4 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…
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…
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…