Related papers: $L_2$-Regularized Empirical Risk Minimization Guar…
It is well known that Empirical Risk Minimization (ERM) may attain minimax suboptimal rates in terms of the mean squared error (Birg\'e and Massart, 1993). In this paper, we prove that, under relatively mild assumptions, the suboptimality…
Calibration is a fundamental concept that aims at ensuring the reliability of probabilistic predictions by aligning them with real-world outcomes. There is a surge of studies on new calibration measures that are easier to optimize compared…
Machine learning models have exhibited exceptional results in various domains. The most prevalent approach for learning is the empirical risk minimizer (ERM), which adapts the model's weights to reduce the loss on a training set and…
This paper investigates robust versions of the general empirical risk minimization algorithm, one of the core techniques underlying modern statistical methods. Success of the empirical risk minimization is based on the fact that for a…
Obtaining guarantees on the convergence of the minimizers of empirical risks to the ones of the true risk is a fundamental matter in statistical learning. Instead of deriving guarantees on the usual estimation error, the goal of this paper…
Recalibrating probabilistic classifiers is vital for enhancing the reliability and accuracy of predictive models. Despite the development of numerous recalibration algorithms, there is still a lack of a comprehensive theory that integrates…
In this paper, we study extended linear regression approaches for quantum state tomography based on regularization techniques. For unknown quantum states represented by density matrices, performing measurements under certain basis yields…
Randomized smoothing is a recently proposed defense against adversarial attacks that has achieved SOTA provable robustness against $\ell_2$ perturbations. A number of publications have extended the guarantees to other metrics, such as…
Algorithmic verification of realistic systems to satisfy safety and other temporal requirements has suffered from poor scalability of the employed formal approaches. To design systems with rigorous guarantees, many approaches still rely on…
Error mitigation techniques, while instrumental in extending the capabilities of near-term quantum computers, often suffer from exponential resource scaling with noise levels. To address this limitation, we introduce a novel approach,…
Quantifying the data uncertainty in learning tasks is often done by learning a prediction interval or prediction set of the label given the input. Two commonly desired properties for learned prediction sets are \emph{valid coverage} and…
Empirical risk minimization is the main tool for prediction problems, but its extension to relational data remains unsolved. We solve this problem using recent ideas from graph sampling theory to (i) define an empirical risk for relational…
We present a novel distributionally robust framework for dynamic programming that uses kernel methods to design feedback control policies. Specifically, we leverage kernel mean embedding to map the transition probabilities governing the…
Recently smoothing deep neural network based classifiers via isotropic Gaussian perturbation is shown to be an effective and scalable way to provide state-of-the-art probabilistic robustness guarantee against $\ell_2$ norm bounded…
Confidence calibration of classification models is a technique to estimate the true posterior probability of the predicted class, which is critical for ensuring reliable decision-making in practical applications. Existing confidence…
As large language models (LLMs) are deployed in consequential settings such as medical question answering and legal reasoning, the ability to estimate when their outputs are likely to be correct is essential for safe and reliable use,…
Rates of convergence for empirical risk minimizers have been well studied in the literature. In this paper, we aim to provide a complementary set of results, in particular by showing that after normalization, the risk of the empirical…
Reinforcement Learning (RL) has achieved remarkable success in safety-critical areas, but it can be weakened by adversarial attacks. Recent studies have introduced "smoothed policies" in order to enhance its robustness. Yet, it is still…
Randomized smoothing (RS) is one of the prominent techniques to ensure the correctness of machine learning models, where point-wise robustness certificates can be derived analytically. While RS is well understood for classification, its…
We investigate $L_2$ boosting in the context of kernel regression. Kernel smoothers, in general, lack appealing traits like symmetry and positive definiteness, which are critical not only for understanding theoretical aspects but also for…