Despite the numerous generalization upper bounds that have been proved over the last two decades, nothing is known about the tightness of these bounds.

A particularly problematic form of distribution shift comes from embedded power structures in data collection.

Boosting is one of the most successful ideas in machine learning.

With the recent rise of generative Artificial Intelligence (AI), the need of selecting high-quality dataset to improve machine learning models has garnered increasing attention. However, some part of this topic remains underexplored, even for simple prediction models. In this work, we study the problem of developing practical algorithms that select appropriate dataset to minimize population loss of our prediction model with high probability. Broadly speaking, we investigate when datasets from different sources can be effectively merged to enhance the predictive model's performance, and propose a practical algorithm with theoretical guarantees. By leveraging an oracle inequality and data-driven estimators, the algorithm reduces population loss with high probability. Numerical experiments demonstrate its effectiveness in both standard linear regression and broader machine learning applications. Code is available at https://github.com/kkrokii/collaborative_prediction.

In many practical machine learning problems, the acquisition of labeled data is often expensive and/or time consuming. This motivates us to study a problem as follows: given a label budget, how to select data points to label such that the learning performance is optimized. We propose a selective labeling method by analyzing the out-of-sample error of Laplacian regularized Least Squares (LapRLS). In particular, we derive a deterministic out-of-sample error bound for LapRLS trained on subsampled data, and propose to select a subset of data points to label by minimizing this upper bound. Since the minimization is a combinational problem, we relax it into continuous domain and solve it by projected gradient descent. Experiments on benchmark datasets show that the proposed method outperforms the state-of-the-art methods.

In many practical machine learning problems, the acquisition of labeled data is often expensive and/or time consuming. This motivates us to study a problem as follows: given a label budget, how to select data points to label such that the learning performance is optimized. We propose a selective labeling method by analyzing the out-of-sample error of Laplacian regularized Least Squares (LapRLS). In particular, we derive a deterministic out-of-sample error bound for LapRLS trained on subsampled data, and propose to select a subset of data points to label by minimizing this upper bound. Since the minimization is a combinational problem, we relax it into continuous domain and solve it by projected gradient descent. Experiments on benchmark datasets show that the proposed method outperforms the state-of-the-art methods.

This paper investigates the asymptotic distribution of the K-fold cross validation error in an i.i.d. setting. As the number of observations n goes to infinity while keeping the number of folds K fixed, the K-fold cross validation error is √ n-consistent for the expected out-of-sample error and has an asymptotically normal distribution. A consistent estimate of the asymptotic variance is derived and used to construct asymptotically valid confidence intervals for the expected out-of-sample error. A hypothesis test is developed for comparing two estimators’ expected out-of-sample errors and a subsampling procedure is used to obtain critical values. Monte Carlo simulations demonstrate the asymptotic validity of our confidence intervals for the expected out-of-sample error and investigate the size and power properties of our test. In our empirical application, we use our estimator selection test to compare the out-of-sample predictive performance of OLS, Neural Networks, and Random Forests for predicting the sale price of a domain name in a GoDaddy expiry auction.

The ultimate goal in machine learning is to construct a model function that has a generalization capability for unseen dataset, based on given training dataset. If the model function has too much expressibility power, then it may overfit to the training data and as a result lose the generalization capability. To avoid such overfitting issue, several techniques have been developed in the classical machine learning regime, and the dropout is one such effective method. This paper proposes a straightforward analogue of this technique in the quantum machine learning regime, the entangling dropout, meaning that some entangling gates in a given parametrized quantum circuit are randomly removed during the training process to reduce the expressibility of the circuit. Some simple case studies are given to show that this technique actually suppresses the overfitting.

The Department of Defense (DoD) has significantly increased its investment in the design, evaluation, and deployment of Artificial Intelligence and Machine Learning (AI/ML) capabilities to address national security needs [1, 2]. While there are numerous AI/ML successes in the academic and commercial sectors, many of these systems have also been shown to be brittle and nonrobust [3]. In a complex and ever-changing national security environment, it is vital that the DoD establish a sound and methodical process to evaluate the performance and robustness of AI/ML models before these new capabilities are deployed to the field [4]. Without an effective evaluation process, the DoD may deploy AI/ML models that are assumed to be effective given limited evaluation metrics but actually have poor performance and robustness on operational data. Poor evaluation practices lead to loss of trust in AI/ML systems by model operators and more frequent--often costly--design updates needed to address the evolving security environment. In contrast, an effective evaluation process can drive the design of more resilient capabilities, flag potential limitations of models before they are deployed, and build operator trust in AI/ML systems. This paper reviews the AI/ML development process, highlights common best practices for AI/ML model evaluation, and makes the following recommendations to DoD evaluators to ensure the deployment of robust AI/ML capabilities for national security needs: - Develop testing datasets with sufficient variation and number of samples to effectively measure the expected performance of the AI/ML model on future (unseen) data once deployed, - Maintain separation between data used for design and evaluation (i.e., the test data is not used to design the AI/ML model or train its parameters) in order to ensure an honest and unbiased assessment of the model's capability, - Evaluate performance given small perturbations and corruptions to data inputs to assess the smoothness of the AI/ML model and identify potential vulnerabilities, and - Evaluate performance on samples from data distributions that are shifted from the assumed distribution that was used to design the AI/ML model to assess how the model may perform on operational data that may differ from the training data. By following the recommendations for evaluation presented in this paper, the DoD can fully take advantage of the AI/ML revolution, delivering robust capabilities that maintain operational feasibility over longer periods of time, and increase warfighter confidence in AI/ML systems.

Support Vector Machines (SVMs) are among the most fundamental tools for binary classification. In its simplest formulation, an SVM produces a hyperplane separating two classes of data using the largest possible margin to the data. The focus on maximizing the margin has been well motivated through numerous generalization bounds. In this paper, we revisit and improve the classic generalization bounds in terms of margins. Furthermore, we complement our new generalization bound by a nearly matching lower bound, thus almost settling the generalization performance of SVMs in terms of margins.