A new method achieves optimal uniformity in designs with minimal flexibility.
problem Achieving optimal uniformity in designs with minimal flexibility.
method Derive a lower bound on the uniformity constant and use a greedy construction to achieve this bound, then extend the scheme for more flexibility.
result A simple greedy construction achieves the optimal uniformity constant.
Paper proposes a new method for efficient hyperparameter optimization.
problem Challenging task of optimizing hyperparameters in machine learning.
method Sequential Uniform Design (SeqUD) strategy for adaptive and efficient exploration of hyperparameter space.
result The proposed SeqUD strategy outperforms existing methods in hyperparameter optimization.
A new model-free subsampling method using uniform designs is proposed.
problem Model-based subsampling methods are often dependent on model assumptions.
method Developed a criterion (GEFD) and a model-free subsampling method based on uniform designs.
result The proposed method outperforms random sampling and is robust under diverse model specifications.
Randomization is minimax-optimal for variance in experimental design, even with structure.
problem Designing optimal randomized experiments for variance minimization.
method Analyzing permutation symmetric and non-symmetric sets of outcomes, proposing inference-constrained MSOD.
result Randomization is minimax-optimal for variance, even with structure, and requires uniformity constraints for Fisher's exact test.
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. New algorithms achieve uniform stability for empirical risk minimization.
problem Designing uniformly stable optimization algorithms for empirical risk minimization.
method Black-box conversion of smooth optimization algorithms and development of Mirror Descent for smooth optimization.
result Optimal algorithms with uniform stability and convergence rates for smooth optimization.
New insights into how to inspect and learn from multi-stage processes and AI reasoning.
problem Understanding how to attribute outcomes to early stages in multi-stage operations and AI reasoning.
method Information-theoretic analysis and mathematical proofs of four key results.
result Uniform checkpoint spacing is minimax-optimal for inspection design under homogeneous signal attenuation.
We design and mathematically analyze sampling-based algorithms for regularized loss minimization problems that are implementable in popular computational models for large data, in which the access to the data is restricted in some way. Our main result is that if the regularizer's effect does not become negligible as th…
The paper tests properties of multiple distributions with limited samples.
problem Testing properties of multiple distributions with few samples.
method Designing testers for uniformity, identity, and closeness testing under specific conditions.
result Sample optimal testers for uniformity, identity, and closeness testing are provided.
Wedge Sampling improves tensor completion with nearly-linear sample complexity.
problem Efficiently completing low-rank tensors from a subset of entries.
method Non-adaptive wedge sampling to promote structured connections in tensor completion.
result Polynomial-time algorithms achieve weak and exact recovery with nearly linear sample complexity.
Uniform AMMs control loss in prediction markets.
problem Controlling loss in prediction markets.
method Loss-versus-rebalancing (LVR) framework and uniform AMMs.
result Uniform AMMs achieve proportional LVR to pool value.
Uniform AMMs control loss in prediction markets.
problem Controlling loss in prediction markets.
method Loss-versus-rebalancing (LVR) framework and uniform AMMs.
result Uniform AMMs achieve proportional LVR to pool value.
Adaptive PCR improves panel data analysis with uniform guarantees.
problem Adaptive data collection in panel data settings.
method Adapting PCR to online settings using martingale concentration.
result Time-uniform guarantees for adaptive PCR in panel data.
The paper provides a uniform convergence bound for smooth calibration error and its relationship with functional gradient.
problem Limited theoretical understanding of learning algorithms achieving high accuracy and good calibration.
method Focuses on smooth calibration error, providing a uniform convergence bound and proving the relationship with functional gradient.
result Derives conditions for simultaneous classification and calibration guarantees in gradient boosting trees, kernel boosting, and neural networks.
Improved sampling accuracy in SG-MCMC methods via non-uniform gradient subsampling.
problem Computational inefficiency and sampling error in stochastic gradient MCMC methods.
method Proposes a non-uniform subsampling scheme to reduce sampling error in EWSG, a variant of SG-MCMC.
result EWSG reduces sampling error compared to uniform subsampling, improving accuracy without sacrificing convergence speed.
Graphical models have become a very popular tool for representing dependencies within a large set of variables and are key for representing causal structures. We provide results for uniform inference on high-dimensional graphical models with the number of target parameters d being possible much larger than sample siz…
Unified bounds for sketched bilinear forms in machine learning and statistics.
problem Uniform bounds on sketched bilinear forms for modern analyses.
method Generic chaining and new techniques for handling suprema over pairs of sets.
result Improved convergence bounds for sketched Federated Learning and bandit algorithms.
This paper proposes a new approach to construct high quality space-filling sample designs. First, we propose a novel technique to quantify the space-filling property and optimally trade-off uniformity and randomness in sample designs in arbitrary dimensions. Second, we connect the proposed metric (defined in the spatia…
New PAC-Bayesian bounds improve understanding of quantum machine learning generalization.
problem Lack of data-dependent, non-uniform generalization bounds for quantum models.
method Derive PAC-Bayesian generalization bounds for quantum models using channel perturbation analysis.
result First non-uniform, data-dependent generalization bounds for quantum models.
Optimizes survey design for private mean estimation with reduced variance.
problem Minimizing variance in private mean estimation with privacy constraints.
method Formulates optimal survey design as an optimization problem, determining optimal subsampling sizes to minimize variance.
result Identifies the first privacy-aware stratified sampling scheme that minimizes variance under different privacy mechanisms.
Aesthetics are critically important to market acceptance. In the automotive industry, an improved aesthetic design can boost sales by 30% or more. Firms invest heavily in designing and testing aesthetics. A single automotive "theme clinic" can cost over $100,000, and hundreds are conducted annually. We propose a model …
Improved neural network training for speech recognition using power-law nonlinearity and uniform distribution criterion.
problem Stability and uniformity of feature distribution in neural network training.
method Power-function based and histogram-based Maximum Uniformity of Distribution (MUD) algorithms.
result Power-function based MUD outperforms conventional MFCCs in speech recognition systems.
New methods learn sampling distributions for particle filters without supervision.
problem Designing accurate sampling distributions for nonlinear dynamical systems.
method Proposed four unsupervised learning methods for multivariate Gaussian and nonparametric distributions.
result Learned sampling distributions outperform designed ones in accuracy.
New algorithms improve best-arm identification with varying rewards.
problem Identifying the best arm with varying reward variances in fixed budget.
method Proposed two algorithms: SHVar for known variances, SHAdaVar for unknown variances; uses non-uniform budget allocation.
result Bounding misidentification probabilities for both algorithms.
This study optimizes offline reinforcement learning methods for various tasks without rewards.
problem Optimizing offline reinforcement learning for multiple tasks without rewards.
method Designing a new model-based approach with singleton absorbing MDPs to achieve optimal convergence rates.
result Achieved optimal convergence rates for offline reinforcement learning in various settings.
UDM reparameterization improves language model generation.
problem Mismatch between UDM training objective and denoising posterior.
method Leave-one-out denoising and absorbing state reformulation.
result Improved UDM generation through leave-one-out parameterization.
The paper provides consistency results for KDE on manifolds with irregular kernels.
problem Analyzing density estimation on manifolds with complex kernels.
method Strong uniform consistency with rates for KDE on Riemannian manifolds with Riemann integrable kernels.
result Strong uniform consistency with rates for KDE on manifolds.
New methods for estimating and inferring nonparametric structural functions and elasticities.
problem Estimating and inferring nonparametric structural functions and their derivatives.
method Data-driven sieve dimension choice and uniform confidence bands construction.
result Optimal estimation and inference procedures with minimax rates of convergence.
These series of notes serve as an introduction to some of both the classical and modern techniques in Reifenberg theory. At its heart, Reifenberg theory is about studying general sets or measures which can be, in one sense or another, approximated on all scales by well behaved spaces, typically just Euclidean space its…
Optimal design for multinomial logit models improves assortment selection efficiency.
problem Optimal experimental design for multinomial logit models with feedback.
method Two complementary approaches: MILP reformulation and lifted design.
result Achieves statistical efficiency and scalability for MNL bandits.
Paper analyzes Annealed Langevin Dynamics for multimodal sampling stability.
problem Ensuring stability of Annealed Langevin Dynamics across dimensions.
method Uniform-in-dimension analysis of ALD for Gaussian-mixture targets.
result ALD achieves prescribed accuracy in KL divergence with spectral conditions.
This paper introduces a new metric, ULI, for RL that ensures both cumulative and instantaneous performance.
problem High-stakes applications require RL algorithms to avoid playing bad policies.
method Introduces uniform last-iterate (ULI) guarantee, a stronger metric capturing both cumulative and instantaneous performance.
result ULI directly implies near-optimal cumulative performance across various metrics, but not the other way around.
Study uses contextual bandits to optimize charity exposure in donation solicitation.
problem Optimizing charity exposure in donation solicitation using survey responses.
method Adaptive experiment design to balance cumulative regret minimization and simple regret minimization.
result Adaptive experimentation yields better policy learning outcomes than uniform randomization.
Unified framework for self-supervised learning via latent distribution matching.
problem Lack of a unifying theoretical framework for diverse SSL methods.
method Casting SSL as latent distribution matching (LDM): maximizing alignment and uniformity.
result Derives a Bayesian filtering model and proves identifiable latent representations.
Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization problem. Almost all previous work assumes no explicit structure of the matrix and uses…
This paper introduces a new method for sampling copulas using GANs and space-filling designs.
problem Lack of feasible inference and sampling methods for copulas in high-dimensional situations.
method Generative adversarial networks (GANs) and space-filling designs.
result Significantly enhances sampling accuracy and computational efficiency compared to existing methods.
We revisit Spakula's uniform K-homology, construct the external product for it and use this to deduce homotopy invariance of uniform K-homology. We define uniform K-theory and on manifolds of bounded geometry we give an interpretation of it via vector bundles of bounded geometry. We further construct a cap product with…
New bounds on random quadratic forms hold under dependence, useful for adaptive modeling.
problem Need for independence in bounds on random quadratic forms.
method Uniform bounds on random quadratic forms of conditionally independent and sub-Gaussian stochastic processes.
result Bounds hold under general dependencies and sequential design.
Study on computational aspects of replicable learning, bridging statistical and algorithmic perspectives.
problem Understanding the computational connections between replicability and various learning paradigms.
method Design of replicable learners, lifting framework, and transformation techniques.
result Efficient replicable learners for specific learning problems under various distributions.
In "Rips complexes and covers in the uniform category" \cite{Rips} the authors define, following James \cite{J}, covering maps of uniform spaces and introduce the concept of generalized uniform covering maps. Conditions for the existence of universal uniform covering maps and generalized uniform covering maps are given…
StatQAT optimizes quantization for deep networks, reducing computational cost and memory usage.
problem Optimal quantization parameters selection for deep neural networks with diverse data distributions.
method Statistical error analysis framework for uniform and floating-point quantization, iterative and analytic quantizers designed for arbitrary and Gaussian-like distributions.
result Improved accuracy and stability in training low-precision neural networks.
Paper proves discrete uniformizations converge to continuous for surfaces of genus ≥1.
problem Computing uniformizations for surfaces of genus >1.
method Discrete conformality and uniformization on triangle meshes.
result Discrete uniformizations approximate continuous uniformization for closed surfaces of genus ≥1.
This paper refines homotopy theory for cubical sets and uniform spaces.
problem Classical homotopy theory limitations in cubical sets and uniform spaces.
method Develops a uniform-theoretic refinement for cubical sets and uniform spaces, lifting to a full and faithful embedding.
result Lifts classical homotopy categories to new uniform homotopy categories, generalizing cohomology theories.
CODA uses a new dropout technique inspired by constructivism learning to improve deep learning performance.
problem Existing dropout methods fail to differentiate among instances, leading to overfitting.
method CODA incorporates structural information and uses a Bayesian nonparametric method to create a better dropout technique.
result CODA outperformed other state-of-the-art dropout techniques on 5 real-world datasets.
SQWA improves low-precision DNNs with model averaging and quantization.
problem Designing good generalization DNNs with quantized weights.
method Floating-point model training, direct quantization, multiple low-precision models, weight averaging, re-quantization, fine-tuning, loss visualization.
result State-of-the-art results for 2-bit QDNNs on CIFAR-100 and ImageNet datasets.
We study the problem of causal structure learning over a set of random variables when the experimenter is allowed to perform at most M experiments in a non-adaptive manner. We consider the optimal learning strategy in terms of minimizing the portions of the structure that remains unknown given the limited number of e…
Survey on uniformization of metric surfaces, including fractal and topological manifolds.
problem Uniformization of metric surfaces homeomorphic to 2D topological manifolds.
method Various uniformization theorems, including quasisymmetric and quasiconformal approaches.
result Uniformization results for metric spheres and arbitrary metric surfaces.
Berestovskii and Plaut introduced the concept of a coverable uniform space when developing their theory of generalized universal covering maps for uniform spaces. Brodskiy, Dydak, LaBuz, and Mitra introduced the concept of a locally uniformly joinable uniform space when developing their theory of generalized uniform co…