Optimal transport for vector Gaussian mixtures improves efficiency and structure preservation.
problem Optimal mass transport for vector-valued Gaussian mixtures.
method Vectorizing Gaussian mixture models and studying optimal mass transport problems.
result Computational efficiency and structure preservation in optimal mass transport.
Random matrix ensembles yield uniform distributions on manifolds.
problem Understanding distributions of vectors in random matrix ensembles.
method Analyzing eigenvalues, singular values, and Autonne-Takagi vectors of various random matrix ensembles.
result Uniform distributions on specific manifolds for different types of random matrix ensembles.
Study on singularities of bundle homomorphisms induced by Morin maps.
problem Characterizing singular points of bundle homomorphisms.
method Analyzing conditions for singularities induced by Morin maps, using Hamilton vector fields for contact structures.
result Characterization of singularities in bundle homomorphisms induced by Morin maps.
New method AM learns optimal vector fields for entire distribution sequences, matching OT.
problem Optimal Transport (OT) problem in generative modeling.
method Action Matching (AM) method learns optimal vector fields for a sequence of distributions.
result AM method achieves optimal transport by learning vector fields for entire distribution sequences.
Proves Sard conjecture for specific distributions, controlling divergence of vector fields.
problem Proving the Sard conjecture for certain types of distributions.
method Constructs a singular distribution capturing essential abnormal lifts, proving the conjecture for rank 3 distributions in dimension 4 and generic corank 1 distributions.
result Proves the Sard conjecture for generic co-rank one distributions.
Transformers infer tasks from context via two modes, geometrically shaped task vectors explain their behavior.
problem Understanding how transformers infer tasks from context and the geometric properties of task vectors.
method Synthetic setting to train small transformers, mathematical characterization of task-vector geometry and inference modes.
result Task-vector geometry shapes in-distribution and out-of-distribution behavior of transformers.
This paper proposes MMD-SVR to improve SVR's margin distribution for better generalization.
problem Improving SVR's generalization performance by maximizing the margin distribution of the whole dataset.
method Introducing MMD-SVR with coupled constraints to convert a non-convex optimization problem into a convex one.
result MMD-SVR significantly improves prediction accuracy and generalization compared to classic SVR.
Geometric structures on surfaces relate to 2-plane distributions in 5D.
problem Understanding geometric properties of vector bundles and distributions.
method Study of horizontal 2-plane distributions on 5-manifolds.
result Established a connection between surface projective differential geometry and 2-plane distribution growth.
A computational technique for calculating nullity vectors and kernel vectors, using the new Finsler package, is introduced. As an application, three interesting counterexamples are given. The first counterexample shows that the two distributions KerR and NR do not coincide. The second shows that the nul…
Novel methods transform correlated neutral vectors into independent variables.
problem Decorrelating correlated neutral vector variables that are not multivariate Gaussian distributed.
method Serial and parallel nonlinear transformations to achieve mutual independence.
result Highly negatively correlated neutral vectors can be transformed into mutually independent scalar variables.
Symmetry distribution in naturally reductive nilpotent Lie groups matches invariant induced by fixed vectors.
problem Understanding symmetry distribution in naturally reductive nilpotent Lie groups.
method Analyzing the invariant distribution induced by fixed vectors of isotropy.
result Symmetry distribution matches the invariant induced by fixed vectors.
A new policy for contextual bandits adapts to reward vector shifts.
problem Learning under reward vector shifts with ordered rewards.
method Adaptive-discretization and optimistic elimination policy.
result Established upper bounds on preference-based regret.
Unified derivation of stochastic order conditions for elliptical distributions.
problem Classifying multivariate elliptical distributions based on stochastic orders.
method Established an identity for comparing expectations of functions of elliptical vectors and used it to derive conditions for stochastic orders.
result Unified derivation of conditions for various stochastic orders in multivariate elliptical distributions.
New algorithms reduce computational burden for principal support vector machines.
problem High computational cost of principal support vector machines for large datasets.
method Two distributed estimation algorithms for principal support vector machines.
result Statistical efficiency is maintained with distributed algorithms.
Random square-tiled surfaces have normal genus distribution and cover all integer vectors.
problem Distribution and properties of random square-tiled surfaces.
method Randomizing model and local central limit theorem for genus.
result The distribution of the genus is asymptotically normal and contains all primitive integer vectors.
In this paper the result of real hypersurfaces in non-flat complex space forms, whose structure vector field ξ belongs to the κ-nullity distribution is extended in case of three dimensional real hypersurfaces in non-flat complex space forms. Furthermore, generalization of notion (κ,μ)-nullity distribution defin…
We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a stochastically independent uniformly distributed unit vector. When the set of unit vectors …
Unsupervised matching method for relational data without alignment info.
problem Matching objects in different relational datasets without correspondence info.
method Model latent vectors, estimate by likelihood, project onto shared space.
result Preserves structural information in latent vectors across datasets.
We investigate the existence of coordinate transformations which bring a given vector field on a manifold equipped with an involutive distribution into the form of a second-order differential equation field with parameters. We define associated connections and we give a coordinate-independent criterion for determining …
In this paper, we derive Hybrid, Bayesian and Marginalized Cramér-Rao lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement vector Sparse Bayesian Learning (SBL) problem of estimating compressible vectors and their prior distribution parameters. We assume the unknown vector to be drawn from a compr…
The study generalizes a specific geometric correspondence to higher dimensions.
problem Understanding nondegenerate lines on holomorphic contact manifolds.
method Analyzing nondegenerate lines and corresponding distributions on higher-dimensional manifolds.
result A generalization of the (2,3,5)-distributions to higher dimensions. A new method for support vector regression using a data-driven insensitive parameter.
problem Determining an optimal insensitive parameter in support vector regression.
method A data-driven approach to approximate the insensitive parameter by minimizing a generalized loss function based on the likelihood principle.
result The proposed method outperforms traditional support vector regression methods and has lower computational costs.
Efficiently handles large support vectors in kernelized online learning.
problem Efficiency in communication for large support vectors in kernelized models.
method Extends a previously proposed protocol to kernelized online learners, introducing a novel communication criterion.
result Communication is bounded by the loss suffered, improving efficiency.
The paper calculates gap distributions for translation surfaces, focusing on the double heptagon.
problem Calculating gap distributions for translation surfaces.
method Describes a procedure to find winning holonomy vectors and applies it to the double heptagon.
result Explicitly computed gap distribution for the regular double heptagon translation surface.
Conformal vector fields on LCP manifolds are orthogonal and Killing.
problem Understanding conformal vector fields on specific geometric manifolds.
method Analyzing properties of conformal vector fields on compact locally conformally product manifolds.
result Conformal vector fields are orthogonal to the flat distribution and Killing.
The paper introduces a new method for tail bounds of random vectors and matrices.
problem Estimating norms of random vectors and matrices under moment assumptions.
method Variational tail bounds for norms of random vectors and matrices.
result Dimension-free concentration inequalities for various norms of random vectors and matrices.
Paper explores vector embeddings, distributional hypothesis, and PIP loss for natural language processing.
problem Understanding the effect of dimensionality on vector embeddings and their functionality.
method Formulates a theoretical framework, proposes PIP loss, and reveals bias-variance trade-off.
result Discovers robustness and forward stability of vector embeddings, answers dimensionality selection problem.
Distributed SVM algorithm improves performance in real-world applications.
problem Improving SVM performance in distributed computing environments.
method Proposes HPSVM, a distributed SVM algorithm that minimizes inter-machine communications.
result HPSVM achieves similar or better results than state-of-the-art SVM techniques.
The paper examines conditions for linearity in a conditional mean estimator under vector Poisson noise.
problem Conditions for linearity of the conditional mean estimator in vector Poisson noise.
method Analyzes prior distributions and their impact on the conditional mean estimator's linearity.
result The only prior distribution that induces linearity is a product gamma distribution, and non-zero dark current parameter prevents linearity.
This paper proposes a new method for embedding sequences using Wasserstein distances.
problem Embedding sequences in a metric space for better pattern recognition.
method Develops a deep learning model that embeds sequences as distributions and uses Wasserstein distances for comparison.
result Distributional embeddings using Wasserstein distances outperform traditional vector embeddings.
Study on InstaHide's security, linking to phase retrieval problem.
problem Security of InstaHide scheme for private dataset sharing.
method Design of a provable algorithm for private vector recovery.
result Private vectors can be recovered using synthetic vectors and public vectors.
New compression schemes save communication in distributed mean estimation.
problem Efficiently compressing vectors for mean estimation in a limited communication setting.
method Collaborative compression schemes that exploit vector similarities without requiring known correlations.
result Analysis shows varying error types with vector similarity.
New results on max-entropy distributions with succinct descriptions and stability.
problem Understanding the complexity and stability of max-entropy distributions.
method Polynomial-time algorithms and bounds on bit complexity.
result Polynomial bit complexity of ε-optimal dual solutions to max-entropy convex programs.
This paper is a starting point towards computing the Hausdorff dimension of submanifolds and the Hausdorff volume of small balls in a sub-Riemannian manifold with singular points. We first consider the case of a strongly equiregular submanifold, i.e., a smooth submanifold N for which the growth vector of the distributi…
A new framework for generative modeling using controlled vector fields.
problem Expressive modeling with limited parameters.
method Continuous-time modeling with modulated fixed vector fields and learned scalar controls.
result Expressive transport achieved with a small number of learned control channels.
Enhances SVM for uncertain data with probabilistic Gaussian distributions.
problem Binary classification with uncertain data and error bounds.
method Probabilistic kernel Support Vector Machines using Gaussian distributions.
result Suitable kernel function for uncertain data.
The paper explores MAE as a loss function for DNN vector-to-vector regression, proving its advantages over MSE.
problem Improving loss function for deep neural network based vector-to-vector regression.
method Presenting performance bounds and new properties of MAE, deriving generalized upper bounds, and interpreting MAE as a Laplacian distribution.
result MAE is a more suitable loss function than MSE for DNN based vector-to-vector regression, especially when errors follow a Laplacian distribution.
CAVs reveal latent concept distributions, but are vulnerable to adversarial attacks.
problem Understanding latent concept encodings in AI models.
method Probabilistic perspective on CAVs, deriving mean and covariance.
result CAVs can be adversarially manipulated, highlighting a vulnerability.
Monotone aggregation of dependent random vectors has an absolutely continuous distribution under certain conditions.
problem Monotone aggregation of dependent random vectors
method Coordinatewise monotonicity and uniform lower-increment conditions
result One-dimensional push-forwards of dependent random vectors have an absolutely continuous distribution
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.
Detects anomalies in vector fields without distributional assumptions.
problem Detecting anomalies in high-dimensional, non-stationary vector fields.
method Optimal Karhunen-Loeve expansion, multilevel orthogonal subspaces, hypothesis tests.
result Reliable anomaly detection without distributional assumptions.
Top2Vec finds topic vectors from documents and words without needing stop words or custom settings.
problem Topic modeling weaknesses, including needing known topics, stop words, and custom settings.
method Joint document and word semantic embedding to find topic vectors automatically.
result Top2Vec finds more informative and representative topics than probabilistic models.
Optimal DP mechanisms for vector queries are found to be staircase distributions.
problem Designing optimal additive mechanisms for vector-valued queries under differential privacy.
method Reduction to radially symmetric distributions and convex rearrangement theory.
result Staircase mechanisms are optimal for any norm and cost function.
A new multi-scale vector quantization method for unsupervised data.
problem Efficiently reconstructing unsupervised data with minimal distortion.
method Reconstruction trees, inspired by decision trees, explore data in a multi-scale fashion.
result Analysis of expected distortion under fixed unknown distribution, with asymptotic and finite sample results.
The paper proposes methods to find a shared active subspace for multivariate vector-valued functions.
problem Minimizing the deviation between function evaluations in the original and reconstructed spaces.
method Manipulating gradients or SPD matrices to identify a shared structure.
result Summing SPD matrices often identifies the best shared active subspace.
Local equivalence found between maximally symmetric rolling and flat Cartan distributions.
problem Establishing local equivalence between maximally symmetric rolling and flat Cartan distributions.
method Using complex parametrisation of su(2), a change of coordinates maps the maximally symmetric rolling (2,3,5)-distribution to the flat Cartan distribution. result Local equivalence between maximally symmetric rolling and flat Cartan distributions established.
We develop time-uniform confidence spheres for estimating means of random vectors.
problem Sequential mean estimation in high-dimensional spaces.
method Derive time-uniform confidence sphere sequences (CSSs) for various types of random vectors.
result Optimal CSSs for log-concave, sub-Gaussian, and sub-ψ random vectors. Motivated by control-affine systems in optimal control theory, we introduce the notion of a point-affine distribution on a manifold X - i.e., an affine distribution F together with a distinguished vector field contained in F. We compute local invariants for point-affine distributions of constant type when dim(X)=n, ran…