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.
New bandit algorithm for non-i.i.d. noise, improving standard rates.
problem Linear stochastic bandit with non-i.i.d. observation noise.
method Developed new confidence sequences and an algorithm based on optimism in uncertainty.
result Regret bounds for the new algorithm, showing recovery of standard rates up to a factor of the mixing time.
We present an new sequential Monte Carlo sampler for coalescent based Bayesian hierarchical clustering. Our model is appropriate for modeling non-i.i.d. data and offers a substantial reduction of computational cost when compared to the original sampler without resorting to approximations. We also propose a quadratic co…
New theory explains consistency of kernel methods with non-i.i.d. data.
problem Consistency of kernel methods under non-i.i.d. data.
method Empirical weak convergence (EWC) as a general assumption.
result Established consistency of SVMs, kernel mean embeddings, and CKMEs with EWC data.
Polynomial time algorithm matches correlated Gaussian matrices without vanishing correlation.
problem Matching vertices in two correlated Erdős-Rényi graphs.
method Iterative matching algorithm for correlated Gaussian Wigner matrices.
result First polynomial time algorithm for graph matching with arbitrarily small constant correlation.
Paper offers robust recovery for 1-bit sensing with partial Gaussian circulant matrices.
problem Accurately recovering vectors from 1-bit measurements using structured matrices.
method Correlation-based optimization with randomly signed partial Gaussian circulant matrices and generative models.
result Recovery guarantees match those for i.i.d. Gaussian matrices but with faster computation.
The paper improves Bayesian optimization by calibrating uncertainty estimates.
problem Improper uncertainty estimates in Bayesian optimization when data is non-stationary.
method Proposes online learning algorithms to maintain calibration on non-i.i.d. data and integrates them into Bayesian optimization.
result Calibrated Bayesian optimization converges to better optima in fewer steps.
New algorithm achieves linear speedup in non-i.i.d. federated bilevel learning.
problem Linear speedup in convergence for non-i.i.d. datasets in federated bilevel optimization.
method Proposes FedMBO with a novel client sampling scheme for non-i.i.d. datasets.
result Achieves a convergence rate of O(1/√(nK) + 1/K + √n/K³/²).
Study on random matrices in deep neural networks using Gaussian data.
problem Distribution of singular values in product of random matrices in deep learning.
method Free probability theory combined with standard techniques of random matrix theory.
result Justification for applying free probability theory to non-independent random data matrices.
Study on Gaussian ensemble of matrix products with mixed moments computed.
problem Understanding the statistical properties of matrix products of Gaussian matrices.
method Analysis of a multi-Wishart ensemble and enumeration of non-crossing pairings.
result Mixed moments of the product matrix are computed and found to be weighted by Fuss-Catalan numbers at large N N N . We simplify matrix computations for block matrices, especially useful for covariance and correlation matrices.
problem Complex computations for block matrices, especially for covariance and correlation matrices.
method Obtained a canonical representation for block matrices, facilitating computation of various matrix operations.
result Simplified computation of matrix operations for block matrices, particularly useful for covariance and correlation matrices.
The paper proves a distribution claim for neural network Jacobians.
problem Distribution of singular values in deep neural networks.
method Free probability and random matrix theory techniques.
result Singular value distribution matches for specific cases.
Generative data augmentation boosts learning performance in various tasks.
problem Theoretical understanding of generative data augmentation's effect.
method Established a stability bound for non-i.i.d. settings, analyzed Gaussian mixture models and generative adversarial nets.
result Generative data augmentation can improve learning guarantees, especially in small train sets.
Optimizes clustering in Gaussian mixtures with varying covariance matrices.
problem Clustering with anisotropic Gaussian mixture models where covariance matrices vary.
method Proposes a computationally feasible hard EM type algorithm.
result Achieves optimal clustering rate with few iterations.
FedBE aggregates local models into a robust global model via Bayesian inference.
problem Challenges in aggregating non-i.i.d. local models into a global model in federated learning.
method FedBE uses Bayesian inference to sample and combine higher-quality global models from local models.
result FedBE leads to more robust aggregation of local models into a global model, especially when data is non-i.i.d.
Paper solves a key problem in learning from high-dimensional covariance matrices.
problem Computing normalizing factors for Riemannian Gaussian distributions on high-dimensional covariance matrices.
method Equivalence with random matrix theory and log-normal matrix ensembles to approximate normalizing factors.
result Efficient approximation of normalizing factors with decreasing error as dimension increases.
MaxCOSD algorithm tackles non-i.i.d. demands and stateful dynamics in online inventory control.
problem Managing inventory with non-i.i.d. demands and stateful dynamics.
method MaxCOSD, an online algorithm with provable guarantees for non-degeneracy assumptions.
result MaxCOSD achieves optimal performance for non-i.i.d. demands and stateful dynamics.
The paper models financial correlation matrices using permutation invariant Gaussian models and predicts market anomalies.
problem Modeling and predicting financial correlation matrices from high-frequency data.
method Constructing permutation invariant Gaussian matrix models with 4 parameters, using graph theory and polynomial functions.
result The permutation invariant Gaussian matrix model predicts the expectation values of cubic and quartic polynomials with strong evidence of fit.
Banded matrices can be used as precision matrices in several models including linear state-space models, some Gaussian processes, and Gaussian Markov random fields. The aim of the paper is to make modern inference methods (such as variational inference or gradient-based sampling) available for Gaussian models with band…
In this paper, we study the problem of compressed sensing using binary measurement matrices and ℓ 1 \ell_1 ℓ 1 -norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to achieve robust sparse recovery with binary matrices. We establish sufficient conditi…
The paper proposes a method to monitor deep learning predictions for retraining, reducing costs.
problem Reducing computational costs in deep learning by detecting when predictions are no longer valid.
method Sequential monitoring of network predictions based on projected second moments monitoring.
result The proposed method can drastically reduce computational costs in deep learning.
New algorithms reduce bias in federated learning for non-i.i.d. data.
problem Client and block biases in federated learning with non-i.i.d. data.
method Multi-model parallel SGD (MM-PSGD) and multi-chain parallel SGD (MC-PSGD) algorithms.
result Achieve a linear speedup with convergence rate O ( 1 / N T ) O(1/\sqrt{NT}) O ( 1/ N T ) . We introduce a wrapped Gaussian for SPD matrices, enhancing data analysis.
problem Handling circular and non-flat data distributions on SPD manifolds.
method Introduced a non-isotropic wrapped Gaussian using the exponential map, derived theoretical properties, and proposed a maximum likelihood framework.
result Demonstrated the robustness and flexibility of the wrapped Gaussian model on synthetic and real-world datasets.
Unified bounds for iterative algorithms with Gaussian data matrices.
problem Establishing non-asymptotic bounds for iterative algorithms with Gaussian data.
method Explicit coupling between iterates and Gaussian process with deterministic covariance.
result Tight, dimension-free bounds for generalized first-order methods.
Lower bounds on private estimation of Gaussian covariance matrices.
problem Private estimation of Gaussian covariance matrices under various parameter regimes.
method Stein-Haff identity and fingerprinting lemma extensions.
result Lower bounds match existing upper bounds in the widest known parameters.
The paper presents a probabilistic framework for SPD matrices in machine learning.
problem Machine learning on SPD matrices is fragmented; this paper aims to unify it.
method Unified probabilistic framework using Gaussian distributions and Bayes classifiers.
result Different SPD machine learning tools can be reinterpreted and extended using Gaussian distributions.
Paper introduces a new distance measure for Gaussian Mixture Models.
problem Developing a new distance measure for Gaussian Mixture Models.
method Embedding K-component Gaussian Mixture Models into the manifold of symmetric positive definite matrices and calculating a lower bound for the Fisher-Rao metric.
result Demonstrated effectiveness through experiments on standard datasets.
Method estimates M-matrices in graphical models with improved accuracy.
problem Estimating M-matrices as precision matrices in Gaussian graphical models.
method Adaptive multiple-stage estimation method solving weighted ℓ1-regularized problems.
result Method outperforms state-of-the-art methods in precision matrix estimation and graph edge identification.
A method to robustly federate learning with non-i.i.d. data and Byzantine workers.
problem Byzantine workers sending malicious messages in federated learning with non-i.i.d. data.
method Resampling strategy to reduce inner and outer variation, stochastic average gradient, robust geometric median aggregation.
result The method reaches a neighborhood of the optimal solution at a linear convergence rate and learning error depends on the number of Byzantine workers.
Method solves Gaussian graphical models on ladder graphs efficiently.
problem Solving Gaussian graphical models on ladder graphs efficiently.
method Proposes a method that depends on the position of zeros in local covariance matrices.
result Efficiently solves Gaussian graphical models on ladder graphs under certain conditions.
Improves signal detection in non-Gaussian noise using transformed data.
problem Signal detection in rank-one signal-plus-noise data matrices.
method Pre-transforming matrix entries and using linear spectral statistics for hypothesis testing.
result Sharp phase transition of largest eigenvalues in spiked rectangular matrices.
Diagonal transformations preserve independence structures in non-Gaussian distributions.
problem Preserving independence structures in non-Gaussian distributions.
method Diagonal nonlinear transformations of multivariate normal variables.
result Independence structures are preserved in non-Gaussian distributions under diagonal transformations.
This work develops a non-parametric test for relational independence in non-i.i.d. data.
problem Testing independence in relational systems where data samples are not i.i.d.
method Kernel mean embedding for relational variables, consistent non-parametric scalable kernel test.
result Empirically validated effectiveness compared to state-of-the-art tests.
Motivated by a sampling problem basic to computational statistical inference, we develop a nearly optimal algorithm for a fundamental problem in spectral graph theory and numerical analysis. Given an n × n n\times n n × n SDDM matrix M {\bf \mathbf{M}} M , and a constant − 1 ≤ p ≤ 1 -1 \leq p \leq 1 − 1 ≤ p ≤ 1 , our algorithm gives efficient access to a…
Optimizes sub-Gaussian matrices for preserving data distances.
problem Improving the performance of sub-Gaussian matrices in preserving data distances.
method Analyzes sub-Gaussian matrices and their dependence on the sub-Gaussian norm, presenting optimal bounds.
result Optimal dependence on the sub-Gaussian norm for sub-Gaussian matrices as near isometries on sets.
Paper analyzes distributed learning with non-i.i.d. samples.
problem Learning rate analysis for distributed kernel ridge regression with dependent samples.
method Integral operator approach and covariance inequality for strong mixing sequences.
result Derives optimal learning rates for distributed kernel ridge regression.
Temporal Difference Learning analysis under non-i.i.d. data and nonlinear approximation.
problem Finite-sample behavior of TD(0) under non-i.i.d. data and nonlinear approximation.
method High-probability, finite-sample analysis of vanilla TD(0) on polynomially mixing Markov data, assuming Holder continuity and bounded generalized gradients.
result Bounds on the convergence rate of TD(0) with high probability, matching known i.i.d. rates and holding even with nonstationary initialization.
Graph alignment problem solved with convex relaxations for correlated matrices.
problem Recovering hidden vertex permutations from correlated Gaussian matrices.
method Convex relaxations of the quadratic assignment problem over doubly stochastic matrices.
result The solution of the convex relaxation concentrates around the ground-truth permutation matrix for certain correlation parameters.
New federated learning framework reduces model complexity and improves performance.
problem Slow convergence in traditional federated learning due to non-i.i.d. data.
method Clients train personalized local models, server trains shared model, addressing heterogeneity.
result Substantial performance gains over baselines, robust to non-i.i.d. data.
New algorithms for regression with adversarial responses on various metric spaces.
problem Regression with adversarial responses under non-i.i.d. sequences.
method Proves universal consistency for a wide range of non-stationary processes.
result Achieves universal consistency for a broader class of sequences than stationary processes.
New method for estimating high-dimensional binary time series coefficients.
problem Statistical inference for high-dimensional binary time series.
method Post-selection estimator and second-order wild bootstrap algorithm.
result Good finite-sample performance of the proposed method.
Study improves KRR for non-i.i.d. data, with applications in denoising.
problem Kernel regression in structured non-i.i.d. settings.
method Developed a blockwise decomposition method for dependent data, deriving excess risk bounds.
result Established generalization guarantees for KRR in non-i.i.d. settings.
Despite their successes, what makes kernel methods difficult to use in many large scale problems is the fact that storing and computing the decision function is typically expensive, especially at prediction time. In this paper, we overcome this difficulty by proposing Fastfood, an approximation that accelerates such co…
Study eigenvector overlaps in large Gaussian matrices, simplifying for GOE.
problem Investigate eigenvector overlaps in large Gaussian matrices.
method Analysis of eigenvector flow under Dyson Brownian motion.
result Explicit computation of limiting rescaled mean squared overlaps.
FedIV uses federated GMM for IV analysis in non-i.i.d. data.
problem Efficient IV analysis in non-i.i.d. federated data.
method Federated GMM via FedGDA algorithm.
result Federated solution consistently estimates local moment conditions.
Selecting hyperparameters for unsupervised learning problems is challenging in general due to the lack of ground truth for validation. Despite the prevalence of this issue in statistics and machine learning, especially in clustering problems, there are not many methods for tuning these hyperparameters with theoretical …
Paper optimizes FL communication efficiency with stochastic optimization.
problem Intermittent connectivity and non-i.i.d. data in FL.
method Convergence analysis of non-convex loss functions, stochastic optimization for client selection and power allocation.
result Significant reduction in communication time compared to random participation.
We study products of random matrices in the regime where the number of terms and the size of the matrices simultaneously tend to infinity. Our main theorem is that the logarithm of the ℓ 2 \ell_2 ℓ 2 norm of such a product applied to any fixed vector is asymptotically Gaussian. The fluctuations we find can be thought of as a…