arXiv research

Additive Gaussian process framework handles monotonicity constraints in high dimensions.

Sharp dimension constraints for positive intermediate curvature metrics are established.

Adapts Bartnik method to Hilbert manifold structure for vacuum constraint equations.

The paper analyzes constrained optimal portfolios in high dimensions using novel statistical learning techniques.

Paper shows affine constraint is unnecessary for high-dimensional data.

In this note we show that the Lagrangian Luttinger surgery preserves the symplectic Kodaira dimension. Some constraints on Lagrangian tori in symplectic four manifolds with non-positive Kodaira dimension are also derived.

For certain manifolds, nonnegative Ricci curvature limits dimension and forces almost abelian fundamental group.

In 5D, integrability is linked to curvature constraints of subconformal structures.

Study on harmonic maps from surfaces to homogeneous spaces, focusing on bubble formation and geometric constraints.

The paper studies the properties of maps with free boundaries, focusing on the obstacle case.

VFlow enhances generative flows by augmenting data dimensions for better expressiveness.

This short paper gives a constraint on Chern classes of closed strictly pseudoconvex CR manifolds (or equivalently, closed holomorphically fillable contact manifolds) of dimension at least five. We also see that our result is ''optimal'' through some examples.

Study contextual bandits with stage-wise constraints, proving regret bounds and extending results.

Geodesics with bounded angles have zero Hausdorff dimension.

The paper explores curvature constraints on Kodaira dimension for specific almost Hermitian manifolds.

Study circle actions on manifolds with 3 fixed points, finding dimension constraints and unique structures.

Deep learning improves portfolio optimization efficiency.

Bayesian optimization improves with transfer learning for aircraft design.

Intersectional constraints improve selection outcomes by reducing inequality.

We break dimension dependence in sparse distribution estimation with communication constraints.

We show that if a co-dimension two knot is deform-spun from a lower-dimensional co-dimension 2 knot, there are constraints on the Alexander polynomials. In particular this shows, for all n, that not all co-dimension 2 knots in S^n are deform-spun from knots in S^{n-1}.

Unified physics-informed learning method improves generalization performance.

Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions, but often lead to unwanted shrinkage. This paper explores instead penalizing the squared distanc…

Unified framework for constrained online decision-making.

We consider the problem of noisy 1-bit matrix completion under an exact rank constraint on the true underlying matrix $M^*$. Instead of observing a subset of the noisy continuous-valued entries of a matrix $M^*$, we observe a subset of noisy 1-bit (or binary) measurements generated according to a probabilistic model. W…

Extends Dirac structures to infinite dimensions for mechanical systems.

We derive the Riemannian Positive Mass theorem in arbitrary dimensions, without any topological constraints. The main new tools are skin structures and surgeries on minimal hypersurfaces.

Algorithm minimizes regret while adhering to unknown safety constraints.

Estimates box dimension of fractal interpolation surfaces using oscillation vectors.

Two new methods solve large-scale stochastic convex problems with linear constraints.

Study shows dimension constraints for isometry groups in non-collapsed Riemannian manifolds.

Superconformal geometries discussed in various spacetime dimensions using local supertwistor bundles.

A new method for fair representation learning using PLS.

The paper extends localisation technique to multiple constraints in Euclidean spaces.

Pluriclosed flow preserves Hermitian-symplectic structures and forms, with topological constraints.

LCBO tackles constrained optimization in high dimensions, offering a polynomial convergence rate.

Proper regularization is critical for speeding up training, improving generalization performance, and learning compact models that are cost efficient. We propose and analyze regularized gradient descent algorithms for learning shallow neural networks. Our framework is general and covers weight-sharing (convolutional ne…

We derive the Space-Time Positive Mass theorem in arbitrary dimensions, without topological constraints. The main new tools are skin structures and surgeries on minimal and marginally outer trapped hypersurfaces.

In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality results are established, representing the solution in terms of path d…

We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills fields, because the scalar field introduces three extra terms into the Lichnerowicz e…

The study shows a 3D manifold's macroscopic dimension is 1 under specific curvature constraints.

Bayesian network models with latent variables are widely used in statistics and machine learning. In this paper we provide a complete algebraic characterization of Bayesian network models with latent variables when the observed variables are discrete and no assumption is made about the state-space of the latent variabl…

This paper deals with the super-replication of non path-dependent European claims under additional convex constraints on the number of shares held in the portfolio. The corresponding super-replication price of a given claim has been widely studied in the literature and its terminal value, which dominates the claim of i…

The paper classifies energy-minimizing sets in specific domains.

Unified framework for hard affine SDP constraints in vRKHSs.

Local Linear embedding (LLE) is a popular dimension reduction method. In this paper, we first show LLE with nonnegative constraint is equivalent to the widely used Laplacian embedding. We further propose to iterate the two steps in LLE repeatedly to improve the results. Thirdly, we relax the kNN constraint of LLE and p…

Embedding models for entities and relations are extremely useful for recovering missing facts in a knowledge base. Intuitively, a relation can be modeled by a matrix mapping entity vectors. However, relations reside on low dimension sub-manifolds in the parameter space of arbitrary matrices---for one reason, compositio…

One-dimensional crystals have convex shapes under certain conditions.