Modified Anderson-Darling test improves counterparty credit risk model accuracy.
problem Limited sample size impacts Anderson-Darling test effectiveness in counterparty credit risk models.
method Proposed a modified Anderson-Darling test for better volatility detection in counterparty credit risk models.
result Modified test detects underestimation of model's volatility more efficiently.
Study top-K ranking with adversarial crowdsourced data, identifying top-K items reliably.
problem Recovering top-K ranked items from partially revealed preferences in an adversarial setting.
method Characterizes minimax limit on sample size for reliable identification, extends to unknown population size.
result Establishes fundamental limits on sample size for top-K recovery in adversarial crowdsourced data.
The study reveals a transition in neural network performance from infinite-width to variance-limited behavior as dataset size increases.
problem Understanding the transition from infinite-width to variance-limited behavior in neural networks.
method Empirical study of the transition from infinite-width to variance-limited behavior as a function of sample size and network width.
result The critical sample size \( P^* \) is approximately \( \sqrt{N} \) for polynomial regression with ReLU networks.
The paper analyzes convergence of neural SDEs as sample size increases.
problem Understanding the limiting behavior of neural SDEs as sample size grows.
method Analyzes Hamilton-Jacobi-Bellman equation and uses stochastic maximum principle.
result Convergence of minima and optimal parameters of neural SDEs as sample size increases.
Median-of-means sampling outperforms mean-of-means for large sample sizes in numerical integration.
problem Improving numerical integration accuracy in high dimensions.
method Median-of-means sampling compared to mean-of-means using RQMC methods.
result Median-of-means sampling is superior for large sample sizes, while mean-of-means is better for smaller sample sizes.
Exact distribution of split conformal prediction coverage found.
problem Determining the reliability of prediction sets in batch mode.
method Analysis of exchangeable data to find universal distribution of empirical coverage.
result Exact distribution of empirical coverage is universal and determined by nominal miscoverage level and calibration sample size.
Study evaluates synthetic data augmentation for small datasets, highlighting inconsistencies in traditional metrics.
problem Inconsistent validation of synthetic data generated for small sample sizes.
method Proposes a normalized Bottleneck distance metric to evaluate synthetic tabular data.
result Common metrics like propensity scoring and MMD fail for small datasets, showing instability and high variability.
Machine learning's predictive power is limited by sample size, as shown by the Limits-to-Learning Gap.
problem The limitations of machine learning in approximating true data-generating processes.
method Characterization of a universal lower bound (LLG) quantifying the discrepancy between empirical fit and population benchmark.
result Standard ML approaches can substantially understate true predictability in financial data.
Extended study improves covariance matrix estimation for portfolio managers.
problem Limited sample sizes and poor performance of PCA estimator in high-dimensional returns.
method Developed a more general shrinkage framework targeting further information.
result Improves the PCA estimator of beta by shrinking it toward a target.
In biospectroscopy, suitably annotated and statistically independent samples (e. g. patients, batches, etc.) for classifier training and testing are scarce and costly. Learning curves show the model performance as function of the training sample size and can help to determine the sample size needed to train good classi…
Study SGD dynamics in high-dimensional models, revealing consistent behavior across different batch sizes and learning rates.
problem Understanding SGD dynamics in high-dimensional multi-index models.
method Asymptotic analysis of SGD, developing mean-field equations and Gaussian diffusion approximations.
result Consistent SGD dynamics across different batch sizes and learning rates, distinct from gradient flow and online SGD.
Polyak step size GD reaches final radius of convergence after log iterations.
problem Statistical and computational complexities of Polyak step size GD.
method Generalized smoothness and Lojasiewicz conditions, stability of gradients.
result Polyak step size GD reaches final statistical radius of convergence after logarithmic number of iterations.
Study ridge ensembles in proportional feature-to-sample size regime, proving risk equivalence and GCV consistency.
problem Characterizing and optimizing ridge ensembles in proportional feature-to-sample size regimes.
method Proportional asymptotics analysis, GCV for tuning, proving risk equivalence.
result Risk of optimal full ridgeless ensemble matches optimal ridge predictor's risk.
Study the limits of discrete DPPs to continuous DPPs as set size grows.
problem Characterize the behavior of discrete DPPs as they approach continuous DPPs.
method Non-asymptotic characterization of the limit in terms of weak coherency.
result Sufficient conditions for weak coherency are identified.
Convolutional denoising autoencoders improve medical image denoising with small sample sizes.
problem Efficient denoising of medical images with limited training data.
method Convolutional denoising autoencoders trained on small datasets.
result Simple autoencoders can denoise images with high noise levels indistinguishable to humans.
New method for MMD with unequal sample sizes improves test power.
problem Existing MMD methods assume equal sample sizes, discarding valuable data.
method Extended generalized U-statistics to handle unequal sample sizes.
result New asymptotic distributions and power optimization for MMD with unequal sample sizes.
The study proves sampling-based GNNs can approximate training on full graphs with small subgraphs.
problem Training Graph Neural Networks (GNNs) on large graphs is computationally expensive.
method Theoretical framework using graph local limits to prove approximation of GNN training on small samples.
result Parameters learned from sampling-based GNNs on small subgraphs are close to those on full graphs.
Proposes a new signal model for high-dimensional, small-sample-size data.
problem Signal detection in high-dimensional, small-sample-size datasets.
method Intrinsic signal model based on dynamical system assumption.
result Taguchi method effectively detects signals in the proposed model.
We consider the problem of providing nonparametric confidence guarantees for undirected graphs under weak assumptions. In particular, we do not assume sparsity, incoherence or Normality. We allow the dimension D D D to increase with the sample size n n n . First, we prove lower bounds that show that if we want accurate infe…
Downsampling can improve generalization in ridgeless linear regression, especially with optimal sketching size.
problem Improving generalization in ridgeless linear regression with limited data.
method Investigating the effects of downsampling on the sketched ridgeless least square estimator in the proportional regime.
result Optimal sketching size minimizes out-of-sample prediction risks and stabilizes risk curves.
A new criterion QIC improves model selection for regular and singular models in small samples.
problem Inaccurate complexity estimation in small sample sizes for regular and singular models.
method Introduced Frequentist Information Criterion (QIC) to improve complexity estimation.
result QIC provides better model selection in small sample sizes for regular and singular models.
pmsims R package uses Gaussian process for flexible sample size estimation in clinical models.
problem Determining adequate sample size for clinical prediction models.
method Simulation-based Gaussian process search for flexible sample size estimation.
result Gaussian process-based method produces more stable sample size estimates, especially in challenging settings.
The paper studies how more data affects prediction risk in high-dimensional models.
problem The impact of increasing data on prediction risk in high-dimensional models.
method Derives central limit theorem and provides finite-sample distribution and confidence interval for prediction risk.
result Demonstrates 'more data hurt' phenomenon in high-dimensional least squares estimation.
The paper improves confidence regions for band-limited functions using tighter norm bounds and majority voting.
problem Constructing reliable confidence regions for band-limited functions from noisy data.
method Improved norm bounds using Hoeffding's inequality and empirical Bernstein bound, majority voting to aggregate intervals.
result Confidence intervals retain their simultaneous coverage guarantee even when aggregated from random subsamples.
The paper analyzes phase retrieval under limited samples, ensuring a benign local landscape for convergence.
problem Ensuring a benign local landscape for phase retrieval under limited samples.
method Fine-grained analysis of local landscape properties under the regime of limited samples.
result Gradient descent can converge to an o d ( 1 ) o_d(1) o d ( 1 ) -loss solution exponentially fast under certain conditions. Neural causal discovery methods fail to accurately uncover causal structures due to the faithfulness property.
problem Accuracy in neural causal discovery is limited, especially when distinguishing between existing and non-existing causal relationships.
method Systematic evaluation of neural causal discovery methods, focusing on their performance in finite sample regimes and their ability to recover ground-truth graphs.
result Neural networks lack the precision to reliably recover ground-truth causal graphs, even for small graphs and large sample sizes.
Study of linear classifiers in infinite imbalance scenarios.
problem Behavior of linear discriminant functions in extreme imbalance conditions.
method Analysis of linear classifiers under infinite imbalance, focusing on weight function properties and limit behavior.
result Limiting coefficient vectors reflect robustness or conservatism, optimizing against worst-case alternatives.
Study wSAA for contextual decisions, improving uncertainty quantification under computational constraints.
problem Uncertainty quantification limitations in wSAA for contextual stochastic optimization.
method Establish central limit theorems and asymptotic-normality-based confidence intervals for optimal costs.
result Over-optimizing can mitigate misspecification and preserve asymptotic normality, albeit at a slower convergence rate.
We analyze SGAs for statistical inference via asymptotics, improving tuning methods.
problem Improper tuning of SGAs for optimization and sampling.
method Characterize large-sample asymptotics of SGAs via step-size and sample-size scaling limits.
result Iterate averaging with large step size is robust and asymptotically has covariance proportional to MLE's.
Flexible framework integrates machine learning and DRO for uncertain parameter prediction.
problem Limited joint observations of uncertain parameters and covariates.
method Wasserstein, sample robust optimization, and phi-divergence-based ambiguity sets.
result Validation of theoretical and practical benefits in limited data scenarios.
This paper examines the convergence of adaptive sampling methods for Bayesian neural networks.
problem Uncertainty quantification in deep neural networks, especially for medical applications.
method Locally adaptive and scalable diffusion-based sampling methods.
result These methods can have a substantial bias in the distribution they sample, even in the limit of vanishing step sizes.
For spherically symmetric distributions, efficient quantisation can be achieved with moderate sample sizes.
problem Optimal quantisation in high dimensions requires large sample sizes, making it impractical.
method Uniformly distributed random quantisers on a sphere of suitable radius achieve exceptional performance.
result For moderate sample sizes, quantisation error can be efficiently computed and approximated.
A novel Hawkes Process model captures order sizes in LOBs, improving fit quality and market impact studies.
problem Capturing the variability in order sizes in Limit Order Books (LOBs).
method Compound Hawkes Process with time-varying parameters and non-parametric calibration.
result Improved fit quality and empirical market impact function replication.
Efficient inference method for adaptive experiments with tighter confidence sequences.
problem Efficient inference of Average Treatment Effect in a changing policy sequential experiment.
method Semiparametric efficient inference using Adaptive Augmented Inverse-Probability Weighted estimator and asymptotic confidence sequences.
result Derives tighter confidence sequences for adaptive experiments under data-dependent stopping times.
The paper improves A/B testing for non-Gaussian data, ensuring reliable results with large sample sizes.
problem Inaccurate A/B testing results due to non-normal data and unequal sample sizes.
method Derives explicit formulas for minimum sample size and introduces an Edgeworth-based correction.
result Corrected method improves reliability of A/B testing in real-world conditions.
Study shows more data improves model explanations, aiding reliable knowledge extraction.
problem Challenges in deriving reliable knowledge from machine learning models due to the Rashōmon effect.
method Examined the influence of sample size on explanations from models in a Rashōmon set using SHAP.
result Explanations from <128 samples are highly variable, but agreement improves with more data.
New bounds for multi-task learning with varying task sizes.
problem Generalization in multi-task learning with tasks of different sizes.
method PAC-Bayesian bounds for unbalanced settings.
result Stronger generalization bounds for multi-task learning with varying task sizes.
A new test improves statistical inference in bandit algorithms without sacrificing adaptiveness.
problem Challenges in statistical inference for adaptive randomised experiments in bandits.
method An allocation probability test for Thompson Sampling without trading-off regret or requiring large sample sizes.
result Improves statistical inference in small samples, showing advantages in mental health experiments.
The paper strengthens the classical result of MLE convergence to a Gaussian distribution.
problem The classical result of MLE convergence to a Gaussian distribution.
method Sub-Gaussian concentration and entropic normality of the normalized MLE.
result Entropic central limit theorem for a smoothed version of the estimator.
Paper improves CLT and bootstrap approximations for LSA with decreasing step size.
problem Improving normal approximation and bootstrap methods for LSA with decreasing step sizes.
method Refined Berry-Esseen bounds and multiplier bootstrap procedure for LSA.
result Approximation rates up to 1 / n 1/\sqrt{n} 1/ n for LSA rescaled error distribution. Study shows DNNs can recover functions with fewer samples than model parameters at overparameterization.
problem Determining reliable function recovery in overparameterized deep neural networks.
method Introducing 'local linear recovery' (LLR) and proving upper bounds on sample sizes for recovery.
result Upper bounds on optimistic sample sizes for function recovery in overparameterized DNNs are achieved.
Neighborhood sampling affects graph neural network training outcomes.
problem Understanding the impact of neighborhood sampling on graph neural network training.
method Theoretical analysis using neural tangent kernels and Gaussian processes.
result Posterior covariance differs for different neighborhood sampling approaches, indicating no dominant approach.
This paper strengthens the central limit theorem for order statistics using relative entropy.
problem Establishing a stronger mode of convergence for central limit behavior of order statistics.
method Using relative entropy to ensure a stronger mode of convergence for central limit behavior of order statistics.
result An order O ( 1 / n ) O(1/\sqrt{n}) O ( 1/ n ) rate of convergence is established under mild conditions. We derive formulas for F measures' standard error and confidence intervals.
problem Estimating F measures' accuracy with confidence.
method Analytic formulas based on asymptotic normality.
result Valid formulas for sample size planning.
DKN adapts to medical imaging data with limited samples and interpretable models.
problem Medical imaging data's unique nature makes general methods like CNN unsuitable.
method DKN uses a Kronecker product structure to adapt to low sample size and provide interpretable models.
result DKN achieves prediction power comparable to CNN and provides model interpretability.
The paper investigates the convergence of Vendi scores under finite samples and introduces a truncated version for better performance.
problem The Vendi score's convergence is hindered by computational limitations when using large sample sizes.
method The authors introduce the t-truncated Vendi score to address this issue by truncating the eigenspectrum of the kernel matrix.
result The t-truncated Vendi score converges to its asymptotic limit with a smaller number of samples, improving upon the standard Vendi score.
A new method for estimating graphlet counts in large networks.
problem Efficiently calculating graph statistics over massive networks.
method Lifting technique for Monte Carlo sampling of graphlets.
result Provable unbiasedness and controlled variance for all graphlets.
The paper analyzes SGD in high-dimensional networks, revealing new scaling limits.
problem Understanding SGD dynamics in high-dimensional networks.
method Analyzing the effective dynamics of SGD using recent work on the subject.
result A new correction term emerges at the critical scaling regime, changing the phase diagram.