相关论文: Optimal Ratio for Data Splitting

Sample splitting is widely used in statistical applications, including classically in classification and more recently for inference post model selection. Motivating by problems in the study of diet, physical activity, and health, we…

We propose an approach for fitting linear regression models that splits the set of covariates into groups. The optimal split of the variables into groups and the regularized estimation of the regression coefficients are performed by…

For many types of machine learning algorithms, one can compute the statistically `optimal' way to select training data. In this paper, we review how optimal data selection techniques have been used with feedforward neural networks. We then…

We consider partitions of a point set into two parts, and the lengths of the minimum spanning trees of the original set and of the two parts. If $w(P)$ denotes the length of a minimum spanning tree of $P$, we show that every set $P$ of $n…

We consider distributed statistical optimization in one-shot setting, where there are $m$ machines each observing $n$ i.i.d. samples. Based on its observed samples, each machine then sends an $O(\log(mn))$-length message to a server, at…

Recent work has shown a variety of ways in which machine learning can be used to accelerate the solution of constrained optimization problems. Increasing demand for real-time decision-making capabilities in applications such as artificial…

When artificial neural networks have demonstrated exceptional practical success in a variety of domains, investigations into their theoretical characteristics, such as their approximation power, statistical properties, and generalization…

Modern sequential recommender systems, ranging from lightweight transformer-based variants to large language models, have become increasingly prominent in academia and industry due to their strong performance in the next-item prediction…

We consider training and testing on mixture distributions with different training and test proportions. We show that in many settings, and in some sense generically, distribution shift can be beneficial, and test performance can improve due…

Big data sets must be carefully partitioned into statistically similar data subsets that can be used as representative samples for big data analysis tasks. In this paper, we propose the random sample partition (RSP) data model to represent…

In this paper we focus on comparative diagnostic trials which are frequently employed to compare two markers with continuous or ordinal results. We derive explicit expressions for the optimal sampling ratio based on a common variance…

Real numbers from the interval [0, 1] are randomly selected with uniform distribution. There are $n$ of them and they are revealed one by one. However, we do not know their values but only their relative ranks. We want to stop on recently…

In this paper I address the practical concern of predicting how much training data is sufficient for a statistical language learning system. First, I briefly review earlier results and show how these can be combined to bound the expected…

Effective methodologies for evaluating recommender systems are critical, so that such systems can be compared in a sound manner. A commonly overlooked aspect of recommender system evaluation is the selection of the data splitting strategy.…

Selective prediction, where a model has the option to abstain from making a decision, is crucial for machine learning applications in which mistakes are costly. In this work, we focus on distributional regression and introduce a framework…

Data selection can reduce the amount of training data needed to finetune LLMs; however, the efficacy of data selection scales directly with its compute. Motivated by the practical challenge of compute-constrained finetuning, we consider the…

The decision to incorporate cross-validation into validation processes of mathematical models raises an immediate question - how should one partition the data into calibration and validation sets? We answer this question systematically: we…

Disparate treatment occurs when a machine learning model yields different decisions for individuals based on a sensitive attribute (e.g., age, sex). In domains where prediction accuracy is paramount, it could potentially be acceptable to…

In real-world classification problems, the class balance in the training dataset does not necessarily reflect that of the test dataset, which can cause significant estimation bias. If the class ratio of the test dataset is known, instance…

Neural networks have become standard tools in many areas, yet many important statistical questions remain open. This paper studies the question of how much data are needed to train a ReLU feed-forward neural network. Our theoretical and…