Proofs high-dimensional spectrum convergence of weighted sample covariance.
problem High-dimensional spectrum convergence of weighted sample covariance.
method Proposes a new, concise proof with stronger assumptions.
result Spectrum convergence proven for different weight distributions.
A new method corrects weight values to improve treatment effect estimation.
problem Estimating heterogeneous treatment effects in high-dimensional data with sample selection bias.
method Differentiable Pareto-Smoothed Weighting (DPSW) framework.
result Our method outperforms existing methods in treatment effect estimation.
A new machine learning method solves high-dimensional Kolmogorov PDEs efficiently.
problem Solving high-dimensional Kolmogorov PDEs and SDEs.
method Stochastic weighted minimization and stochastic gradient descent with Malliavin weights.
result Accurate approximation of high-dimensional Kolmogorov PDEs and SDEs without curse of dimensionality.
Method identifies change points in high-dimensional models using sample weights.
problem Identifying change points in high-dimensional generalized linear models.
method Sample-weighted empirical risk minimization (Weighted ERM).
result Weighted ERM yields precise asymptotic performance characterization for Gaussian designs.
Let M be an n-dimensional closed Riemannian manifold with metric g, dμ=e−φ(x)dν be the weighted measure and Δp,φ be the weighted p-Laplacian. In this article we will investigate monotonicity for the first eigenvalue problem of the weighted p-Laplace operator acting on the space of functions along th…
The paper analyzes how re-weighting helps in reducing variance in high-dimensional kernel methods under covariate shifts.
problem The challenge of high-dimensional kernel methods under covariate shifts and the role of re-weighting.
method Derives asymptotic expansion of high-dimensional kernels under covariate shifts, analyzes bias-variance decomposition, and characterizes the regularized kernel.
result Re-weighting helps in decreasing variance and can be seen as a data-dependent regularization.
A new method reduces high-dimensional data's impact on CWMs using TSNE.
problem High-dimensional data hampers CWMs' accuracy and speed.
method TSNE for dimensionality reduction, parsimonious technique, expectation maximization.
result TSNE enhances CWMs' performance in high-dimensional space.
Study on optimal ReLU networks with weight decay for interpolation.
problem Interpolating data with radially symmetric distributions using shallow ReLU networks.
method Weight decay regularization in infinite neuron, infinite data limit; analysis of growth rates.
result Existence and growth rates of unique radially symmetric minimizers with weight decay.
New conditions for weighted composition operators in group homomorphisms.
problem Conditions for weighted composition operators in group homomorphisms.
method Range decreasing group homomorphisms.
result New insights into weighted composition operators and their algebraic structure.
New method optimizes model selection in high-dimensional regression models.
problem Model selection in high-dimensional misspecified regression models with covariate shift.
method Importance-weighted orthogonal greedy algorithm (IWOGA) and high-dimensional importance-weighted information criterion (HDIWIC).
result IWOGA + HDIWIC achieves optimal convergence rates in terms of prediction error.
Study semilinear equations on weighted manifolds to prove rigidity.
problem Prove rigidity of weighted manifolds via classification of semilinear equations.
method Classify positive solutions at the Sobolev-critical exponent, proving rigidity and weight triviality.
result Existence of positive solutions implies rigidity and weight triviality under certain curvature conditions.
This paper optimizes binary linear classifiers by tuning their weight vectors.
problem Optimizing the weight vector of binary linear classifiers for better performance.
method Parameterization of the discriminant through a scalar to control trade-offs between informative and noisy terms.
result Weight vector tuning compensates for non-optimal native hyperparameters, improving classification performance.
In this paper we prove L∞ type gap theorems in Yang-Mills theory for complete four-dimensional manifolds with a weighted Poincaré inequality. We apply the theorems to a broad class of complete manifolds satisfying weighted Poincaré inequalities. In particular, we obtain a gap theorem on the Euclidean space wi…
Generalizes neural network approximation to infinite-dimensional manifolds and derivatives.
problem Approximating differentiable maps on infinite-dimensional manifolds.
method Proves a weighted Nachbin theorem to establish universal approximation for differentiable maps, including derivatives.
result Linear functions of the signature can approximate path space functionals including their derivatives.
Positive weights improve kernel quadrature's accuracy.
problem Improving kernel quadrature weights to be positive and stable.
method Using convex geometry to approximate the kernel mean embedding with positive weights.
result Positive weights lead to improved kernel quadrature bounds with Monte-Carlo-beating rates.
Paper studies weighted Fermat-Frechet problem for simplex edge lengths.
problem Finding optimal edge lengths for simplex deformations.
method Isometric embedding techniques for K-Space. result New variational method to solve weighted Fermat-Frechet problem.
Study on stable minimal hypersurfaces under Ricci curvature constraints.
problem Stability of weighted minimal hypersurfaces under Ricci curvature bounds.
method Derive geometric consequences and prove a Schoen-Yau type criterion.
result Structure theorem for three-dimensional weighted manifolds of non-negative Ricci curvature.
We study the use of power weighted shortest path distance functions for clustering high dimensional Euclidean data, under the assumption that the data is drawn from a collection of disjoint low dimensional manifolds. We argue, theoretically and experimentally, that this leads to higher clustering accuracy. We also pres…
Improves feature selection in high-dimensional data using LLM-generated weights.
problem Inaccurate LLM-generated weights degrade feature selection performance.
method Integrates LLM-generated weights into prior inclusion probabilities using LLM Sparsity Prior (LSP).
result Improves prediction accuracy and identifies clinically relevant features.
New neural network rates for unbounded domains with weighted Sobolev spaces.
problem Improving neural network approximation rates for unbounded domains.
method Embedding results for weighted Fourier-Lebesgue spaces in weighted Sobolev spaces, followed by asymptotic approximation rates.
result Asymptotic approximation rates for shallow neural networks without curse of dimensionality for unbounded domains and Muckenhoupt weights.
This text is dedicated to the real Killing equation on 3-dimensional Weyl manifolds. Any manifold admitting a real Killing spinor of weight 0 satisfies the conditions of a Gauduchon-Tod geometry. Conversely, any simply connected Gauduchon-Tod geometry has a 2-dimensional space of solutions of the real Killing equation …
Study Gaussian approximation for deep neural networks with random weights.
problem Understanding the distribution of deep neural networks with random weights.
method Established Gaussian approximation bounds in Wasserstein-1 norm.
result Convergence rates of order n−(1/6)L−1+ε for deep networks with proportional layer widths. The local linear embedding algorithm (LLE) is a non-linear dimension-reducing technique, widely used due to its computational simplicity and intuitive approach. LLE first linearly reconstructs each input point from its nearest neighbors and then preserves these neighborhood relations in the low-dimensional embedding. W…
For each cardinal κ, each natural number n and each simplicial complex K we construct a space νκn(K) and a map π:νκn(K)→K such that the following conditions are satisfied. 1. νκn(K) is a complete metric n-dimensional space of weight κ. 2. νκn(K) is an absolute neighborhood extensor i…
Hypernetworks are neural networks that generate weights for another neural network. We formulate the hypernetwork training objective as a compromise between accuracy and diversity, where the diversity takes into account trivial symmetry transformations of the target network. We explain how this simple formulation gener…
Study calibrates high-dimensional binary classifiers using angle between estimator and true weights.
problem Calibrating high-dimensional binary classifiers with provable properties.
method Interpolates with a chance classifier to construct well-calibrated predictor based on angle between estimator and true weights.
result Angular calibration approach is provably well-calibrated in high dimensions, minimizing Bregman divergence.
New geometric analysis of PWSPDs balances density and geometry in high-dimensional data.
problem Balancing density and geometry in high-dimensional data.
method Power-weighted shortest-path distances (PWSPDs) and their geometric and computational analyses.
result High probability guarantees on the equivalence of PWSPDs on complete and nearest neighbor graphs.
Functional input neural networks approximate continuous functions on weighted spaces.
problem Approximating continuous functions on infinite-dimensional weighted spaces.
method Additive family mapping, non-linear activation, linear readouts, Stone-Weierstrass theorem.
result Global universal approximation of continuous functions on weighted spaces.
Universal approximation theorem for differentiable maps on infinite-dimensional manifolds
problem Approximation of differentiable maps on infinite-dimensional manifolds
method Weighted universal approximation theorem
result Universal approximation theorem for differentiable maps
Novel Bayesian method for high-dimensional count data prediction.
problem Count data in high-dimensional settings requires feature selection.
method Pseudo-Bayesian framework with scaled Student prior and exponential weights.
result Strong performance compared to Lasso in various settings.
Paper extends positive energy theorem to anti-de Sitter spacetimes.
problem Proving positive energy theorem for weighted anti-de Sitter spacetimes.
method Generalized positive energy theorem for 3D anti-de Sitter initial data sets.
result Positive energy theorem proved for weighted anti-de Sitter spacetimes.
Rozansky and Witten proposed in 1996 a family of new three-dimensional topological quantum field theories, indexed by compact (or asymptotically flat) hyperkaehler manifolds. As a byproduct they proved that hyperkaehler manifolds also give rise to Vassiliev weight systems. These may be thought of as invariants of hyper…
New theorem splits weighted Lorentz-Finsler manifolds into simpler parts.
problem Understanding the geometry of weighted Lorentz-Finsler manifolds.
method Developed a splitting theorem using weighted Berwald spacetimes and Busemann functions.
result Weighted Lorentz-Finsler manifolds with certain properties split into simpler isometric translations.
We use a new approach that we call unification to prove that standard weighted double bubbles in n-dimensional Euclidean space minimize immiscible fluid surface energy, that is, surface area weighted by constants. The result is new for weighted area, and also gives the simplest known proof to date of the (unit weight…
Data-driven model shows deep learning weights behave like a liquid.
problem Understanding the structure of deep neural network optimization landscapes.
method Statistical mechanics framework to model high-dimensional weight spaces.
result Deep networks' weight spaces are well-connected, not hierarchical, unlike shallow networks.
Diffusion models adapt to low-dimensional structures for nonparametric density estimation.
problem High-dimensional statistical inference challenges.
method Viewing diffusion models as implicit density estimators and exploiting their low-dimensional structure.
result Achieves minimax optimal rate for total variation distance with factorizable density.
This paper presents a new fuzzy k-means algorithm for the clustering of high-dimensional data in various subspaces. Since high-dimensional data, some features might be irrelevant and relevant but may have different significance in the clustering process. For better clustering, it is crucial to incorporate the contribut…
Latent FxLMS accelerates ANC by adapting along low-dimensional filter weights.
problem Improving active noise control with neural adaptive filters.
method Training an auto-encoder on filter coefficients, constraining weights to latent variables, and updating in latent space.
result Latent FxLMS converges in fewer steps with comparable error to standard FxLMS.
AdaTrans adapts to feature and sample transfer in high-dimensional regression.
problem High-dimensional linear regression with more features than samples.
method F-AdaTrans and S-AdaTrans methods using fused-penalties and adaptive weights.
result AdaTrans achieves convergence rates close to oracle estimators and near-minimax optimal rates.
With the development of multimedia era, multi-view data is generated in various fields. Contrast with those single-view data, multi-view data brings more useful information and should be carefully excavated. Therefore, it is essential to fully exploit the complementary information embedded in multiple views to enhance …
Study shows how to approximate and estimate high-dimensional classification functions without the curse of dimensionality.
problem Approximating and estimating classification functions in high-dimensional spaces.
method Modified existing results to show that RBV2 functions can be approximated by neural networks with bounded weights. Proved the existence of a neural network with bounded weights approximating a classification function. Leveraged these bounds to quantify estimation rates. result Neural networks can approximate RBV2 functions without the curse of dimensionality, leading to efficient estimation rates. This work investigates the ways in which deep learning methods can benefit from random projection (RP), a classic linear dimensionality reduction method. We focus on two areas where, as we have found, employing RP techniques can improve deep models: training neural networks on high-dimensional data and initialization o…
Next generation deep neural networks for classification hosted on embedded platforms will rely on fast, efficient, and accurate learning algorithms. Initialization of weights in learning networks has a great impact on the classification accuracy. In this paper we focus on deriving good initial weights by modeling the e…
A new statistical model uses Orlicz-Sobolev spaces with Gaussian weight.
problem Statistical modeling of infinite-dimensional probability measures.
method Affine statistical bundle on Gaussian Orlicz-Sobolev space.
result Provides tools for solving infinite-dimensional evolution problems.
New method clusters matrix-valued data by latent variables.
problem Clustering matrix-valued data with hidden structure.
method Latent variable model with hierarchical clustering.
result Algorithm attains clustering consistency in high dimensions.
Estimates Gaussian mixtures from weighted samples efficiently.
problem Estimating Gaussian mixtures from weighted samples with correct weight treatment.
method Density interpretation and expectation-maximization method considering weights.
result Correctly estimates Gaussian mixtures with weighted samples.
We show that the skip-gram formulation of word2vec trained with negative sampling is equivalent to a weighted logistic PCA. This connection allows us to better understand the objective, compare it to other word embedding methods, and extend it to higher dimensional models.
PS^2 selects assets then weights for high-dimensional investing.
problem High-dimensional mean--variance investing challenges.
method Two-step framework: Lasso screening followed by standard portfolio estimation.
result FPS^2 with defactored returns improves performance.