Paper optimizes portfolios with non-identical asset return variances using statistical mechanics.
problem Optimizing portfolios with assets having different return variance.
method Replica analysis of statistical mechanical informatics.
result Asymptotic behaviors of minimal investment risk and concentrated investment level determined analytically.
VRL-SGD reduces communication complexity in non-identical data settings.
problem Training machine learning models with non-identical data distribution.
method VRL-SGD, which eliminates gradient variance dependency and achieves linear speedup with lower communication complexity.
result VRL-SGD reduces communication complexity from $O(T^{ rac{3}{4}} N^{ rac{3}{4}})$ to $O(T^{ rac{1}{2}} N^{ rac{3}{2}})$.
Study ridge regression for non-identically distributed data with varying variances.
problem Investigate high-dimensional regression with non-identical data variance.
method Propose a random effect model and use tools from random matrix theory.
result Highlight the double descent phenomenon in high-dimensional regression for certain variance profiles.
The paper analyzes ridge regression with random features for non-identically distributed data.
problem Analyzing ridge regression performance for data with heterogeneous variance profiles.
method Combining linear-plus-chaos approximation and operator-valued free probability.
result Derives asymptotic equivalents for training and test risks under non-identically distributed data.
Study large deviations in life insurance portfolios without identical distributions.
problem Large deviations in life insurance portfolios with bounded losses and variances.
method Upper bound from standard large deviations, counterexample for full large deviation principle.
result Exponential bound for average loss exceeding a threshold.
The paper examines percentiles of non-identical random variables and provides non-asymptotic bounds.
problem Investigating percentiles of independent but non-identical random variables.
method Analyzing the 100(1−p)%-th percentile X(pn) for a wide class of distributions. result Discovering a connection between the median and the harmonic mean of standard deviations for certain distributions.
The study classifies Riemannian manifolds with specific Hessian properties.
problem Classifying Riemannian manifolds with a special Hessian structure.
method Analyzing manifolds with a non-identically vanishing function f whose Hessian is minus f times the Ricci tensor.
result Partial classification of manifolds with this Hessian structure.
This work examines how non-identical data distributions affect Federated Learning performance.
problem The impact of non-identical data distributions on Federated Learning performance.
method Synthesized datasets with varying degrees of data distribution similarity, evaluated Federated Averaging algorithm performance, proposed server momentum mitigation.
result Performance of Federated Learning degrades as data distributions differ more, and a mitigation strategy improves accuracy.
We strengthen the results of \cite{A1}, consequently, we improve the claims of \cite{A2} obtaining the best possible results. Namely, we prove that if a subgroup Γ of Diff+(I) contains a free semigroup on two generators then Γ is not C0-discrete. Using this, we extend the Hölder's Theorem in $\math…
New class of heavy-tailed distributions shows weighted averages dominate individual variables.
problem Understanding and comparing risks in heavy-tailed distributions.
method Introducing a new class of heavy-tailed distributions and proving stochastic dominance relations.
result Weighted averages of random variables in this class are stochastically larger than individual variables.
Novel framework for data sharing and coordinated exploration in concurrent RL with non-identical environments.
problem Learning more data-efficient and better policies in concurrent RL with non-identical environments.
method Proposes a novel algorithmic framework that leverages causal inference via ANM-MM to extract model parameters and a new data sharing scheme based on similarity measures.
result Demonstrates superior learning speeds on various tasks and effectiveness of diverse action selection.
Macbeath gave a formula for the number of fixed points for each non-identity element of a cyclic group of automorphisms of a compact Riemann surface in terms of the universal covering transformation group of the cyclic group. We observe that this formula generalizes to determine the fixed-point set of each non-identity…
The paper provides guarantees for learning nonlinear representations from multiple non-identically distributed data sources.
problem Learning from non-identically distributed and dependent data.
method Established statistical guarantees for learning general nonlinear representations from multiple data sources.
result The excess risk of the estimated function decays as a function of the sample complexity and task diversity.
Meta-analysis improves interpretation and efficiency across similar but non-identical datasets.
problem Meta-analysis of heterogeneous data in high dimensions.
method Integrative sparse regression with a global parameter for adaptability and anonymity.
result Superior identification of global parameter for high-dimensional linear models.
We prove that if Γis subgroup of Diff_{+}^{1+ε}(I) and N is a natural number such that every non-identity element of Γhas at most N fixed points then Γis solvable. If in addition Γis a subgroup of Diff_{+}^{2}(I) then we can claim that Γis metaabelian.
This paper tackles computational bottlenecks in federated learning on mobile devices.
problem Computationally heterogeneous mobile devices hinder federated learning efficiency.
method Proposes efficient algorithms to schedule mobile devices based on data heterogeneity.
result Achieves up to 100x speedup and 7% accuracy gain in federated learning.
The study examines property testing and estimation under non-identically distributed samples, finding necessary and sufficient sample complexities.
problem Property testing and estimation under non-identically distributed samples.
method Analysis of distributional property testing and estimation in settings with heterogeneous entities.
result Necessary and sufficient sample complexities for property testing and estimation under non-identically distributed samples.
FedProx tackles heterogeneity in federated learning networks.
problem Significant variability in systems characteristics and non-identically distributed data in federated networks.
method FedProx is a framework that generalizes and re-parametrizes FedAvg, introducing modifications to handle both systems and statistical heterogeneity.
result FedProx demonstrates significantly more stable and accurate convergence behavior than FedAvg, improving test accuracy by 22% on average in highly heterogeneous settings.
In [13], it is proved that any subgroup of Diff+ω(I) (the group of orientation preserving analytic diffeomorphisms of the interval) is either metaabelian or does not satisfy a law. A stronger question is asked whether or not the Girth Alternative holds for subgroups of Diff+ω(I). In th…
Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using ℓ1 penalization methods. However, current methods assume that the data are independent and identically distributed. If the distribution, and hence the graph, evolves over time t…
LD-SGD improves communication in decentralized SGD.
problem Efficiently combining local updates and decentralized communication.
method Proposes LD-SGD integrating local updates and decentralized SGD, with a convergence analysis.
result LD-SGD converges to a critical point for non-convex objectives with non-identically distributed data.
A distributed algorithm reduces communication complexity for non-convex optimization.
problem Efficiently solving non-convex optimization problems in a distributed setting.
method Parallel Restarted SPIDER algorithm, incorporating SPIDER gradient estimator.
result Achieves optimal communication complexity O(ε−1) and optimal computation complexity. We give effective proofs of residual finiteness and conjugacy separability for finitely generated nilpotent groups. In particular, we give precise asymptotic bounds for a function introduced by Bou-Rabee that measures how large the quotients that are need to separate non-identity elements of bounded length from the ide…
We consider the Dolbeault operator of K1/2 -- the square root of the canonical line bundle which determines the spin structure of a compact Hermitian spin surface (M,g,J). We prove that the Dolbeault cohomology groups of K1/2 vanish if the scalar curvature of g is non-negative and non-identically zero. Moreov…
Optimal rates for learning hidden tree structures are determined.
problem Learning hidden tree structures from noisy data.
method Study of the (noisy) information threshold and the Chow-Liu algorithm.
result Optimal rates for structure recovery are inversely proportional to the information threshold squared.
In many machine learning problems, labeled training data is limited but unlabeled data is ample. Some of these problems have instances that can be factored into multiple views, each of which is nearly sufficent in determining the correct labels. In this paper we present a new algorithm for probabilistic multi-view lear…
Client adaptation improves federated learning performance with non-IID data.
problem Improving model performance in federated learning with non-identically and non-independently distributed data.
method Simulates heterogeneous clients to learn client-specific conditioning using a conditional gated activation unit.
result Client adaptation enhances model performance across balanced and imbalanced data sets from audio and image domains.
MCPCA improves data dimensionality by maximizing nonlinear correlations.
problem PCA's limitations in handling nonlinearity and categorical data.
method MCPCA computes nonlinear transformations of variables to maximize covariance matrix Ky Fan norm.
result MCPCA outperforms other methods in dimensionality reduction tasks.
We prove that any smooth action of Zm−1,m≥3 on an m-dimensional manifold that preserves a measure such that all non-identity elements of the suspension have positive entropy is essentially algebraic, i.e. isomorphic up to a finite permutation to an affine action on the torus or its factor by $\pm\Id$…
Wide neural networks with asymmetrical node scaling converge globally and learn features.
problem Global convergence and feature learning in over-parameterised shallow networks.
method Gradient-based optimisation of wide, shallow neural networks with asymmetrical node scaling.
result Gradient flow and gradient descent converge to a global minimum and learn features, unlike in the NTK parameterisation.
New robust discriminant analysis for non-Gaussian data.
problem Classical discriminant analysis struggles with non-Gaussian distributions and contaminated datasets.
method Each data point follows its own ES distribution with arbitrary scale, leading to robust classification.
result Maximum-likelihood estimation and classification are simple, fast, and robust.
Study introduces new Bernstein inequalities for dependent data in Hilbert spaces.
problem Learning from non-independent and non-identically distributed data.
method Data-dependent Bernstein inequalities tailored for vector-valued processes in Hilbert space.
result Achieved novel risk bounds for covariance operator estimation and operator learning.
New examples of hyperbolic links with generalized torsion elements found.
problem Finding generalized torsion elements in the fundamental groups of hyperbolic links.
method Analyzing the Weeks manifold, figure-eight sister manifold, and Whitehead sister link to identify generalized torsion elements.
result First examples of hyperbolic links with link groups admitting generalized torsion elements.
A new robust and flexible classification method for non-Gaussian data.
problem Robustness to scale changes and non-Gaussian distributions in classical discriminant analysis.
method FEMDA uses arbitrary Elliptically Symmetrical distributions and scale parameters for each data point.
result FEMDA is robust to scale changes and outperforms other methods.
The paper solves a problem related to curvature in complex geometry.
problem Resolving the prescribed Chern scalar curvature problem.
method Divided into three cases based on the sign of the Gauduchon degree, analyzed separately.
result Proves that certain functions are Chern scalar curvatures of conformal metrics.
Paper proposes FedPer to combat statistical heterogeneity in federated learning for personalized tasks.
problem Statistical heterogeneity in federated learning data degrades performance of traditional federated averaging.
method FedPer: a base + personalization layer approach for federated training of deep feedforward neural networks.
result FedPer effectively combats statistical heterogeneity in non-identical data partitions of CIFAR datasets and personalized image aesthetics datasets.
Random representations of surface groups approach asymptotic freeness in large n limit.
problem Asymptotic freeness of Haar unitary matrices for surface groups.
method Interplay between Dehn's work and classical invariant theory.
result Expected value of trace of a fixed non-identity element is bounded as no∞. Study robust estimation under varying corruption probabilities in data.
problem Robust estimation in scenarios with heterogeneous corruption rates.
method Developed estimators for mean and regression under various corruption patterns.
result Optimal estimators can discard corrupted samples beyond a specific threshold.
Proves equations for high-dimensional gradient-based methods from Gaussian data.
problem High-dimensional asymptotics of gradient-based learning algorithms.
method Closed-form equations derived from dynamical mean-field theory.
result Equations match those from discretized DMFT for gradient flow.
The study shows that certain spacetimes are isospectrally rigid.
problem Isospectrality of Margulis-Smilga spacetimes for specific Lie groups.
method Analysis of polynomials and rational expressions related to Margulis invariants of semisimple Lie groups.
result Zariski dense finitely generated subgroups of spacetimes are isospectrally rigid.
Paper proposes using synthetic data to improve face recognition accuracy.
problem Improving face recognition accuracy using real data alone.
method Proposes a GAN that disentangles identity attributes and generates photo-realistic synthetic images.
result Synthetic images generated by the model are photo-realistic and can increase face recognition accuracy.
A method for matching vertices in large networks using seeds.
problem Matching vertices in large, overlapping networks.
method Identify seeds in local neighborhoods, match induced subgraphs, rank matches.
result Principled approach for large networks, demonstrated through simulations and real data.
Investigates VaR behavior for sums of one-sided random variables, showing impossibilities and conditions for super-additivity.
problem Investigates the behavior of Value-at-Risk (VaR) for sums of one-sided random variables.
method Analyzes the extremal aggregation behavior of VaR, introduces structural conditions for super-additivity.
result Characterizes when VaR is fully super-additive and provides unified framework for various dependence structures.
The paper tackles learning optimal predictions from a single trajectory of a stochastic dynamical system.
problem Learning from a single finite trajectory of an ergodic stochastic dynamical system.
method The approach involves estimating the optimal one-step prediction function using nonlinear least squares and deriving high-probability guarantees.
result The study provides high-probability guarantees for the optimal prediction function, accounting for the non-independent and non-identically distributed nature of trajectory data.
New Gaussian min-max theorem extends classical results to non-i.i.d. Gaussian matrices.
problem Extending classical Gaussian min-max theorems to non-i.i.d. Gaussian matrices.
method Identifying a new pair of Gaussian processes that satisfy comparison inequalities.
result New Gaussian min-max and convex Gaussian min-max theorems with applications in multi-source Gaussian regression and binary classification.
FedNAS automates federated learning by searching for better architectures.
problem Non-I.I.D. data makes predefined model architectures suboptimal.
method Federated Neural Architecture Search (FedNAS) for collaborative architecture optimization.
result FedNAS searches for better architectures that outperform predefined models.
Study noisy rewards in online decision-making with unknown distributions.
problem Learning optimal decisions in online settings with noisy and unknown reward distributions.
method Proposes algorithms integrating learning and decision-making via LCB thresholding.
result Achieves competitive ratios of 1 - 1/e and 1/2 in various settings.
FedSmart optimizes federated learning models for non-IID data.
problem Model performance on non-IID data is poor and privacy is at risk.
method FedSmart optimizes models by sharing global gradients and adjusting weights based on local validation set accuracy.
result FedSmart improves model performance by allocating more weight to similar data distributions.