相关论文: Optimal SQ Lower Bounds for Robustly Learning Disc…

Quantum key distribution (QKD) could be the most significant application of quantum information theory. In nearly four decades, although substantial QKD protocols are developed, the BB84 protocol and its variants are still the most…

This paper studies the learning-to-control problem under process and sensing uncertainties for dynamical systems. In our previous work, we developed a data-based generalization of the iterative linear quadratic regulator (iLQR) to design…

The stochastic gradient descent (SGD) optimization algorithm plays a central role in a series of machine learning applications. The scientific literature provides a vast amount of upper error bounds for the SGD method. Much less attention…

By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…

In many applications, data is collected in batches, some of which are corrupt or even adversarial. Recent work derived optimal robust algorithms for estimating discrete distributions in this setting. We consider a general framework of…

In this paper optimal designs for regression problems with spherical predictors of arbitrary dimension are considered. Our work is motivated by applications in material sciences, where crystallographic textures such as the missorientation…

We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula…

We study structured convex optimization problems, with additive objective $r:=p + q$, where $r$ is ($\mu$-strongly) convex, $q$ is $L_q$-smooth and convex, and $p$ is $L_p$-smooth, possibly nonconvex. For such a class of problems, we…

We study the information-theoretic lower bound of the sample complexity of the correct recovery of diffusion network structures. We introduce a discrete-time diffusion model based on the Independent Cascade model for which we obtain a lower…

We consider optimal sensor scheduling with unknown communication channel statistics. We formulate two types of scheduling problems with the communication rate being a soft or hard constraint, respectively. We first present some structural…

Many data mining and statistical machine learning algorithms have been developed to select a subset of covariates to associate with a response variable. Spurious discoveries can easily arise in high-dimensional data analysis due to enormous…

Quantum state learning is a fundamental problem in physics and computer science. As near-term quantum devices are error-prone, it is important to design error-resistant algorithms. Apart from device errors, other unexpected factors could…

This work provides several new insights on the robustness of Kearns' statistical query framework against challenging label-noise models. First, we build on a recent result by \cite{DBLP:journals/corr/abs-2006-04787} that showed noise…

We prove the first superpolynomial lower bounds for learning one-layer neural networks with respect to the Gaussian distribution using gradient descent. We show that any classifier trained using gradient descent with respect to square-loss…

We study the problem of high-dimensional robust linear regression where a learner is given access to $n$ samples from the generative model $Y = \langle X,w^* \rangle + \epsilon$ (with $X \in \mathbb{R}^d$ and $\epsilon$ independent), in…

We propose a novel method for semi-supervised learning (SSL) based on data-driven distributionally robust optimization (DRO) using optimal transport metrics. Our proposed method enhances generalization error by using the unlabeled data to…

The reliability of neural networks is essential for their use in safety-critical applications. Existing approaches generally aim at improving the robustness of neural networks to either real-world distribution shifts (e.g., common…

For a practical quantum key distribution (QKD) system, parameter optimization - the choice of intensities and probabilities of sending them - is a crucial step in gaining optimal performance, especially when one realistically considers…

We study the problem of distributed mean estimation and optimization under communication constraints. We propose a correlated quantization protocol whose leading term in the error guarantee depends on the mean deviation of data points…

In this work, we study the optimal discretization error of stochastic integrals, in the context of the hedging error in a multidimensional It\^{o} model when the discrete rebalancing dates are stopping times. We investigate the convergence,…