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This thesis focuses on developing efficient algorithmic tools for processing large datasets. In many modern data analysis tasks, the sheer volume of available datasets far outstrips our abilities to process them. This scenario commonly arises in tasks incl ...
We establish a sharp estimate on the negative moments of the smallest eigenvalue of the Malliavin matrix gamma z of Z := (u(s, y), u(t , x) - u(s, y)), where u is the solution to a system of d non-linear stochastic heat equations in spatial dimension k >= ...
Kernel methods are fundamental tools in machine learning that allow detection of non-linear dependencies between data without explicitly constructing feature vectors in high dimensional spaces. A major disadvantage of kernel methods is their poor scalabili ...
We present EKLT, a feature tracking method that leverages the complementarity of event cameras and standard cameras to track visual features with high temporal resolution. Event cameras are novel sensors that output pixel-level brightness changes, called “ ...
Maximum-Entropy Distributions offer an attractive family of probability densities suitable for moment closure problems. Yet finding the Lagrange multipliers which parametrize these distributions, turns out to be a computational bottleneck for practical clo ...
Random binning features, introduced in the seminal paper of Rahimi and Recht '07, are an efficient method for approximating a kernel matrix using locality sensitive hashing. Random binning features provide a very simple and efficient way to approximate the ...
In this paper we revisit the kernel density estimation problem: given a kernel K(x, y) and a dataset of n points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query q, a (1 + epsilon)-approximation to mu := ...
Enabling analysis of non-linear systems in linear form, the Koopman operator has been shown to be a powerful tool for system identification and controller design. However, current data-driven methods cannot provide quantification of model uncertainty given ...
The accuracy of monocular 3D human pose estimation depends on the viewpoint from which the image is captured. While freely moving cameras, such as on drones, provide control over this viewpoint, automatically positioning them at the location which will yie ...
We consider the robust linear regression problem in the online setting where we have access to the data in a streaming manner, one data point after the other. More specifically, for a true parameter , we consider the corrupted Gaussian linear model $ y=\la ...