15 citations · 19 across the 7 of their papers we have counts for
7 papers
Dimension-free Bounds for Covariance Estimation with Tensor-Train Structure
Artsiom Patarusau, Nikita Puchkin, Maxim Rakhuba +1
We consider a problem of covariance estimation from a sample of i.i.d. high-dimensional random vectors. To avoid the curse of dimensionality, we impose an additional assumption on…
Dimension-free bounds in high-dimensional linear regression via error-in-operator approach
Fedor Noskov, Nikita Puchkin, Vladimir Spokoiny
We consider a problem of high-dimensional linear regression with random design. We suggest a novel approach referred to as error-in-operator which does not estimate the design cova…
Sharper dimension-free bounds on the Frobenius distance between sample covariance and its expectation
Nikita Puchkin, Fedor Noskov, Vladimir Spokoiny
We study properties of a sample covariance estimate given a finite sample of i.i.d. centered random elements in with the covariance matrix . We derive di…
Manifold-based time series forecasting
Nikita Puchkin, Aleksandr Timofeev, Vladimir Spokoiny
Prediction for high dimensional time series is a challenging task due to the curse of dimensionality problem. Classical parametric models like ARIMA or VAR require strong modeling…
Reconstruction of manifold embeddings into Euclidean spaces via intrinsic distances
Nikita Puchkin, Vladimir Spokoiny, Eugene Stepanov +1
We consider the problem of reconstructing an embedding of a compact connected Riemannian manifold in a Euclidean space up to an almost isometry, given the information on intrinsic…
Structure-adaptive manifold estimation
Nikita Puchkin, Vladimir Spokoiny
We consider a problem of manifold estimation from noisy observations. Many manifold learning procedures locally approximate a manifold by a weighted average over a small neighborho…
An adaptive multiclass nearest neighbor classifier
Nikita Puchkin, Vladimir Spokoiny
We consider a problem of multiclass classification, where the training sample is generated from the model , $1 \le…