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Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization

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The shear stiffness of headed stud connector is a critical parameter for the calculation of deflection and inter-facial shear force for steel-concrete composite structure. Thus, this study presented a promising data-driven model auto-tuning Deep Forest (AT ...

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Near-Minimax Optimal Estimation With Shallow ReLU Neural Networks

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We study the problem of estimating an unknown function from noisy data using shallow ReLU neural networks. The estimators we study minimize the sum of squared data-fitting errors plus a regularization term proportional to the squared Euclidean norm of the ...

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This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...

EPFL2023

Kernel Methods and Similarity Learning Applied in Computational Chemistry

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Over the last two decades, data-powered machine learning (ML) tools have profoundly transformed numerous scientific fields. In computational chemistry, machine learning applications have permitted faster predictions of chemical properties and provided powe ...

EPFL2022

Multikernel Regression with Sparsity Constraint

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In this paper, we provide a Banach-space formulation of supervised learning with generalized total-variation (gTV) regularization. We identify the class of kernel functions that are admissible in this framework. Then, we propose a variation of supervised l ...

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NrOS: Effective Replication and Sharing in an Operating System

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Writing a correct operating system kernel is notoriously hard. Kernel code requires manual memory management and type-unsafe code and must efficiently handle complex, asynchronous events. In addition, increasing CPU core counts further complicate kernel de ...

USENIX ASSOC2021

Midas: Systematic Kernel TOCTTOU Protection

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Double-fetch bugs are a plague across all major operating system kernels. They occur when data is fetched twice across the user/kernel trust boundary while allowing concurrent modification. Such bugs enable an attacker to illegally access memory, cause den ...

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Deterministic error bounds for kernel-based learning techniques under bounded noise

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We consider the problem of reconstructing a function from a finite set of noise-corrupted samples. Two kernel algorithms are analyzed, namely kernel ridge regression and epsilon-support vector regression. By assuming the ground-truth function belongs to th ...

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Recently, several theories including the replica method made predictions for the generalization error of Kernel Ridge Regression. In some regimes, they predict that the method has a 'spectral bias': decomposing the true function f* on the eigenbasis of the ...

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Convex optimization in sums of Banach spaces

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We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...

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AN l(p) THEORY OF PCA AND SPECTRAL CLUSTERING

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Principal Component Analysis (PCA) is a powerful tool in statistics and machine learning. While existing study of PCA focuses on the recovery of principal components and their associated eigenvalues, there are few precise characterizations of individual pr ...

Institute of Mathematical Statistics2022

What can linearized neural networks actually say about generalization?

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For certain infinitely-wide neural networks, the neural tangent kernel (NTK) theory fully characterizes generalization, but for the networks used in practice, the empirical NTK only provides a rough first-order approximation. Still, a growing body of work ...

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Convergence of adaptive algorithms for constrained weakly convex optimization

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We analyze the adaptive first order algorithm AMSGrad, for solving a constrained stochastic optimization problem with a weakly convex objective. We prove the

\tilde O(t^{-1/2})

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Functional estimation of anisotropic covariance and autocovariance operators on the sphere

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