New method estimates precision matrices without models, achieving dense, consistent, and model-free properties.
problem Lack of methods that are dense, consistent, and model-free for precision matrix estimation.
method General class of estimators that unify dense, consistent, and model-free properties within a nonasymptotic framework.
result Ridgeless regression exhibits the double descent phenomenon, establishing a precision matrix analogue to linear regression's double descent.
Generative model captures hubs and dense communities in social networks.
problem Capturing both hubs and dense communities in social networks.
method Graphon mixture model with a new condition on sparse graphs.
result Estimation of hub normalized degree and graphon for sparse components.
New framework for dense weighted networks with community-specific patterns.
problem Dense networks with varying edge weights across communities.
method Proposes a new model with functions mapping node characteristics to edge weights, requiring few parameters.
result Developed a bootstrap methodology for generating new networks.
Estimates for Schrödinger operators on manifolds with bounded Ricci curvature.
problem Quantifying unique continuation for Schrödinger operators on manifolds with specific curvature conditions.
method Proving quantitative unique continuation estimates for Schrödinger operators on manifolds with Ricci curvature bounded below.
result Upper bound for energy range and constant in terms of Ricci curvature and parameters of relatively dense set.
Crowdsourcing is a strategy to categorize data through the contribution of many individuals. A wide range of theoretical and algorithmic contributions are based on the model of Dawid and Skene [1]. Recently it was shown in [2,3] that, in certain regimes, belief propagation is asymptotically optimal for data generated f…
For a wide range of clinical applications, such as adaptive treatment planning or intraoperative image update, feature-based deformable registration (FDR) approaches are widely employed because of their simplicity and low computational complexity. FDR algorithms estimate a dense displacement field by interpolating a sp…
Using a Bayesian approach, we consider the problem of recovering sparse signals under additive sparse and dense noise. Typically, sparse noise models outliers, impulse bursts or data loss. To handle sparse noise, existing methods simultaneously estimate the sparse signal of interest and the sparse noise of no interest.…
New estimator learns symmetric dynamics from few observations.
problem Learning parameters of stochastic linear dynamics from limited data.
method Method of moments estimator using T=O(logN) observations. result Achieves small maximum element-wise error on symmetric matrices.
New solver MPLP++ outperforms existing solvers for dense graph models.
problem Efficiently solving dense, discrete Graphical Models with pairwise potentials.
method Dual Block-Coordinate Ascent with MPLP++ modification.
result MPLP++ significantly outperforms existing solvers, including TRWS.
New algorithms estimate matrix leverage scores using rank revealing and randomization.
problem Estimating leverage scores for matrices of arbitrary rank.
method Combining rank revealing methods with randomized dimensionality reduction.
result Effective estimators for leverage scores, even in rank deficient cases.
New method uses temperature to control sparse MoE convergence rates.
problem Sparse MoE convergence rates are slow due to temperature interactions.
method Proposes a novel activation gate to improve convergence rates.
result Improved convergence rates to polynomial rates via novel gate.
The paper explores graphons of line graphs from sparse finite graphs.
problem Estimating graph limits from sparse finite graphs.
method Mapping finite graphs to their line graphs and analyzing graphs with the square-degree property.
result Graphons of line graphs can distinguish between sparse graphs like star graphs and superlinear preferential attachment graphs.
Paper improves confidence intervals and variance estimation for deep learning models.
problem Improving confidence intervals and variance estimation in deep learning models.
method Residual-based framework for conditional variance estimation; robust bootstrap procedure for confidence intervals.
result First non-asymptotic bounds for variance estimation using ReLU networks.
Generic Hitchin representations generate dense subgroups.
problem Understanding dense subgroups in SL_n(R) representations.
method Using a theorem by Rapinchuk, Benyash-Krivetz, and Chernousov.
result Generic Hitchin representations are strongly dense.
We present a self-supervised approach to training convolutional neural networks for dense depth estimation from monocular endoscopy data without a priori modeling of anatomy or shading. Our method only requires monocular endoscopic videos and a multi-view stereo method, e.g., structure from motion, to supervise learnin…
New lattices in higher dimensions have dense surface subgroups.
problem Finding dense subgroups in higher-dimensional arithmetic lattices.
method Exhibited nonuniform arithmetic lattices in SO(n,1).
result Contain Zariski-dense surface subgroups.
Heavy-tailed distributions are frequently used to enhance the robustness of regression and classification methods to outliers in output space. Often, however, we are confronted with "outliers" in input space, which are isolated observations in sparsely populated regions. We show that heavy-tailed stochastic processes (…
Sparse covariance estimation in the vertical-split model achieves exponential improvement over dense estimates.
problem Minimax estimation error for distributed covariance matrix estimation in the vertical-split setting.
method Elementwise s-sparsity is shown to reduce communication and sample complexity. result Minimax lower bounds for 1-sparse cross-covariance estimation are established. We discuss dense embeddings of surface groups and fully residually free groups in topological groups. We show that a compact topological group contains a nonabelian dense free group of finite rank if and only if it contains a dense surface group. Also, we obtain a characterization of those Lie groups which admit a dens…
The paper studies PCA of probability measures with varying sample sizes and finds optimal convergence rates.
problem PCA of multiple probability measures with varying sample sizes.
method Double asymptotic regime analysis with convergence rates n−1/2+m−α for empirical covariance and PCA risk. result Optimal convergence rates for empirical covariance and PCA risk in the dense regime are proven.
Paper develops Dense NN models for temporal-spatial data with improved performance.
problem Improving predictive performance and robustness in temporal-spatial modeling.
method Fully connected neural networks with ReLU activation, non-asymptotic bounds, manifold modeling, short-range dependence.
result Demonstrates superior performance in temporal-spatial modeling across various synthetic functions.
Inverse modeling for the estimation of non-Gaussian hydraulic conductivity fields in subsurface flow and solute transport models remains a challenging problem. This is mainly due to the non-Gaussian property, the non-linear physics, and the fact that many repeated evaluations of the forward model are often required. In…
Bi-Lipschitz rigidity theorem for dense subgroups of algebraic groups.
problem Characterizing dense subgroups of algebraic groups.
method Bi-Lipschitz rigidity theorem for Zariski dense discrete subgroups.
result No C1-smooth slim limit set for higher rank semisimple algebraic groups. Principal Component Analysis (PCA) has wide applications in machine learning, text mining and computer vision. Classical PCA based on a Gaussian noise model is fragile to noise of large magnitude. Laplace noise assumption based PCA methods cannot deal with dense noise effectively. In this paper, we propose Cauchy Princ…
The study finds conditions for certain groups to be dense in a specific mathematical space.
problem Conditions for linear reflection groups to be dense in a projective space.
method Analyzes necessary and sufficient conditions for Zariski-density, applies to Coxeter groups and surface subgroups.
result Establishes conditions for Zariski-dense subgroups in SLn(Z) for various n. New representations of hyperbolic 3-manifold groups into larger groups.
problem Finding representations of hyperbolic 3-manifold groups into larger matrix groups.
method Holonomy representations from projective deformations of hyperbolic structures.
result First examples of strongly dense representations into SL(4,R) and SU(3,1). Detects dense subhypergraphs in heterogeneous random hypergraphs.
problem Testing for the existence of a dense subhypergraph in heterogeneous random hypergraphs.
method Established detection boundaries and constructed asymptotically powerful and adaptive tests.
result Developed tests for distinguishing between null and alternative hypotheses.
Dense neural networks can't approximate all functions.
problem Approximation capabilities of dense neural networks.
method Model compression approach combining weak regularity lemma and graph neural networks.
result Existence of Lipschitz continuous functions not approximable by dense neural networks.
The key idea of current deep learning methods for dense prediction is to apply a model on a regular patch centered on each pixel to make pixel-wise predictions. These methods are limited in the sense that the patches are determined by network architecture instead of learned from data. In this work, we propose the dense…
Estimates social network structure from random walk subgraphs.
problem Recovering population structure from random walk subgraphs in stochastic block models.
method Maximum likelihood estimation, SAEM algorithm, de-biasing techniques.
result New de-biased estimator provides more accurate recovery of network structure.
We develop a new modeling framework for Inter-Subject Analysis (ISA). The goal of ISA is to explore the dependency structure between different subjects with the intra-subject dependency as nuisance. It has important applications in neuroscience to explore the functional connectivity between brain regions under natural …
Odd-dimensional SL(n,Q) contains dense surface subgroups.
problem Finding dense subgroups in SL(n,Q) for odd n.
method Constructing a continuous path of representations.
result Existence of dense surface subgroups in SL(n,Q) for odd n.
Classifies manifolds with dense conjugacy classes in their mapping class groups.
problem Classifying manifolds based on conjugacy classes in their mapping class groups.
method Analyzing connected orientable 2-manifolds and their mapping class groups.
result Mapping class groups of certain manifolds have dense conjugacy classes.
The paper finds dense subgroups in certain Lie groups.
problem Finding dense subgroups in Lie groups.
method Constructing dense surface subgroups in specific Lie groups.
result Uniform lattices contain infinitely many dense Hitchin representations.
New examples of rigid Lie foliations with dense leaves found.
problem Infinitesimal rigidity of Lie foliations with dense leaves.
method Construction of specific Lie foliations.
result First examples of infinitesimally rigid Riemannian foliations with dense leaves.
We analyze the sample complexity of learning graphical games from purely behavioral data. We assume that we can only observe the players' joint actions and not their payoffs. We analyze the sufficient and necessary number of samples for the correct recovery of the set of pure-strategy Nash equilibria (PSNE) of the true…
Proposes a new method for ensembling neural subnetworks.
problem Computational expense and limited flexibility of traditional deep ensembles.
method Sequential Bayesian neural subnetwork ensembling.
result Outperforms traditional ensembles in various metrics.
Effective estimates for lattice orbits in homogeneous spaces.
problem Distribution of lattice orbits in homogeneous spaces.
method Refined techniques on equidistribution of regions under flows.
result Effective convergence of orbit distribution to a limiting density.
Sharp boundaries for detecting dense subhypergraphs established.
problem Detecting dense subhypergraphs in random hypergraphs.
method Established sharp detection boundaries for known and unknown edge probabilities.
result Sharp detectable regions differ significantly from graph counterparts.
Method generates dense fields from sparse measurements without needing spatial statistics or examples.
problem Generating dense physical fields from sparse measurements.
method Introduces a differentiable numerical simulator into neural network training.
result Superior results on fluid mechanics problems compared to statistical and neural network methods.
Brooks and Makover introduced an approach to random Riemann surfaces based on associating a dense set of them - Belyi surfaces - with random cubic graphs. In this paper, using Bollobas model for random regular graphs, we examine the topological structure of these surfaces, obtaining in particular an estimate for the ex…
Deforms surface groups to be Zariski dense in SL(n,R)
problem Finding Zariski dense surface groups in SL(n,R)
method Deforming K-integral representations of surface groups result Generalizes Long and Thistlethwaite's method to SL(n,R)
Paper tackles dense subgraph discovery with noisy feedback.
problem Discover dense subgraphs in edge-weighted graphs with noisy feedback.
method Proposes polynomial-time and scalable algorithms for dense subgraph discovery.
result Polynomial-time algorithm obtains nearly-optimal solution with high probability.
Wave fronts on certain surfaces become dense.
problem Density of wave fronts on surfaces.
method Proof of density for specific surfaces.
result Wave fronts become dense on flat torus, square billiard, Klein bottle, and cube surface.
Example shows dense subgroup of SL5(Z) not finitely presented.
problem Finding dense subgroups of SL5(Z) that are not finitely presented.
method Discussing an example of a Zariski-dense finitely generated subgroup of SL5(Z).
result Example shows a subgroup that is dense but not finitely presented.
The paper finds free semigroups in dense subgroups of Lie groups with critical exponents arbitrarily close to the subgroup's.
problem Finding free semigroups with critical exponents arbitrarily close to a subgroup's in dense subgroups of Lie groups.
method Analyzing Zariski dense discrete subgroups of Lie groups, showing the existence of free semigroups with critical exponents arbitrarily close to the subgroup's.
result The existence of free semigroups with critical exponents arbitrarily close to the subgroup's in dense subgroups of Lie groups.
We prove that every Bers slice of quasi-Fuchsian space is Zariski dense in the character variety.
A dense amalgam connects boundaries of groups split by finite subgroups.
problem Understanding boundaries of groups split by finite subgroups.
method Introducing dense amalgam and applying it to EZ-boundaries. result Boundaries of groups split by finite subgroups have a dense amalgam structure.