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publications
Alternating Least Squares in Generalized Linear Models
Published in Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 2019
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Excess-Risk Consistency of Group-hard Thresholding Estimator in Robust Estimation of Gaussian Mean
Published in Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 2020
This paper proves that using properly chosen threshold for group-hard thresholding estimator yields the optimal constant in front of parametric rate ($p/n$) in the risk bound for the expected error between the true mean value of Gaussian distribution and our estimator.
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All-in-one Robust Estimator for the Gaussian Mean
Published in Annals of Statistics (to appear), 2021
This paper presents a new robust estimator called Iteratively Re-weighted Mean (IRM) which enjoys 5 key properties desired for a robust estimator: computationally tractable, equivariant under similarity transformations, have a breakdown point around $0.28$, minimax optimal (up to logarithmic factor) and asymptotically efficient. IRM is obtained by an iterative reweighting approach assigning weights by solving a convex optimization problem (SDP). Dimension-free non-asymptotic risk bound for the expected error of the proposed estimator is proved. The results are extended for sub-Gaussian distributions, as well as for unknown contamination level or unknown covariance matrix. Joint work with A. S. Dalalyan.
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Optimal detection of the feature matching map in presence of noise and outliers
Published in Electronic Journal of Statistics (submitted), 2021
We consider the problem of finding the matching map between two sets of $d$ dimensional vectors from noisy observations, where the second set contains outliers. The main result shows that, in the high-dimensional setting, a detection region of unknown injection can be characterized by the sets of vectors for which the inlier-inlier distance is of order at least $d^{1/4}$ and the inlier-outlier distance is of order at least $d^{1/2}$. These rates are achieved using the estimated matching minimizing the sum of logarithms of distances between matched pairs of points. We also prove lower bounds establishing optimality of these rates. Joint work with T. Galstyan and A. S. Dalalyan.
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talks
Talk 1 on Relevant Topic in Your Field
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Conference Proceeding talk 3 on Relevant Topic in Your Field
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teaching
Teaching experience 1
Undergraduate course, University 1, Department, 2014
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Teaching experience 2
Workshop, University 1, Department, 2015
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