuralLio) for structure-preserving parameter transitions and a gating mechanism for robust generalization.
result Demonstrates significant improvement in generalization accuracy and robustness across various datasets.
New method generates data across domains using latent variables.
problem Understanding and adapting to distribution changes across domains.
method Causal Generative Domain Adaptation Network (CG-DAN) with latent variable decomposition.
result CG-DAN improves learning efficiency and data generation across domains.
Deep neural networks reveal a low-dimensional manifold structure in data.
problem Understanding the structure of data for better model performance.
method Model-centric analysis of the data manifold using the local data matrix and Fisher information matrix.
result The dataset lies on a data leaf with a dimension bounded by the number of labels.
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.
Diffusion models adapt to data geometry through log-domain smoothing.
problem Understanding why diffusion models generalize well across diverse domains.
method Investigating the role of score matching and log-domain smoothing in diffusion models.
result Log-domain smoothing adapts the diffusion model to the data manifold.
The paper analyzes reflected diffusion models on hypercube data.
problem Challenges in modeling bounded domains with low-dimensional data.
method Employed an infinite series expansion of transition densities to bound the score function and its approximation.
result Established convergence rates for generative algorithm adapting to intrinsic dimensionality.
A new method tackles Bayesian inverse problems with complex PDEs.
problem Bayesian inverse problems with expensive forward model evaluations and high-dimensional priors.
method Domain-decomposed variational auto-encoder Markov chain Monte Carlo (DD-VAE-MCMC) method.
result The method efficiently solves Bayesian inverse problems in parallel and low-dimensional latent spaces.
Empirical Bayes improves causal representation learning across multiple domains.
problem Estimating causal representations from data across multiple domains.
method Developed an EB f-modeling algorithm for linearly-mixed causal representations. result Our method achieves more accurate estimation of causal variables than other methods.
TMDA aligns subdomain data distribution discrepancies across domains using manifold representations.
problem Transfer learning challenges due to domain divergence.
method TMDA uses low-dimensional manifolds to represent subdomains and aligns local data distribution discrepancies across domains using M3D.
result TMDA is a promising method for various transfer learning tasks.
This paper improves cross-domain learning using random forests for manifold alignment.
problem Improving cross-domain learning and feature integration.
method Semi-supervised manifold alignment using random forest proximities.
result Random forest proximities enhance downstream classification accuracy.
In this paper, we propose a non-parametric conditional factor regression (NCFR)model for domains with high-dimensional input and response. NCFR enhances linear regression in two ways: a) introducing low-dimensional latent factors leading to dimensionality reduction and b) integrating an Indian Buffet Process as a prior…
Two semi-supervised manifold alignment methods improve cross-domain classification.
problem Aligning data from multiple sources for better analysis.
method SPUD and MASH methods using graph integration and diffusion.
result SPUD and MASH methods outperform existing methods in cross-domain classification.
Paper develops a new method for solving IBVPs on star-shaped domains.
problem Solving Inverse Boundary Value Problems (IBVP) for parallel transport equations.
method Covariant tomography, integrating geometric decomposition with specific interior extensions.
result Formal solvability criterion for higher-order IBVPs, validated through examples.
A new method for manifold learning robust to irregular sampling.
problem Nonlinear dimensionality reduction of high-dimensional datasets with poor sampling and arbitrary topology.
method Parallel transport unfolding (PTU) for quasi-isometric low-dimensional mapping.
result Improved robustness to irregularity and voids in sampling compared to Isomap.
A scattering transform defines a signal representation which is invariant to translations and Lipschitz continuous relatively to deformations. It is implemented with a non-linear convolution network that iterates over wavelet and modulus operators. Lipschitz continuity locally linearizes deformations. Complex classes o…
Finding minima of a real valued non-convex function over a high dimensional space is a major challenge in science. We provide evidence that some such functions that are defined on high dimensional domains have a narrow band of values whose pre-image contains the bulk of its critical points. This is in contrast with the…
Study on reliability of latent reuse in diffusion models under distribution shift.
problem When can latent spaces from a source dataset be reused for a target dataset with different distributions?
method Considered a source-target setting with approximately low-dimensional datasets near different subspaces. Analyzed the target-domain score error due to principal-angle misalignment and target ambient noise.
result Latent reuse is reliable only if the source and target subspaces are close and the target ambient noise is not too amplified.
Proposes a method to compare noisy high-dimensional datasets with low-dimensional manifolds.
problem Comparing distributions on manifolds in noisy high-dimensional datasets.
method Linking low-rank structure to manifold geometry, developing a scale-invariant distance measure.
result Superior robustness and statistical power compared to existing methods.
DROCC improves anomaly detection across various domains without requiring domain-specific transformations.
problem Anomaly detection in structured domains like images and tabular data.
method DROCC assumes class points lie on a low-dimensional manifold and uses a robust loss function to avoid representation collapse.
result DROCC achieves up to 20% higher accuracy than state-of-the-art methods across multiple domains.
Proposes HetSANN for learning heterogeneous graph structures without meta-paths.
problem Learning low-dimensional vector space of heterogeneous information networks.
method Implicitly represents heterogeneous information through entity space transformation and attention mechanism.
result Significant improvements over state-of-the-art solutions on public datasets.
CNNs adapted for graph data with fast localized spectral filters.
problem Generalizing CNNs to irregular domains like graphs.
method Spectral graph theory for efficient localized convolutional filters.
result Efficient deep learning system for graph data with linear complexity.
The paper tackles automatic interpretation of manifold coordinates.
problem Finding physical meaning of abstract manifold coordinates.
method Proposes a method to explain embedding coordinates as compositions of functions from a dictionary.
result Demonstrates the effectiveness of the method on data.
Bayesian optimization helps find best nuclear interaction parameters.
problem Finding best coupling constants in complex nuclear interaction models.
method Bayesian optimization applied to chiral effective field theory.
result Bayesian optimization performs well in low-dimensional parameter domains.
Proposes dynamic graph and node feature learning in GCNNs for better adaptability.
problem Fixed graphs for all GCNN layers limit adaptability to node feature structures.
method Dynamic graph and node feature learning using Mahalanobis distance metric.
result Superior performance in point clouds and citation networks.
A new method for generative modeling of discrete data using geometric latent subspaces.
problem Learning generative models for discrete data with statistical dependencies.
method Geometric latent-subspace framework in exponential parameter space of product manifolds of categorical distributions.
result Low-dimensional latent space encodes statistical dependencies and accurately models high-dimensional discrete data.
New BMI interface stabilizes user experience over long periods.
problem Inconsistent neural signal data leads to interface recalibration.
method Adversarial Domain Adaptation Network to match residual distributions.
result Adversarial Domain Adaptation Network outperforms other methods.
Unified approach for learning state representations from streaming data.
problem Learning reusable state representations from high-dimensional, non-stationary data.
method Unified mathematical formulation for learning latent relations, enabling flexible and principled shaping of latent space.
result Improved understanding and evaluation of existing unsupervised learning approaches.
PLIs improve classifier performance by fine-tuning latent representations.
problem Difficult interpretation of high-dimensional latent representations in neural networks.
method Back-propagation of manual changes to low-dimensional embeddings using t-distributed stochastic neighbourhood embeddings.
result Manual separation of class clusters in latent space enhances classifier performance.
Q-NETs use neural networks to estimate integrals of low-dimensional functions efficiently.
problem Estimating integrals of multidimensional functions with costly evaluations.
method Fixed neural networks (Q-NETs) that operate on proxy function parameters to calculate exact integrals over subsets of dimensions.
result Q-NETs can calculate integrals over any subset of dimensions without resampling or retraining the proxy.
This work refines Cover's theory for binary classification on low-dimensional data.
problem The challenge of analyzing how low-dimensional data structures affect classification models.
method Refines Cover's function-counting theory to account for low-dimensional data structure.
result Derives dichotomy counts and analyzes the impact of data structure on classification models.
A new method reduces sample complexity for meta-learning.
problem Efficiently learn new tasks with minimal data.
method Alternating minimization method (MLLAM) for linear regression tasks.
result MLLAM achieves nearly-optimal estimation error with Ω(logd) samples per task. VQShape learns interpretable time-series representations and achieves comparable performance to specialist models.
problem Lack of interpretability in existing time-series models.
method Vector quantization of time-series data into abstracted shapes.
result VQShape achieves comparable performance to specialist models in classification tasks.
We characterize general pseudo-harmonic morphisms from a Riemannian manifold to a Hermitian manifold as pseudo horizontally weakly conformal maps with an additional property. We study to what extent we can (locally) describe these submersive pseudo-harmonic morphisms via the foliation given by the kernel of the associa…
The paper tackles high-dimensional Bayesian optimization using tree-structured additive models.
problem Scaling Bayesian Optimization to high-dimensional problems.
method Tree-structured additive models with hybrid graph learning and zooming-based algorithms.
result Demonstrates faster model learning and reduced model complexity in high-dimensional settings.