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.
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.
This note displays an interesting phenomenon for percentiles of independent but non-identical random variables. Let X1,⋯,Xn be independent random variables obeying non-identical continuous distributions and X(1)≥⋯≥X(n) be the corresponding order statistics. For any p∈(0,1), we investig…
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.
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.
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…
In this paper, we study and partially classify those Riemannian man-ifolds carrying a non-identically vanishing function f whose Hessian is minus f times the Ricci-tensor of the manifold.
Federated Learning enables visual models to be trained in a privacy-preserving way using real-world data from mobile devices. Given their distributed nature, the statistics of the data across these devices is likely to differ significantly. In this work, we look at the effect such non-identical data distributions has o…
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.
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.
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.
To accelerate the training of machine learning models, distributed stochastic gradient descent (SGD) and its variants have been widely adopted, which apply multiple workers in parallel to speed up training. Among them, Local SGD has gained much attention due to its lower communication cost. Nevertheless, when the data …
Federated Learning is a distributed learning paradigm with two key challenges that differentiate it from traditional distributed optimization: (1) significant variability in terms of the systems characteristics on each device in the network (systems heterogeneity), and (2) non-identically distributed data across the ne…
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.
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…
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…
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 portfolio optimization problem in which the variances of the return rates of assets are not identical is analyzed in this paper using the methodology of statistical mechanical informatics, specifically, replica analysis. We define two characteristic quantities of an optimal portfolio, namely, minimal investment ris…
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…
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…
The emerging paradigm of federated learning strives to enable collaborative training of machine learning models on the network edge without centrally aggregating raw data and hence, improving data privacy. This sharply deviates from traditional machine learning and necessitates the design of algorithms robust to variou…
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.
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.
We consider the task of meta-analysis in high-dimensional settings in which the data sources are similar but non-identical. To borrow strength across such heterogeneous datasets, we introduce a global parameter that emphasizes interpretability and statistical efficiency in the presence of heterogeneity. We also propose…
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.
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∞. In this paper we investigate the feasibility of using synthetic data to augment face datasets. In particular, we propose a novel generative adversarial network (GAN) that can disentangle identity-related attributes from non-identity-related attributes. This is done by training an embedding network that maps discrete id…
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.
Consider two networks on overlapping, non-identical vertex sets. Given vertices of interest in the first network, we seek to identify the corresponding vertices, if any exist, in the second network. While in moderately sized networks graph matching methods can be applied directly to recover the missing correspondences,…
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.
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.
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.
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.
Unified analysis for decentralized SGD across various topologies and updates.
problem Analysis of decentralized SGD methods with changing topologies and local updates.
method Unified convergence analysis covering local SGD updates and adaptive network topology.
result Universal convergence rates for smooth problems, interpolating between heterogeneous and iid-data settings.
Electronic medical records (EMRs) supports the development of machine learning algorithms for predicting disease incidence, patient response to treatment, and other healthcare events. But insofar most algorithms have been centralized, taking little account of the decentralized, non-identically independently distributed…
Two algorithms improve Federated RL in diverse environments.
problem Collaborative learning in environments with varying dynamics.
method Proposed two federated RL algorithms, QAvg and PAvg, and a personalization heuristic.
result Achieved better performance and generalization in diverse environments.
LP-FT improves personalized model training in FL by balancing generalization and personalization.
problem Federated Learning struggles with balancing global generalization and local personalization due to non-identical data distributions.
method Adapting Linear Probing followed by full Fine-Tuning (LP-FT) to the FL setting.
result LP-FT outperforms standard fine-tuning in balancing personalization and generalization across various datasets and PFT variants.
OBSER framework infers sub-environments from objects, outperforming scene-based methods.
problem Zero-shot recognition of environments from object distributions.
method Bayesian framework using metric and self-supervised learning models to estimate object distributions in latent space.
result OBSER framework reliably performs inference in open-world and photorealistic environments, outperforming scene-based methods.