arXiv research

Learnable multiclass hypothesis classes don't always have a sample compression scheme of fixed size.

Study non-monotonic loss functions in CRC, achieving valid risk control with large calibration samples.

Estimates neural representation dimensionality from small sample sizes.

In the information-based paradigm of inference, model selection is performed by selecting the candidate model with the best estimated predictive performance. The success of this approach depends on the accuracy of the estimate of the predictive complexity. In the large-sample-size limit of a regular model, the predicti…

Kurtosis is seen as a measure of the discrepancy between the observed data and a Gaussian distribution and is defined when the 4th moment is finite. In this work an empirical study is conducted to investigate the behaviour of the sample estimate of kurtosis with respect to sample size and the tail index when applied to…

The paper improves methods for estimating set size using samples.

This study analyzes LTS in sparse models with finite sample error bounds.

We study the sample complexity of private synthetic data generation over an unbounded sized class of statistical queries, and show that any class that is privately proper PAC learnable admits a private synthetic data generator (perhaps non-efficient). Previous work on synthetic data generators focused on the case that …

It was proved in 1998 by Ben-David and Litman that a concept space has a sample compression scheme of size d if and only if every finite subspace has a sample compression scheme of size d. In the compactness theorem, measurability of the hypotheses of the created sample compression scheme is not guaranteed; at the same…

Study bounds variance modulation function for K-spider distributions.

Proposes SVI for covariate-shift generalization with sparse variable independence.

Privacy affects how much data is needed for CVaR optimization.

Avare improves optimization and sampling with adaptive importance sampling.

Bitcoin volatility analysis shows decreasing HE with longer sampling periods.

The study reveals a transition in neural network performance from infinite-width to variance-limited behavior as dataset size increases.

Exact distribution of split conformal prediction coverage found.

New method reduces over-parametrization in neural networks, ensuring sparsity and finite network size.

Enhanced DFO using adaptive batch-based FD estimates.

Deep learning method improves regression accuracy.

The paper studies how more data affects prediction risk in high-dimensional models.

High-dimensional models become unstable when sample size falls below a critical level, leading to a phase transition.

The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset of the sample to be dependent on the sample size, a feature not presented in a …

We provide finite-sample analysis of a general framework for using k-nearest neighbor statistics to estimate functionals of a nonparametric continuous probability density, including entropies and divergences. Rather than plugging a consistent density estimate (which requires $k \to \infty$ as the sample size $n \to \in…

This work introduces COLA, a strategy to aggregate conformal prediction sets efficiently.

Meta-learners improve causal effect estimation in small samples.

A new method calculates intrinsic effective sample size for manifold-valued data.

New method improves zeroth-order stochastic optimization with adaptive sampling.

This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through feature maps; in this way, in addition to treating the consistency of logistic reg…

In reinforcement learning (RL) , one of the key components is policy evaluation, which aims to estimate the value function (i.e., expected long-term accumulated reward) of a policy. With a good policy evaluation method, the RL algorithms will estimate the value function more accurately and find a better policy. When th…

This paper analyzes momentum Q-learning with finite-sample guarantees.

New method reduces ensemble size for linear bandits, achieving near optimal regret.

A study on a surprising phase transition in model generalization error as parameters approach sample size.

Paper overcomes sample size barrier in reinforcement learning with generative models.

The paper analyzes convergence of neural SDEs as sample size increases.

We introduce a simulation method for dynamic portfolio valuation and risk management building on machine learning with kernels. We learn the dynamic value process of a portfolio from a finite sample of its cumulative cash flow. The learned value process is given in closed form thanks to a suitable choice of the kernel.…

New findings show modern neural networks have finite sample complexity in o-minimal structures.

Develops robust MDPs for unknown disturbances with performance guarantees.

Flexible framework integrates machine learning and DRO for uncertain parameter prediction.

We analyze SGAs for statistical inference via asymptotics, improving tuning methods.

Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample size, making it difficult to apply them to massive data. Moreover, resampling i…

We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process samples are assumed uncorrelated over time and having a time-varying marginal dist…

The paper investigates the convergence of Vendi scores under finite samples and introduces a truncated version for better performance.

The Fisher information approximation (FIA) is an implementation of the minimum description length principle for model selection. Unlike information criteria such as AIC or BIC, it has the advantage of taking the functional form of a model into account. Unfortunately, FIA can be misleading in finite samples, resulting i…

This work studies the statistical performance of Sinkhorn iterations in estimating Schrödinger bridges.

We present asymptotic and finite-sample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood fitting when the number of classes is allowed to grow as the root of the network size …

Three privacy-preserving methods for median regression are proposed.

Paper provides unbiased spectral moment estimates from finite data.

In this short note we observe that the sample complexity of PAC machine learning of various concepts, including learning the maximum (EMX), can be exactly determined when the support of the probability measures considered as models satisfies an a-priori bound. This result contrasts with the recently discovered undecida…