SuperMix uses sparse regularization to accurately estimate discrete mixing measures.
problem Estimating discrete mixing measures in kernel mixture models.
method Data fitting and regularization convex program with l1-regularization.
result The estimator accurately identifies the true mixing measure with support localization.
The paper provides guarantees for learning switching non-linear systems from a single trajectory.
problem Learning non-linear dynamical systems with switching dynamics.
method Non-asymptotic bounds derived under stability assumptions for i.i.d. switching modes.
result Explicit convergence rates for Hölder and linear function classes based on effective sample size.
Paper debunks value aggregation's convergence and provides stability conditions.
problem Value aggregation's convergence in imitation learning problems.
method Iterative policy optimization and evaluation in an online learning setting.
result Identified a critical stability condition for convergence and provided a performance bound.
Proof of Gaussian ML estimator consistency in linear auto-regressive models.
problem Consistency of Gaussian maximum likelihood estimator in linear auto-regressive models.
method Information-theoretic proof without stability assumptions.
result Nearly optimal non-asymptotic rates for parameter recovery.
A new algorithm reduces bias in estimating model parameters.
problem Efficient estimation of model parameters in non-linear state-space models.
method Parisian particle Gibbs (PPG) algorithm for bias reduction in online learning.
result Non-asymptotic bounds on bias and variance for PPG.
New method improves generalization in deep learning models.
problem Improving generalization in overparameterized deep neural networks.
method Stochastic Gauss-Newton method with Levenberg-Marquardt damping and mini-batch sampling.
result Established finite-time convergence and non-asymptotic generalization bounds.
This study analyzes AdaGrad's stability and convergence in non-convex optimization.
problem Lack of theoretical analysis for AdaGrad in non-convex optimization.
method Novel stopping time-based techniques from probability theory.
result Established stability and derived convergence rates for AdaGrad.
Paper stabilizes bandit learning with regularization, improving inference under adaptive sampling.
problem Challenges in statistical inference with adaptive sampling.
method Refined stability condition for online algorithms, using regularized stochastic-mirror-descent-style methods.
result Derives precise regret bounds and asymptotic normality, showing necessity of regularization for valid inference.
The present paper provides a new generic strategy leading to non-asymptotic theoretical guarantees on the Leave-one-Out procedure applied to a broad class of learning algorithms. This strategy relies on two main ingredients: the new notion of Lq stability, and the strong use of moment inequalities. Lq stability e…
Unified theory explains GAN convergence, highlighting interaction term's dual roles.
problem Understanding and accelerating convergence of GANs.
method Unified non-asymptotic local convergence theory for smooth two-player games.
result Interaction term explains slow-down and exponential convergence for GAN training.
The paper analyzes Karcher means on restricted PSD matrices with statistical guarantees.
problem Statistical analysis of non-linear manifolds in machine learning.
method Intrinsic mean model on restricted PSD matrices, Karcher mean analysis, extrinsic signal-plus-noise model.
result Non-asymptotic statistical analysis of Karcher means with deterministic error bounds.
The paper analyzes methods for estimating linear functionals from observational data, proving upper bounds and showing optimal procedures.
problem Estimating linear functionals from observational data in causal inference and bandit literature.
method Two-stage procedures that first estimate treatment effect function, then use it to estimate the linear functional.
result Proves non-asymptotic upper bounds on mean-squared error for two-stage procedures and shows instance-dependent optimality.
New algorithms improve sampling from complex distributions.
problem Sampling from high-dimensional target distributions with super-linearly growing potentials.
method Proposed aHOLA and aHOLLA algorithms with non-asymptotic convergence bounds.
result Achieved state-of-the-art rates of convergence in non-convex settings.
The study examines how much data is needed for generative and vision-language models to make reliable predictions.
problem Ensuring reliable predictions with low data for models used in medical decision support.
method Analyzes uniform convergence bounds for VLM-induced classifiers under low-dimensional semantic representations.
result Finite-sample uniform convergence bounds for accuracy and calibration functionals of VLM-induced classifiers.
This work achieves finite-time stabilization of uncertain LQ systems using random feedbacks.
problem Stabilizing linear systems with unknown dynamics in finite time.
method Random linear feedbacks to achieve finite-time stabilization.
result High probability guarantees for finite time stabilization of LQ systems.
Study efficient iterative method for distribution matching using sliced optimal transport.
problem Efficiently match distributions using sliced optimal transport.
method Slice-matching scheme based on sliced optimal transport, with quantitative non-asymptotic rates derived.
result Derive quantitative non-asymptotic rates for convergence to target distribution.
Unified framework for solving fixed-point equations in deterministic and stochastic settings.
problem Solving fixed-point equations for seminorm-contractive operators in both deterministic and stochastic contexts.
method Fixed-point theorem and stochastic approximation analysis.
result Unified finite-sample bounds for various reinforcement learning algorithms.
Flow matching adapts to manifold structures without diffusion.
problem Theoretical understanding of flow matching in manifold-supported settings.
method Flow matching with linear interpolation on smooth manifolds, analyzing velocity field and density estimator.
result Non-asymptotic convergence guarantee and statistical consistency of flow matching on manifolds.
Single trajectory learns LTI system realization.
problem Learning LTI system realization from a single trajectory.
method Finite time analysis of Markov parameters, Ho-Kalman algorithm stability, sample complexity.
result Data needed for accurate balanced realization learning.
The paper examines stable capillary hypersurfaces in hyperbolic space.
problem Stability of capillary hypersurfaces with free boundary on a horosphere.
method Analysis of umbilical and totally geodesic hypersurfaces using stability criteria.
result Umbilical and totally geodesic hypersurfaces are the only stable capillary hypersurfaces with boundary on a horosphere.
New findings show GD converges to a linear interpolator even with quadratic loss function under certain conditions.
problem Understanding convergence of Gradient Descent with quadratic loss functions.
method Parameterized linear regression with quadratic loss function, empirical and theoretical analysis.
result Gradient Descent converges to a linear interpolator even with quadratic loss function under the Edge of Stability regime.
Study stability and bifurcation of liquid interfaces in cylindrical supports.
problem Stability and bifurcation of liquid interfaces in cylindrical support surfaces.
method Analysis of eigenvalues of the Jacobi operator, Plateau-Rayleigh instability, bifurcation theory.
result Conditions for the emergence of new morphologies and bifurcations from circular cylinders.
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical successes in various fields ranging from image to audio processing, there have only …
Develops a provable convex tensor clustering method.
problem Cluster analysis of tensors, especially in high dimensions.
method Provably convex formulation of tensor co-clustering.
result Non-asymptotic error bound revealing 'blessing of dimensionality'.
GCNs converge and remain stable on large random graphs, revealing geometric insights.
problem Understanding the behavior of GCNs on large, sparse random graphs.
method Analysis of GCNs on random graph models with latent variables and geometric edge probabilities.
result GCNs converge to their continuous counterparts as graph size increases, and are stable to small graph deformations.
We stabilize the Kumaraswamy distribution for efficient sampling and differentiation.
problem Numerical instabilities in the Kumaraswamy distribution's inverse CDF and log-pdf.
method Identified and resolved numerical issues, introduced a stabilized KS distribution.
result Stabilized Kumaraswamy distribution supports efficient sampling and differentiation.
We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS…
Random forests are stable and provide reliable prediction intervals.
problem Stability and reliability of random forest prediction intervals.
method Established stability under mild conditions and proved coverage bounds.
result Non-asymptotic lower and upper bounds for prediction interval coverage.
TUSLA algorithm solves non-convex optimization problems with ReLU activations.
problem Non-convex stochastic optimization with super-linearly growing and discontinuous gradients.
method Non-asymptotic analysis of TUSLA algorithm for non-convex learning.
result TUSLA provides non-asymptotic error bounds in Wasserstein distances for non-convex learning.
The cohomology of complex irreducible polynomials stabilizes with degree or variables.
problem Understanding the cohomology of complex irreducible polynomials.
method Proving homological stability in cohomology as degree or variables increase.
result Cohomology stabilizes with respect to both degree and number of variables.
We present sufficient conditions for topological stability of continuous functions f:R→R having finitely many local extrema with respect to averagings by discrete measures with finite supports.
The paper examines the stability of Killing cylinders in hyperbolic space.
problem Stability of Killing cylinders in hyperbolic space.
method Explicit computation of Morse index for Jacobi operator on various support surfaces.
result Delaunay surfaces can be bifurcated from Killing cylinders supported on geodesic planes.
Gaussian and bootstrap methods improve ATE estimator accuracy.
problem Improving the accuracy of Average Treatment Effect (ATE) estimators.
method Gaussian approximation and bootstrap procedures.
result Precise bounds on ATE estimator accuracy quantifying key parameters.
Implicit Q-learning and SARSA adjust step-sizes automatically, improving stability and performance.
problem Numerical instability and slow progress in Q-learning and SARSA due to step-size calibration.
method Reformulate iterative updates as fixed-point equations, scaling step-sizes inversely with feature norms.
result Implicit methods maintain stability over broader step-size ranges and achieve comparable convergence rates.
SAIL improves AIL by weighting adversarial rewards with support estimation.
problem Training instability and reward bias in AIL.
method Support-weighted Adversarial Imitation Learning (SAIL) extends AIL with support estimation to improve reinforcement signals.
result SAIL achieves better performance and stability on benchmark tasks.
This study proves local stability of SGP μ-WGAN and shows penalizing data or sample manifold is key.
problem Stabilizing and regularizing WGAN with gradient penalty.
method Proves local stability of SGP μ-WGAN using measure valued differentiation.
result Penalizing data or sample manifold is key to regularizing WGAN.
The paper improves OT map estimation rates without strict assumptions.
problem Estimating optimal transport maps under practical conditions.
method Developed new convergence rates and scalable algorithms.
result Improved convergence rates for OT map estimation without restrictive assumptions.
Study on compact and finite-type support in mapping class group homology.
problem Understanding non-trivial classes supported on compact or finite-type subsurfaces.
method Use of shiftable subsurfaces and homological stability for finite-type surfaces.
result Almost-complete answer for surfaces with positive genus, partial answer for zero genus.
New method stabilizes GAN training by addressing two critical Jacobian factors.
problem Stability issues in GAN training dynamics.
method Mathematical analysis and new Jacobian Regularization (JARE).
result JARE simultaneously addresses two critical Jacobian factors for better GAN stability.
The paper improves the empirical bootstrap method for non-normal estimators.
problem Theoretical properties of empirical bootstrap for non-asymptotically normal estimators.
method Establishing limiting distribution, deriving consistency conditions, proposing alternative methods.
result The empirical bootstrap method can be asymptotically consistent under stability conditions.
High-dimensional models become unstable when sample size falls below a critical level, leading to a phase transition.
problem Instability in high-dimensional learning models when sample size is insufficient.
method Proved the necessity of a Fisher eigenvalue threshold for stability, introduced Fisher floor for verification.
result A sharp phase transition between reliable concentration and inevitable failure in high-dimensional learning.
Study on special Hermitian metrics and their stability.
problem Existence and stability of Hermitian metrics with specific properties.
method Analysis of Hermitian metrics with $∂ar{∂}ω^k=0$ for k=1 to n−1. result Stability of metrics at blow-up and deformations.
Novel approach ensures stability of compact schemes for variable PDEs.
problem Ensuring stability of compact schemes for variable coefficient PDEs.
method Difference equation approach to derive stability conditions.
result Derives sufficient condition for unconditional stability.
Sharp bounds for Dirichlet sums lead to improved Bayesian algorithm analysis.
problem Improving Bayesian algorithm performance through precise deviation bounds.
method Novel integral representation of Dirichlet sum density, Gaussian approximation, complex analysis.
result Significantly sharpened regret bounds for Multinomial Thompson Sampling.
We propose an algebraic geometric stability criterion for a polarised variety to admit an extremal Kaehler metric. This generalises conjectures by Yau, Tian and Donaldson which relate to the case of Kaehler-Einstein and constant scalar curvature metrics. We give a result in geometric invariant theory that motivates thi…
The paper improves NBR for count data using elastic-net regularization, achieving consistency and weak signal detection.
problem Sparse negative binomial regression for count data with non-asymptotic advantages.
method Elastic-net estimator with oracle inequalities derived under Compatibility Factor Condition and Stabil Condition.
result Sign consistency and grouping effect with high probability, and true variable set recovery under certain conditions.
Non-asymptotic rates for SGD via martingale CLT.
problem Improving the convergence rates of SGD.
method Combining Stein's method and Lindeberg's argument for multivariate martingale CLT, then applying to SGD.
result Explicit rates for multivariate martingale CLT and SGD convergence.
Robotic grasp stability improved with fingertip slippage detection.
problem Improving grasp stability in robotic manipulation.
method Task-relevant feature extraction and efficient classifier design for fingertip slippage detection.
result The proposed method effectively detects object slippage with fingertips in an online fashion.