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Concept

Principal component regression

Related publications (28)

Quantifying the Unknown: Data-Driven Approaches and Applications in Energy Systems

Paul Scharnhorst

In light of the challenges posed by climate change and the goals of the Paris Agreement, electricity generation is shifting to a more renewable and decentralized pattern, while the operation of systems like buildings is increasingly electrified. This calls ...

EPFL2024

Bayes-optimal Learning of Deep Random Networks of Extensive-width

Lenka Zdeborová, Florent Gérard Krzakala, Hugo Chao Cui

We consider the problem of learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights. We consider the asymptotic limit where the number of samples, the input dimension and the network width ...

2023

Stable parameterization of continuous and piecewise-linear functions

Michaël Unser, Alexis Marie Frederic Goujon, Joaquim Gonçalves Garcia Barreto Campos

Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the parameter and function s ...

2023

BigNeuron: a resource to benchmark and predict performance of algorithms for automated tracing of neurons in light microscopy datasets

Pascal Fua, Sean Lewis Hill, Jiancheng Yang, Amos Sironi, Jian Yang

BigNeuron is an open community bench-testing platform with the goal of setting open standards for accurate and fast automatic neuron tracing. We gathered a diverse set of image volumes across several species that is representative of the data obtained in m ...

Nature Publishing Group2023

Local Kernel Regression and Neural Network Approaches to the Conformational Landscapes of Oligopeptides

Michele Ceriotti, Anne-Clémence Corminboeuf, Alberto Fabrizio, Benjamin André René Meyer, Raimon Fabregat I De Aguilar-Amat, Edgar Albert Engel, Veronika Juraskova

The application of machine learning to theoretical chemistry has made it possible to combine the accuracy of quantum chemical energetics with the thorough sampling of finite-temperature fluctuations. To reach this goal, a diverse set of methods has been pr ...

2022

Distribution-on-distribution regression via optimal transport maps

Victor Panaretos, Laya Ghodrati

We present a framework for performing regression when both covariate and response are probability distributions on a compact interval. Our regression model is based on the theory of optimal transportation, and links the conditional Frechet mean of the resp ...

OXFORD UNIV PRESS2022

Improving sample and feature selection with principal covariates regression

Michele Ceriotti, Edgar Albert Engel, Benjamin Aaron Helfrecht

Selecting the most relevant features and samples out of a large set of candidates is a task that occurs very often in the context of automated data analysis, where it improves the computational performance and often the transferability of a model. Here we ...

2021

Sparsest piecewise-linear regression of one-dimensional data

Michaël Unser, Julien René Fageot, Thomas Jean Debarre, Quentin Alain Denoyelle

We study the problem of one-dimensional regression of data points with total-variation (TV) regularization (in the sense of measures) on the second derivative, which is known to promote piecewise-linear solutions with few knots. While there are efficient a ...

Elsevier2021

Inkjet-printed polymer composites for the detection of volatile organic compounds

Mohammadmahdi Kiaee

Sensors capable of detecting and classifying volatile organic compounds (VOC) have been gaining more attention by the advent of internet-of-things (IoT) enabled devices and integration of various sensing elements into hand-held and portable devices. The re ...

EPFL2021

Counting People by Estimating People Flows

Pascal Fua, Mathieu Salzmann, Weizhe Liu

Modern methods for counting people in crowded scenes rely on deep networks to estimate people densities in individual images. As such, only very few take advantage of temporal consistency in video sequences, and those that do only impose weak smoothness co ...

2022

Physics-enhanced machine learning with symmetry-adapted and long-range representations

Andrea Grisafi

Theoretical and computational approaches to the study of materials and molecules have, over the last few decades, progressed at an exponential rate. Yet, the possibility of producing numerical predictions that are on par with experimental measurements is t ...

EPFL2021

Effects of eight neuropsychiatric copy number variants on human brain structure

Lester Melie Garcia, Borja Rodriguez Herreros

Many copy number variants (CNVs) confer risk for the same range of neurodevelopmental symptoms and psychiatric conditions including autism and schizophrenia. Yet, to date neuroimaging studies have typically been carried out one mutation at a time, showing ...

SPRINGERNATURE2021

Human-Centered Scene Understanding via Crowd Counting

Weizhe Liu

Human-centered scene understanding is the process of perceiving and analysing a dynamic scene observed through a network of sensors with emphasis on human-related activities. It includes the visual perception of human-related activities from either single ...

EPFL2021

Compact atomic descriptors enable accurate predictions via linear models

Kevin Rossi

We probe the accuracy of linear ridge regression employing a three-body local density representation derived from the atomic cluster expansion. We benchmark the accuracy of this framework in the prediction of formation energies and atomic forces in molecul ...

AIP Publishing2021

Structure-property maps with Kernel principal covariates regression

Michele Ceriotti, Guillaume André Jean Fraux, Benjamin Aaron Helfrecht, Rose Kathleen Cersonsky-Adorf

Data analyses based on linear methods constitute the simplest, most robust, and transparent approaches to the automatic processing of large amounts of data for building supervised or unsupervised machine learning models. Principal covariates regression (PC ...

2020

Optimal Convergence for Distributed Learning with Stochastic Gradient Methods and Spectral Algorithms

Volkan Cevher, Junhong Lin

We study generalization properties of distributed algorithms in the setting of nonparametric regression over a reproducing kernel Hilbert space (RKHS). We first investigate distributed stochastic gradient methods (SGM), with mini-batches and multi-passes o ...

2020

A non-intrusive multifidelity method for the reduced order modeling of nonlinear problems

Jan Sickmann Hesthaven, Mengwu Guo, Mariella Kast

We propose a non-intrusive reduced basis (RB) method for parametrized nonlinear partial differential equations (PDEs) that leverages models of different accuracy. From a collection of low-fidelity (LF) snapshots, parameter locations are extracted for the e ...

ELSEVIER SCIENCE SA2020

Functional lagged regression with sparse noisy observations

Victor Panaretos, Tomas Rubin

A functional (lagged) time series regression model involves the regression of scalar response time series on a time series of regressors that consists of a sequence of random functions. In practice, the underlying regressor curve time series are not always ...

WILEY2020

Generalization error in high-dimensional perceptrons: Approaching Bayes error with convex optimization

Lenka Zdeborová, Florent Gérard Krzakala

We consider a commonly studied supervised classification of a synthetic dataset whose labels are generated by feeding a one-layer non-linear neural network with random iid inputs. We study the generalization performances of standard classifiers in the high ...

Curran Associates, Inc.2020

Scaling up Kernel Ridge Regression via Locality Sensitive Hashing

Mikhail Kapralov, Amir Zandieh, Navid Nouri, Ameya Velingker

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 ...

ADDISON-WESLEY PUBL CO2020