A new method transfers data between domains using a common space and adaptive functions.
problem Domain transfer learning between different datasets.
method Mapping data to a common space, learning a classifier there, and adapting it for each domain.
result The method outperforms existing transfer learning methods on benchmark datasets.
Optimizes portfolios using neural network approximations of asset sensitivities to common drivers.
problem Optimizing portfolios with complex asset dynamics and common drivers.
method Model asset dynamics with PDEs, approximate sensitivities with neural networks, and use hierarchical clustering on sensitivity matrix for optimization.
result Achieves over-performance in portfolio optimization across various markets and datasets.
The study examines free products of hyperbolic manifold groups and their model geometries.
problem Understanding when free products of hyperbolic groups have a common model geometry.
method Utilizes residual finiteness and graph covering theorems to analyze quasi-isometry classes.
result Provides examples of hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry.
Developed LQ MFG theory with common noise, proving existence and uniqueness.
problem Linear-quadratic mean field games with common noise.
method Coupled forward-backward stochastic evolution equations (FBSEEs) in Hilbert spaces.
result Existence and uniqueness of solutions for small and arbitrary finite time horizons.
A new model generates samples with a succinct common representation using Wyner's common information.
problem Generating samples with a succinct common representation.
method Proposes a variational Wyner model trained to minimize symmetric Kullback-Leibler divergence with regularization terms.
result Demonstrates utility through joint and conditional generation experiments.
Geometrically transforms word embeddings into a common space for better comparison.
problem Comparing embeddings from different sources is challenging.
method Applies orthogonal rotations and Mahalanobis scaling to transform embeddings into a shared latent space.
result The method improves word similarity and analogy tasks.
Robust Q-learning for mean-field control under Wasserstein uncertainty
problem Mean-field control under Wasserstein uncertainty
method Quantization-and-projection scheme with Wasserstein dual reformulation
result Convergence and finite-time iteration bounds
Geometric approach learns bilingual mappings from monolingual embeddings.
problem Bilingual lexicon induction and cross-lingual word similarity.
method Decouples learning into rotations and a metric, modeled as optimization on Riemannian manifolds.
result Outperforms previous approaches on bilingual lexicon induction and cross-lingual word similarity tasks.
A new method embeds distributions in a common space for optimal transport comparison.
problem Comparing distributions in different metric spaces.
method Sub-embedding robust Wasserstein (SERW) distance.
result SERW mimics GW distance properties and provides a cost relation.
Optimizes portfolios by identifying causal drivers of diversification.
problem Achieving efficient portfolio optimization based on asset and diversification dynamics.
method Commonality Principle, Reichenbach Common Cause Principle, conformal maps, Bayesian networks, correlation-based algorithms, neural networks, SDEs.
result Optimal portfolio diversification achieved through causal methodologies and sensitivity forecasting.
Generalizes Milnor's axiomatic homology theorems to Polish spaces.
problem Characterize (co)homology of Polish spaces.
method Eilenberg-Steenrod axioms, Milnor's map excision axiom, and a generalized additivity axiom.
result Unique characterization of (co)homology of Polish spaces.
This study calculates the average number of common zeros of holomorphic functions on complex manifolds.
problem Calculating the average number of common zeros of holomorphic functions.
method Defined a Hermitian mixed volume for a mix of non-negative Hermitian forms and proved the average number of common zeros equals this mixed volume.
result The average number of common zeros of holomorphic functions equals the mixed volume of the manifold.
A framework for federated learning with heterogeneous data.
problem Federated learning with data from clients using different data representations.
method FLIC framework that maps client data into a common feature space via local embedding functions, learned federally using Wasserstein barycenters and trained locally via distribution alignment.
result FLIC outperforms FL benchmarks with heterogeneous input feature spaces.
Einstein metrics on homogeneous torus bundles
problem Einstein metrics on total space of homogeneous torus bundles
method Descend to common base and establish estimates
result Prove precompactness theorem for Einstein manifolds
ZSL-KG learns class representations from common sense knowledge graphs.
problem Predicting classes without labeled examples using semantic class representations.
method TrGCN, a novel transformer graph convolutional network, embeds nodes from common sense knowledge graphs in a vector space.
result ZSL-KG improves over existing methods on five out of six zero-shot benchmark datasets.
Study pairs of subspaces with or without a common complement in Hilbert spaces.
problem Characterize pairs of subspaces with or without a common complement in Hilbert spaces.
method Analyze pairs of subspaces (S, T) in the Grassmann manifold Gr(H) of a Hilbert space H, identifying Delta and Gamma based on the existence of a common complement.
result Delta is open and its connected components are parametrized by dimension and codimension. Gamma is a C^\infty submanifold characterized by dimensions and semi-Fredholm indices.
Framework for robust control in cooperative systems with uncertain common noise.
problem Optimizing collective behavior of agents in the presence of uncertain common noise.
method Proposes a robust mean-field control framework and proves existence of optimal controls.
result Existence of optimal open-loop controls linked to a lifted robust Markov decision problem.
D-GCCA improves multi-view data analysis by separating common and distinctive components.
problem Analyzing multi-view high-dimensional data with latent factors.
method Decomposes each view's data matrix into common and distinctive sources with orthogonality constraints.
result Consistent estimators with good performance and efficient computation.
Inspired by the Gromov-Hausdorff distance, we define the intrinsic flat distance between oriented m dimensional Riemannian manifolds with boundary by isometrically embedding the manifolds into a common metric space, measuring the flat distance between them and taking an infimum over all isometric embeddings and all c…
Alexander's conjecture extended to infinite simplicial complexes.
problem Alexander's conjecture for infinite simplicial complexes.
method Generalization of recent result for finite simplicial complexes.
result Alexander's conjecture holds for infinite simplicial complexes.
RECol generates error columns to improve outlier detection.
problem Outlier detection in data with complex relationships.
method Generates reconstruction error columns for leave-one-out feature sets.
result Improves ROC-AUC and PR-AUC values of common outlier detection methods.
The paper finds and visualizes unique geometric polyhedra and tori with few vertices.
problem Finding and visualizing geometric polyhedra and tori with specific vertex configurations.
method Using Schlegel diagrams and geometric realization in 3D and 4D space.
result Identifies and visualizes 12 triangulations of the 2-torus and 12 triangulations of the 2D projective plane.
Paper disproves Kähler submanifolds in symmetrized polydisc.
problem Existence of Kähler submanifolds in symmetrized polydisc.
method Proof by contradiction using canonical metrics.
result Non-existence of Kähler submanifolds in symmetrized polydisc.
SepVAE separates patient-specific patterns from healthy ones using contrastive VAE.
problem Separating patient-specific patterns from healthy ones in medical datasets.
method SepVAE uses a contrastive VAE with disentangling and classification losses to differentiate between common and salient features.
result SepVAE outperforms previous methods in three medical applications and a CelebA dataset.
Extends smoothness results for submanifolds and mean curvature flows with a common boundary.
problem Smoothness of submanifolds and mean curvature flows with a common boundary.
method Analyzes area-stationary and Brakke flows with common boundaries to show smoothness.
result Smoothness of boundaries and submanifolds in area-stationary and Brakke flows.
BNN learns shared features between two data sources for specific tasks.
problem Learning shared features between two data sources for specific tasks.
method BNN uses two CNNs to project data sources into a feature space and learns a common representation for each task.
result BNN achieves state-of-the-art performance on various tasks.
NestedVAE isolates common factors from paired images without additional supervision.
problem Reduction of data-driven biases in machine learning models.
method Combines deep latent variable models with information bottleneck theory.
result NestedVAE significantly outperforms alternative methods in various tasks.
A new graph kernel uses LCS and Wasserstein distance for better graph comparisons.
problem Graph learning methods can be limited by information from distant vertices and path length constraints.
method Proposes a Graph Kernel based on LCS similarity and Wasserstein distance in a novel metric space.
result The new kernel emphasizes comparisons between similar paths and reduces information loss.
Learning multiple tasks across heterogeneous domains is a challenging problem since the feature space may not be the same for different tasks. We assume the data in multiple tasks are generated from a latent common domain via sparse domain transforms and propose a latent probit model (LPM) to jointly learn the domain t…
Modeling continuous movement of entities in latent space for interaction timing.
problem Analyzing timing and frequency of instantaneous interactions.
method Latent position model with continuous trajectories.
result Individual trajectories estimated from interaction data.
We study the classification of ultrametric spaces based on their small scale geometry (uniform homeomorphism), large scale geometry (coarse equivalence) and both (all scale uniform equivalences). We prove that these equivalences can be characterized with parallel constructions using a combinatoric tool called common zi…
The relationship between the Chern-Simons invariant and eta-invariant of a 3-manifold is shown to lead to an obstruction to a group being the fundamental group of a closed oriented 3-manifold. The proof uses Sunada's construction of isospectral manifolds as covering spaces over a common base space.
Fuzzy Forests reduces feature space in high-dimensional survey data.
problem High-dimensional and highly correlated datasets in social science.
method Fuzzy Forests algorithm, a variant of Random Forests.
result Partisan polarization was the strongest factor in the 2020 presidential election.
TLR learns better latent representations for unsupervised domain adaptation.
problem Learning models in a target domain using data from a source domain.
method Designing a simple linear autoencoder objective function to derive robust latent representations.
result TLR reduces domain shift and preserves common properties of both domains.
On a smooth line bundle L over a compact Kähler Riemann surface Σ, we study the family of vortex equations with a parameter s. For each s∈[1,∞], we invoke techniques in \cite{Br} by turning the s-vortex equation into an s-dependent elliptic partial differential equation, studied in \cite{kw}, provi…
Study shows gradient variance increases during deep learning training, contrary to common belief.
problem Understanding and minimizing gradient variance in deep learning models.
method Gradient Clustering method using stratified sampling to minimize gradient variance.
result Gradient variance increases during training, and smaller learning rates coincide with higher variance.
CDPA identifies common and distinctive patterns in high-dimensional datasets.
problem Existing methods fail to capture the common pattern between coefficient matrices of shared latent factors.
method Proposes CDPA, an unsupervised learning method that incorporates both common and distinctive patterns of coefficient matrices.
result CDPA provides better characterization of common and distinctive patterns in high-dimensional datasets.
The common assertion that the Ricci flows of Einstein spaces with cosmological constant can be modelled by certain classes of nonholonomic frame, metric and linear connection deformations resulting in nonhomogeneous Einstein spaces is examined in the light of the role played by topological three dimensional (3D) Taub-N…
Enhanced Teichmüller space for surfaces with decorations and enhancements.
problem Parameterizing and understanding Teichmüller spaces with enhancements and decorations.
method Introduced a new variation of Teichmüller space, constructed parameterization, and introduced lamination space.
result Compatibility of shear coordinates and λ-length coordinates in the new deformation space.
We study topology of configuration spaces of planar linkages having one leg of variable length. Such telescopic legs are common in modern robotics where they are used for shock absorbtion and serve a variety of other purposes. Using a Morse theoretic technique, we compute explicitly, in terms of the metric data, the Be…
Common perpendiculars equidistribute in negatively curved spaces.
problem Equidistribution of common perpendiculars in negatively curved spaces.
method Analyzing the Bowen-Margulis measure and geodesic flow properties.
result Lebesgue measures of common perpendiculars equidistribute to the Bowen-Margulis measure.
Let G be a finitely generated group. Two simplicial G-trees are said to be in the same deformation space if they have the same elliptic subgroups (if H fixes a point in one tree, it also does in the other). Examples include Culler-Vogtmann's outer space, and spaces of JSJ decompositions. We discuss what features are co…
In this paper, we express surfaces parametrically through a given spacelike (timelike) asymptotic curve using the Frenet frame of the curve in Minkowski 3-space. Necessary and sufficient conditions for the coefficients of the Frenet frame to satisfy both parametric and asymptotic requirements are derived. We also prese…
A new method for projecting multimodal data to a common subspace for one-class classification.
problem Classifying data from multiple sources with varying features.
method Iterative transformation to a common subspace, separate transformations for each modality, regularization strategies.
result Outperforms competing methods across multiple datasets.
Study local properties of homogeneous ANR-spaces, proving dimension full-valuedness.
problem Understand local structure of homogeneous ANR-spaces.
method Describe local structure and use it to prove dimension full-valuedness.
result Every finite-dimensional homogeneous metric ANR-compactum is dimensionally full-valued.
Study finds stocks with common firm fears earn lower returns.
problem Identifying and quantifying firm-level investor fears.
method Analysis of equity options to identify common firm-level fears and their impact on stock returns.
result Stocks with exposure to common bad fears earn lower returns and require higher compensation.
Proposes MV-Co-VH for multi-view clustering using visible and hidden views.
problem Lack of efficient algorithms for fully utilizing multi-view data.
method Projects multiple views to a common hidden space using NMF, then applies collaborative learning.
result Competitive clustering performance on UCI and real-world datasets.
Neural story generation gains common sense through targeted training.
problem Lack of common sense reasoning in neural-generated stories.
method Multi-task learning with auxiliary datasets for common sense grounding.
result Improved common sense reasoning and state-of-the-art perplexity.