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Concept

Nonlinear dimensionality reduction

Related publications (31)

A structured prediction approach for robot imitation learning

Aude Billard, Iason Batzianoulis

We propose a structured prediction approach for robot imitation learning from demonstrations. Among various tools for robot imitation learning, supervised learning has been observed to have a prominent role. Structured prediction is a form of supervised le ...

Sage Publications Ltd2023

Dimensionality reduction of time-series data, and systems and devices that use the resultant embeddings

Mackenzie Mathis, Steffen Schneider

Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for dimensionality reduction of time-series using contrastive learning. A method can include receiving multidimensional input time series data that includes ...

2023

Automatic Parameterization for Aerodynamic Shape Optimization via Deep Geometric Learning

Pascal Fua, Zhen Wei

We propose two deep learning models that fully automate shape parameterization for aerodynamic shape optimization. Both models are optimized to parameterize via deep geometric learning to embed human prior knowledge into learned geometric patterns, elimina ...

2023

Stochastic adaptive resampling for the estimation of discrete choice models

Michel Bierlaire, Matthieu Marie Cochon de Lapparent, Nicola Marco Ortelli

In the field of choice modeling, the availability of ever-larger datasets has the potential to significantly expand our understanding of human behavior, but this prospect is limited by the poor scalability of discrete choice models (DCMs): as sample sizes ...

2023

Localized model order reduction and domain decomposition methods for coupled heterogeneous systems

Jan Sickmann Hesthaven, Niccolo' Discacciati

We propose a model order reduction technique to accurately approximate the behavior of multi-component systems without any a-priori knowledge of the coupled model. In the offline phase, we construct independent surrogate models by solving the local problem ...

Wiley2023

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Axel Elie Joseph Séguin

The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

EPFL2023

Benign Overfitting in Deep Neural Networks under Lazy Training

Volkan Cevher, Grigorios Chrysos, Fanghui Liu, Zhenyu Zhu

This paper focuses on over-parameterized deep neural networks (DNNs) with ReLU activation functions and proves that when the data distribution is well-separated, DNNs can achieve Bayesoptimal test error for classification while obtaining (nearly) zero-trai ...

2023

Learning curves for the multi-class teacher-student perceptron

Lenka Zdeborová, Bruno Loureiro, Elisabetta Cornacchia, Rodrigo Soares Veiga

One of the most classical results in high-dimensional learning theory provides a closed-form expression for the generalisation error of binary classification with a single-layer teacher-student perceptron on i.i.d. Gaussian inputs. Both Bayes-optimal (BO) ...

IOP Publishing Ltd2023

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

Aggregation and Exploration of High-Dimensional Data Using the Sudokube Data Cube Engine

Christoph Koch, Sachin Basil John, Peter Lindner, Zhekai Jiang

We present Sudokube, a novel system that supports interactive speed querying on high-dimensional data using partially materialized data cubes. Given a storage budget, it judiciously chooses what projections to precompute and materialize during cube constru ...

Association for Computing Machinery2023

Deep Learning Meets Sparse Regularization

Rahul Parhi

Deep learning (DL) has been wildly successful in practice, and most of the state-of-the-art machine learning methods are based on neural networks (NNs). Lacking, however, is a rigorous mathematical theory that adequately explains the amazing performance of ...

2023