Filters

2016 - 20204

More filters

2019 - 201912020 - 20223
Reset filters

Settings

Author: Avanesov, Valeriy × DDC: 510 ×

Search Results

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    Data-driven confidence bands for distributed nonparametric regression
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Avanesov, Valeriy
    Gaussian Process Regression and Kernel Ridge Regression are popular nonparametric regression approaches. Unfortunately, they suffer from high computational complexity rendering them inapplicable to the modern massive datasets. To that end a number of approximations have been suggested, some of them allowing for a distributed implementation. One of them is the divide and conquer approach, splitting the data into a number of partitions, obtaining the local estimates and finally averaging them. In this paper we suggest a novel computationally efficient fully data-driven algorithm, quantifying uncertainty of this method, yielding frequentist $L_2$-confidence bands. We rigorously demonstrate validity of the algorithm. Another contribution of the paper is a minimax-optimal high-probability bound for the averaged estimator, complementing and generalizing the known risk bounds.
  • Thumbnail Image
    Item
    Nonparametric change point detection in regression
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Avanesov, Valeriy
    This paper considers the prominent problem of change-point detection in regression. The study suggests a novel testing procedure featuring a fully data-driven calibration scheme. The method is essentially a black box, requiring no tuning from the practitioner. The approach is investigated from both theoretical and practical points of view. The theoretical study demonstrates proper control of first-type error rate under H0 and power approaching 1 under H1. The experiments conducted on synthetic data fully support the theoretical claims. In conclusion, the method is applied to financial data, where it detects sensible change-points. Techniques for change-point localization are also suggested and investigated
  • Thumbnail Image
    Item
    How to gamble with non-stationary X-armed bandits and have no regrets
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Avanesov, Valeriy
    In X-armed bandit problem an agent sequentially interacts with environment which yields a reward based on the vector input the agent provides. The agent's goal is to maximise the sum of these rewards across some number of time steps. The problem and its variations have been a subject of numerous studies, suggesting sub-linear and sometimes optimal strategies. The given paper introduces a new variation of the problem. We consider an environment, which can abruptly change its behaviour an unknown number of times. To that end we propose a novel strategy and prove it attains sub-linear cumulative regret. Moreover, the obtained regret bound matches the best known bound for GP-UCB for a stationary case, and approaches the minimax lower bound in case of highly smooth relation between an action and the corresponding reward. The theoretical result is supported by experimental study.
  • Thumbnail Image
    Item
    Consistency results and confidence intervals for adaptive l1-penalized estimators of the high-dimensional sparse precision matrix
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Avanesov, Valeriy; Polzehl, Jörg; Tabelow, Karsten
    In this paper we consider the adaptive '1-penalized estimators for the precision matrix in a finite-sample setting. We show consistency results and construct confidence intervals for the elements of the true precision matrix. Additionally, we analyze the bias of these confidence intervals. We apply the estimator to the estimation of functional connectivity networks in functional Magnetic Resonance data and elaborate the theoretical results in extensive simulation experiments.