arXiv research

Proves exponential sample complexity separations in local differential privacy.

Proves conditions for separating regions in homogeneous spaces without trivial topology.

Improves arc separation result for homogeneous spaces.

This work examines a semi-blind single-channel source separation problem. Our specific aim is to separate one source whose local structure is approximately known, from another a priori unspecified background source, given only a single linear combination of the two sources. We propose a separation technique based on lo…

This work learns sparse tensor representations using mixtures of separable dictionaries.

The paper proves local laws for non-separable sample covariance matrices.

Gradient descent-ascent converges to strict local minmax equilibria with a finite timescale separation.

Study reveals structure of local minima in GMMs, identifying key cluster centers.

New local ID estimators based on data separability.

A tensor field generates separation of variables for certain metrics.

Localized sum-of-norms clustering separates balls in data.

Study models deep learning training dynamics using locally elastic SDEs to reveal feature separability.

It is shown that the hyperspace of all nonempty closed subsets $\Cld_{AW}(X)$ of a separable metric space $X$ endowed with the Attouch-Wets topology is homeomorphic to a separable Hilbert space if and only if the completion of $X$ is proper, locally connected and contains no bounded connected component, $X$ is topologi…

Neural networks can learn Boolean circuits with local correlation.

Local Gradient Descent with local steps converges to the centralized model in the interpolation regime.

For an infinite cardinal $κ$ let $\ell_2(κ)$ be the linear hull of the standard othonormal base of the Hilbert space $\ell_2(κ)$ of density $κ$. We prove that a non-separable convex subset $X$ of density $κ$ in a locally convex linear metric space if homeomorphic to the space (i) $\ell_2^f(κ)$ if and only if $X$ can be…

New approach for classification using trigonometric polynomial kernels from signal processing.

Paper investigates separating times for general diffusions, providing new insights.

New methods test discrete distributions faster with local privacy constraints.

We consider the closeness testing problem for discrete distributions. The goal is to distinguish whether two samples are drawn from the same unspecified distribution, or whether their respective distributions are separated in $L_1$-norm. In this paper, we focus on adapting the rate to the shape of the underlying distri…

Categorical d-separation criterion simplifies probability graph analysis.

Enhanced Hopfield model boosts memory retrieval capacity.

NLSSC improves clustering by enhancing separability in sparse coding.

We show that all groups in a very large class of Coxeter groups are locally quasiconvex and have uniform membership problem solvable in quadratic time. If a group in the class satisfies a further hypothesis it is subgroup separable and relevant homomorphisms are also calculable in quadratic time. The algorithm also dec…

The paper introduces toric separable geometries and finds new extremal metrics.

We compute the Hilbert polynomial and the Poincare function counting the number of fixed jet-order differential invariants of conformal metric structures modulo local diffeomorphisms, and we describe the field of rational differential invariants separating generic orbits of the diffeomorphism pseudogroup action. This r…

We consider the problem of high-dimensional Ising (graphical) model selection. We propose a simple algorithm for structure estimation based on the thresholding of the empirical conditional variation distances. We introduce a novel criterion for tractable graph families, where this method is efficient, based on the pres…

New kernels capture both local and non-local interactions efficiently.

The study quantifies how many objects can be linearly classified under all views.

A new unsupervised method separates speech sources without requiring labeled data.

In this paper we continue the study of bi-conformal vector fields started in {\em Class. Quantum Grav.} {\bf 21} 2153-2177. These are vector fields defined on a pseudo-Riemannian manifold by the differential conditions $\lie P_{ab}=φP_{ab}$, $\lieΠ_{ab}=χΠ_{ab}$ where $P_{ab}$, $Π_{ab}$ are orthogonal and complementary…

EM algorithm achieves optimal sample complexity for well-separated Gaussian mixtures.

Novel method separates astrophysical components from noisy data.

Rationality of the Wightman functions is proven to follow from energy positivity, locality and a natural condition of global conformal invariance (GCI) in any number D of space-time dimensions. The GCI condition allows to treat correlation functions as generalized sections of a vector bundle over the compactification o…

New research shows certain arithmetic lattices can't be LERF.

We propose a new class of data-independent locality-sensitive hashing (LSH) algorithms based on the fruit fly olfactory circuit. The fundamental difference of this approach is that, instead of assigning hashes as dense points in a low dimensional space, hashes are assigned in a high dimensional space, which enhances th…

The paper studies conditions for exact posterior modeling in Bayesian networks.

Hybrid model improves music source separation by 1.4 dB.

Understanding separation effects on parameter estimation in finite Gaussian mixtures

We give an explicit local formula for any formal deformation quantization, with separation of variables, on a Kähler manifold. The formula is given in terms of differential operators, parametrized by acyclic combinatorial graphs.

We consider a pseudo-Riemannian metric that changes signature along a smooth curve on a surface, called the discriminant curve. The discriminant curve separates the surface locally into a Riemannian and a Lorentzian domain. We study the local behaviour and properties of geodesics at a point on the discriminant where th…

Bayesian Federated Inference combines local data analyses to estimate regression models.

Surrogate-based analysis of interactions via local effect smooths

The paper discusses conditions for gluing multiple Alexandrov spaces into an Alexandrov space.

We introduce a comprehensive and statistical framework in a model free setting for a complete treatment of localized data corruptions due to severe noise sources, e.g., an occluder in the case of a visual recording. Within this framework, we propose i) a novel algorithm to efficiently separate, i.e., detect and localiz…

CNNs require fewer samples than LCNs and FCNs for image-based tasks due to locality and weight sharing.

New insights into spurious local minima in k-means clustering.

This is the first of two companion papers in which a thorough study of the normal form and the first integrability conditions arising from {\em bi-conformal vector fields} is presented. These new symmetry transformations were introduced in {\em Class. Quantum Grav.} \textbf{21}, 2153-2177 and some of their basic proper…