相关论文: Training-Free Certified Bounds for Quantum Regress…

Quantum learning encounters fundamental challenges when estimating non-linear properties, owing to the inherent linearity of quantum mechanics. Although recent advances in single-copy randomized measurement protocols have achieved optimal…

This paper presents a new perspective on the identification at infinity for the intercept of the sample selection model as identification at the boundary via a transformation of the selection index. This perspective suggests generalizations…

A novel framework is introduced to formalize identifiability in well-specified but ill-posed linear regression models. The framework is distribution-free and accommodates highly correlated features that may or may not relate to the…

While quantum weight enumerators establish some of the best upper bounds on the minimum distance of quantum error-correcting codes, these bounds are not optimized to quantify the performance of quantum codes under the effect of arbitrary…

Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum error-correcting code. Physical noise sources are efficiently approximated by random insertions of Pauli operators. For a single qubit,…

This paper studies quantile regression with an endogenous regressor and measurement error in the dependent variable. Standard quantile regression estimators ignoring these two elements can induce substantial bias. We adopt a…

The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…

We formulate the first differentiable analog quantum computing framework with a specific parameterization design at the analog signal (pulse) level to better exploit near-term quantum devices via variational methods. We further propose a…

As with classical neural networks, quantum machine learning (QML) models are vulnerable to small input perturbations that can significantly alter output predictions. Certifying the robustness of QML models, particularly on NISQ hardware, is…

In scientific machine learning, regression networks have been recently applied to approximate solution maps (e.g., potential-ground state map of Schr\"odinger equation). In this paper, we aim to reduce the generalization error without…

We consider the task of privately obtaining prediction error guarantees in ordinary least-squares regression problems with Gaussian covariates (with unknown covariance structure). We provide the first sample-optimal polynomial time…

Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…

Expectile regression is a useful tool for exploring the relation between the response and the explanatory variables beyond the conditional mean. This article develops a continuous threshold expectile regression for modeling data in which…

The recent advances in machine learning hold great promise for the fields of quantum sensing and metrology. With the help of reinforcement learning, we can tame the complexity of quantum systems and solve the problem of optimal experimental…

We establish optimal Statistical Query (SQ) lower bounds for robustly learning certain families of discrete high-dimensional distributions. In particular, we show that no efficient SQ algorithm with access to an $\epsilon$-corrupted binary…

We consider a univariate semimartingale model for (the logarithm of) an asset price, containing jumps having possibly infinite activity (IA). The nonparametric threshold estimator of the integrated variance IV proposed in Mancini 2009 is…

Consider a regression problem where there is no labeled data and the only observations are the predictions $f_i(x_j)$ of $m$ experts $f_{i}$ over many samples $x_j$. With no knowledge on the accuracy of the experts, is it still possible to…

The random feature (RF) approach is a well-established and efficient tool for scalable kernel methods, but existing literature has primarily focused on kernel ridge regression with random features (KRR-RF), which has limitations in handling…

The design and optimization of realistic architectures for fault-tolerant quantum computation requires error models that are both reliable and amenable to large-scale classical simulation. Perhaps the simplest and most practical…

We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This…