Concept

High-dimensional statistics

Related publications (31)

Hybrid regularisation and the (in)admissibility of ridge regression in infinite dimensional Hilbert spaces

We consider the problem of estimating the slope function in a functional regression with a scalar response and a functional covariate. This central problem of functional data analysis is well known to be ill-posed, thus requiring a regularised estimation p ...

2019

Crosslingual Document Embedding as Reduced-Rank Ridge Regression

Martin Jaggi, Robert West, Martin Josifoski

There has recently been much interest in extending vector-based word representations to multiple languages, such that words can be compared across languages. In this paper, we shift the focus from words to documents and introduce a method for embedding doc ...

2019

Efficient Multi-dimensional Diracs Estimation with Linear Sample Complexity

Martin Vetterli, Thierry Blu, Hanjie Pan

Estimating Diracs in continuous two or higher dimensions is a fundamental problem in imaging. Previous approaches extended one dimensional methods, like the ones based on finite rate of innovation (FRI) sampling, in a separable manner, e.g., along the hori ...

2018

Methodology And Convergence Rates For Functional Time Series Regression

Victor Panaretos, Tung Huy Pham

The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite-dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose inverse is by defi ...

STATISTICA SINICA2018

Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces

Volkan Cevher, Junhong Lin

In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms, including ridge regressi ...

2020

Dimensionally Tight Bounds for Second-Order Hamiltonian Monte Carlo

Nisheeth Vishnoi, Oren Rami Mangoubi

Hamiltonian Monte Carlo (HMC) is a widely deployed method to sample from high-dimensional distributions in Statistics and Machine learning. HMC is known to run very efficiently in practice and its popular second-order "leapfrog" implementation has long bee ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

Mapping and characterization of positive and negative BOLD responses to visual stimulation in multiple brain regions at 7T

Rolf Gruetter, Wietske Van der Zwaag, Patricia Figueiredo, João Pedro Forjaco Jorge

External stimuli and tasks often elicit negative BOLD responses in various brain regions, and growing experimental evidence supports that these phenomena are functionally meaningful. In this work, the high sensitivity available at 7T was explored to map an ...

Wiley2018

Scalable Low-rank Matrix and Tensor Decomposition on Graphs

Nauman Shahid

In many signal processing, machine learning and computer vision applications, one often has to deal with high dimensional and big datasets such as images, videos, web content, etc. The data can come in various forms, such as univariate or multivariate time ...

EPFL2017

Efficient inference for genetic association studies with multiple outcomes

Anthony Christopher Davison, Jörg Hager, Hélène Ruffieux

Combined inference for heterogeneous high-dimensional data is critical in modern biology, where clinical and various kinds of molecular data may be available from a single study. Classical genetic association studies regress a single clinical outcome on ma ...

Oxford University Press2017

Structured Dimensionality Reduction for Additive Model Regression

Pascal Frossard, Alhussein Fawzi

Additive models are regression methods which model the response variable as the sum of univariate transfer functions of the input variables. Key benefits of additive models are their accuracy and interpretability on many real-world tasks. Additive models a ...

Institute of Electrical and Electronics Engineers2016

Efficient Statistical Parameter Selection for Nonlinear Modeling of Process/Performance Variation

Giovanni De Micheli, Pierre-Emmanuel Julien Marc Gaillardon, Hassan Ghasemzadeh Mohammadi

With the growing number of process variation sources in deeply nano-scaled technologies, parameterized device and circuit modeling is becoming very important for chip design and verification. However, the high dimensionality of parameter space, for process ...

Ieee-Inst Electrical Electronics Engineers Inc2016