Uniformly observable systems can be transformed into a triangular form with non-Lipschitz functions.
problem Uniformly observable and differentially observable systems with higher order than state dimension.
method Established triangular canonical form with non-Lipschitz functions.
result Characterization of points where non-Lipschitzness occurs and its relation to uniform infinitesimal observability.
Non-asymptotic uniform rates for k-NN regression are derived.
problem Estimating functions from noisy observations with unknown lower dimensionality.
method Derives high-probability finite-sample uniform rates of consistency for k-NN regression.
result k-NN regression rates are optimal up to logarithmic factors and adapt to unknown lower dimensions.
Unified framework for uniform signal recovery in nonlinear GCS with 1-bit/quantized measurements.
problem Uniform recovery guarantees for nonlinear generative compressed sensing.
method Unified framework using generalized Lasso and Lipschitz approximation.
result Uniform recovery of all signals in the ball up to an error of ε using approximately O(k/ε^2) samples.
Simpler, faster algorithm for uniformity testing in the shuffle model.
problem Testing uniformity of data in the shuffle model with privacy constraints.
method Simplified analysis and use of privacy amplification via shuffling.
result An algorithm with the same guarantees but simpler and more streamlined.
Study on order book dynamics with uniform catastrophes, explaining volatility and trends.
problem Understanding volatility and trends in financial markets with different types of liquidity.
method Stochastic models and population processes with uniform catastrophes.
result Law of large numbers, central limit theorem, and large deviations proved for the model.
A new method for matrix completion with model-free weights.
problem Matrix completion under non-uniform missing structures.
method Constructs weights via convex optimization to adjust for non-uniformity without modeling observation probabilities.
result Recover matrix with stronger theoretical guarantees, especially in heterogeneous missing settings.
Improved matrix completion for non-uniformly sampled data.
problem Estimating unobserved entries in a matrix with varying sampling probabilities.
method Developed entry-specific bounds for low-rank matrix completion under structured non-uniform sampling.
result Error bounds for each entry match minimax lower bounds under certain conditions.
Study sets limits for detecting a subhypergraph in uniform hypergraphs.
problem Recovering a subhypergraph from a uniform hypergraph with different edge probabilities.
method Information-theoretic analysis for weak and exact recovery.
result Sharp conditions for weak or exact recovery of the subhypergraph.
Paper tackles estimating initial conditions of spatio-temporal processes from sparse data.
problem Estimating initial conditions of spatio-temporal advection-diffusion processes from sparse data.
method Regularized convex optimization problem with Alternating Direction Method of Multipliers.
result Efficient solutions for non-uniform and shifted uniform sampling schemes.
The paper completes matrices from non-uniformly sampled entries, especially when columns are randomly selected and fully observed.
problem Matrix completion from non-uniformly sampled entries, including fully and partially observed columns.
method First, recover the column space from fully observed columns. Then, for each partially observed column, find a vector in the recovered column space with the observed entries. For low-rank matrices, recover them from Ω(rnlnn) entries. result The algorithm can exactly recover a low-rank matrix from merely Ω(rnlnn) entries. Study on materials with disclinations, limiting their size.
problem Limiting the size of disclinations in materials with symmetries.
method Defining material-uniform hyperelastic bodies with disclinations, rigorously analyzing their properties.
result The size of disclinations is limited by the symmetries of the constitutive relation.
New model learns SDEs without gradient matching for non-uniform time increments.
problem Learning non-parametric drift and diffusion functions for SDEs.
method Formulates sensitivity equations for learning and optimizes path distributions.
result Robust and efficient learning of SDE systems with non-uniform time increments.
The paper develops a uniform function estimator in RKHS for regression.
problem Reconstructing functions from noisy data at random locations.
method Using reproducing kernel Hilbert spaces and Gaussian random fields.
result The estimator converges uniformly to the conditional expectation.
This study uses neural networks to approximate Bayesian filtering problems.
problem Estimating latent time-series signal statistics from observation sequences.
method Formulated a generic recurrent neural network framework to learn recursive mappings directly.
result Approximation error bounds for filtering in non-compact domains and strong time-uniform bounds.
Develops anytime-valid stopping rules for SGD based on observed trajectory.
problem Stopping stochastic gradient descent (SGD) based on observed trajectory.
method Develops anytime-valid confidence sequences for stochastic gradient methods.
result Statistically valid, time-uniform stopping rules for SGD across convex and nonconvex settings.
New algorithm FLUTE achieves uniform-PAC convergence in RL with linear approx.
problem RL with linear function approximation lacks uniform-PAC guarantees.
method FLUTE algorithm with minimax value function estimator and multi-level partition scheme.
result Uniform-PAC convergence to optimal policy with high probability.
Uniform convergence fails to explain deep learning generalization.
problem Understanding why overparameterized deep networks generalize well despite having many parameters.
method Developed and tested various generalization bounds based on uniform convergence.
result Uniform convergence cannot explain generalization in overparameterized deep networks.
New methods for private statistical inference under local differential privacy.
problem Private statistical inference for population means with bounded observations.
method Nonparametric, nonasymptotic statistical inference using a generalized randomized response mechanism.
result Private confidence intervals and sequences for population means under LDP constraints.
This paper introduces time-uniform CLT-based confidence intervals for statistical inference.
problem Developing valid statistical inference methods for sequential data.
method Time-uniform central limit theory and strong invariance principles.
result Asymptotic confidence sequences (CSs) that are uniformly valid over time.
PAC-Bayesian theory applied to data-dependent hypothesis sets yields uniform generalization bounds.
problem Proving uniform generalization bounds for data-dependent hypothesis sets.
method Applying PAC-Bayesian framework on 'random sets' and considering data-dependent hypothesis sets.
result Data-dependent uniform generalization bounds are proven, providing tighter and unified results.
Active seriation recovers item order from noisy pairwise similarity measurements.
problem Recovering an unknown item ordering from noisy pairwise similarity measurements.
method Proposes an active seriation algorithm that provably recovers the latent ordering with high probability.
result Establishes optimal performance guarantees for successful recovery under a uniform separation condition.
This paper improves matrix completion by leveraging element importance and non-uniform sampling.
problem The challenge of completing low-rank matrices from noisy, subsampled measurements.
method Employing leverage scores to characterize element importance and devising a biased sampling procedure.
result Theoretical and empirical evidence shows that a smaller number of entries (about O(nrlog2(n))) can recover a low-rank matrix with noise. New method detects communities in hypergraphs by embedding them into a vector space.
problem Detecting communities in hypergraphs with multi-way interactions.
method Augmenting non-uniform hypergraphs, embedding into a vector space, using an alternative updating scheme.
result Asymptotic consistencies in community detection and hypergraph estimation established.
New GMM model with uniform background for better clustering.
problem Outliers and non-interesting observations in data.
method Robust loss minimization for clustering.
result Algorithm performs well in clustering GMM with a uniform background.
We consider the problem of diagnosis where a set of simple observations are used to infer a potentially complex hidden hypothesis. Finding the optimal subset of observations is intractable in general, thus we focus on the problem of active diagnosis, where the agent selects the next most-informative observation based o…
Frequency bias affects neural network training on non-uniform data.
problem Understanding how frequency bias impacts neural networks trained on non-uniformly distributed data.
method Used the Neural Tangent Kernel (NTK) model to explore the effect of variable density on training dynamics.
result Convergence time for learning a pure harmonic function depends on the local density at a point.
The paper derives uniform stability-based coverage bounds for conformal prediction methods.
problem Establishing theoretical guarantees for conformal prediction methods.
method Uniform stability perspective applied to full-conformal, jackknife+, and CV+ prediction regions.
result Coverage bounds for finite-dimensional models derived using a concentration argument.
Paper extracts features from time series to improve forecasting accuracy.
problem Forecasting time series generated by Itô-type processes with unknown coefficients.
method Statistical adjustment of mixture-type models to extract features from time series data.
result Additional statistical features enhance time series prediction accuracy.
A fast matrix factorization method for sparse data with non-uniform missing data weights.
problem Sparse and imbalanced data in real-world learning systems.
method Non-uniform weighting of missing data, efficient learning method with truncated SVD and eALS.
result Improved performance in downstream applications compared to uniform weighting.
Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time significantly. For theoretical performance guarantees, each row must be sampled with pr…
We develop time-uniform confidence spheres for estimating means of random vectors.
problem Sequential mean estimation in high-dimensional spaces.
method Derive time-uniform confidence sphere sequences (CSSs) for various types of random vectors.
result Optimal CSSs for log-concave, sub-Gaussian, and sub-ψ random vectors. Algorithm identifies bilinear dynamical systems from noisy data.
problem Learning a realization of a partially observed bilinear dynamical system.
method Regression of outputs to highly correlated covariates for Markov-like parameters.
result High probability error bounds on identification algorithm under uniform stability assumption.
Bayesian network structure learning is often performed in a Bayesian setting, by evaluating candidate structures using their posterior probabilities for a given data set. Score-based algorithms then use those posterior probabilities as an objective function and return the maximum a posteriori network as the learned mod…
New methods for cost-sensitive learning in noisy data without needing noise rate.
problem Cost-sensitive classification in the presence of uniform label noise.
method Two schemes: 1) Regularized ERM with weighted margin loss, 2) Resampling-based method.
result Cost-sensitive, uniform noise robust classifiers without noise rate tuning.
Adding noise controls capacity of function compositions.
problem Large capacity of function compositions with bounded capacity classes.
method Adding Gaussian noise to the output of F before composing with H. result Noise effectively controls the capacity of H∘F, offering a general recipe for modular design. Uniform-in-time analysis for Stein Variational Gradient Descent across various metrics.
problem Understanding long-term behavior of finite-particle systems in relation to their mean-field limits.
method Developed uniform-in-time propagation-of-chaos results for continuous-time SVGD using cutoff strategies and finite-dimensional theories.
result Uniform-in-time propagation-of-chaos bounds in various metrics, including Langevin kernel Stein discrepancy, Wasserstein-1, and Wasserstein-2 distances.
The paper explores how language models can provide reliable state measurements without being interpreted as beliefs.
problem How to use language models to reliably infer states without misinterpreting them as beliefs.
method Developed a semantic map and semiparametric inverse to link language probabilities to state probabilities, avoiding hidden models.
result Conditions for existence, identification, stable recovery, and uniform stability of posterior states from observable language probabilities.
Uniform distance distortion estimate for Ricci flows with bounded scalar curvature.
problem Analyzing Ricci flows with collapsing initial data.
method Uniform distance distortion estimate through renormalized metric-measure quantities.
result Uniform lower bounds of the renormalized heat kernel match with the lower bound of the renormalized volume ratio, proving distance distortion estimate.
This thesis relaxes assumptions for causal discovery, making methods applicable to more complex systems.
problem Learning causal structures from observational data with latent variables.
method Alternative definition of k-Triangle Faithfulness for non-Gaussian distributions and uniform consistency proof.
result Uniform consistency of causal discovery algorithm under modified faithfulness assumption.
Selective sampling improves matrix completion with known structure.
problem Reconstructing a low-rank matrix with incomplete data.
method Designing observation sets based on matrix structure and selective sampling.
result Improved reconstruction accuracy with selective sampling.
PCA++ improves robustness to background noise in contrastive learning.
problem Recovering shared signal subspaces from positive pairs in high-dimensional data with structured background noise.
method PCA++ uses hard uniformity-constrained contrastive learning to enforce identity covariance on projected features.
result PCA++ outperforms standard PCA and alignment-only PCA+ in simulations and real-world datasets.
New model captures complex network phenomena like strong local clustering and community structure.
problem Improving community detection in complex networks with higher-order structures.
method Introduces a Superimposed Stochastic Block Model (SupSBM) and analyzes higher-order spectral clustering methods.
result Proves upper bounds on misclustering error for spectral community detection on SupSBM.
Adaptive sampling improves graph diffusion models by maintaining uniform information speed.
problem Standard diffusion models overlook non-homogeneous dynamics on complex manifolds.
method Information-geometric framework using Fisher-Rao metric and Drift Variation Score (DVS).
result DVS solver ensures uniform rate of distributional change, improving structural fidelity and efficiency.
Study exact community recovery in noisy SBM with limited queries.
problem Community recovery in noisy stochastic block models with limited queries.
method Balanced uniform querying, two-stage adaptive strategy, sublinear queries, subsampled graph.
result Adaptive querying can improve exact recovery limits in noisy SBM.
Improved real-time visualizations of conversation turns using dynamic attention weights.
problem Uniform attention weights in sequential analysis tasks prevent meaningful visualization.
method Developed a method to track changes in turn importance over time.
result More informative real-time visuals confirmed by human reviewers.
We find prominent similarities in the features of the time series for the (model earthquakes or) overlap of two Cantor sets when one set moves with uniform relative velocity over the other and time series of stock prices. An anticipation method for some of the crashes have been proposed here, based on these observation…
Unified framework for robust clustering under various dissimilarity measures.
problem Improving center-based clustering methods to handle outliers and non-Euclidean data.
method Median-of-Means (MoM) estimation framework with uniform concentration bounds.
result Strong consistency and error rate of O(n−1/2) under mild conditions. We find prominent similarities in the features of the time series for the overlap of two Cantor sets when one set moves with uniform relative velocity over the other and time series of stock prices. An anticipation method for some of the crashes have been proposed here, based on these observations.