arXiv research

The paper analyzes ridge regression with random features for non-identically distributed data.

The paper provides guarantees for learning nonlinear representations from multiple non-identically distributed data sources.

Study introduces new Bernstein inequalities for dependent data in Hilbert spaces.

VRL-SGD reduces communication complexity in non-identical data settings.

New neural network captures spatial correlations in wind speed predictions.

This note displays an interesting phenomenon for percentiles of independent but non-identical random variables. Let $X_1,\cdots,X_n$ be independent random variables obeying non-identical continuous distributions and $X^{(1)}\geq \cdots\geq X^{(n)}$ be the corresponding order statistics. For any $p\in(0,1)$, we investig…

Study ridge regression for non-identically distributed data with varying variances.

Study resolvent convergence for random matrices with general covariance 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 $\mathrm{Diff}_{+}(I)$ contains a free semigroup on two generators then $Γ$ is not $C_0$-discrete. Using this, we extend the Hölder's Theorem in $\math…

New class of heavy-tailed distributions shows weighted averages dominate individual variables.

Novel framework for data sharing and coordinated exploration in concurrent RL with non-identical environments.

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…

Proves equations for high-dimensional gradient-based methods from Gaussian data.

In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance of the data. However, PCA has two major weaknesses. Firstly, it only considers li…

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.

LP-FT improves personalized model training in FL by balancing generalization and personalization.

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.

Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$ 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 $\mathrm{Diff}_{+}^{ω}(I)$ (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 $\mathrm{Diff}_{+}^{ω}(I)$. In th…

Study large deviations in life insurance portfolios without identical distributions.

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 $K^{1/2}$ -- 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 $K^{1/2}$ 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.

We prove that any smooth action of $\mathbb Z^{m-1}, m\ge 3$ 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.

New robust discriminant analysis for non-Gaussian data.

New examples of hyperbolic links with generalized torsion elements found.

This monograph deals with adaptive supervised classification, using tools borrowed from statistical mechanics and information theory, stemming from the PACBayesian approach pioneered by David McAllester and applied to a conception of statistical learning theory forged by Vladimir Vapnik. Using convex analysis on the se…

A new robust and flexible classification method for non-Gaussian data.

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.

Random representations of surface groups approach asymptotic freeness in large $n$ limit.

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.

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,…

The study shows that certain spacetimes are isospectrally rigid.

Investigates VaR behavior for sums of one-sided random variables, showing impossibilities and conditions for super-additivity.

New Gaussian min-max theorem extends classical results to non-i.i.d. Gaussian matrices.

FedNAS automates federated learning by searching for better architectures.

Study noisy rewards in online decision-making with unknown distributions.

FedSmart optimizes federated learning models for non-IID data.