15 citations · 19 across the 7 of their papers we have counts for
4 papers · 1 filter
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…
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…
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…