Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence

نویسندگان

  • Nihar B. Shah
  • Sivaraman Balakrishnan
  • Joseph K. Bradley
  • Abhay Parekh
  • Kannan Ramchandran
  • Martin J. Wainwright
چکیده

Nihar B. Shah† [email protected] Sivaraman Balakrishnan# [email protected] Joseph Bradley† [email protected] Abhay Parekh† [email protected] Kannan Ramchandran† [email protected] Martin J. Wainwright† ? [email protected] † Department of Electrical Engineering and Computer Sciences ? Department of Statistics, University of California, Berkeley Berkeley, CA-94720, USA

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Optimal estimation of low rank density matrices

The density matrices are positively semi-definite Hermitian matrices of unit trace that describe the state of a quantum system. The goal of the paper is to develop minimax lower bounds on error rates of estimation of low rank density matrices in trace regression models used in quantum state tomography (in particular, in the case of Pauli measurements) with explicit dependence of the bounds on t...

متن کامل

On Estimation of L{r}-Norms in Gaussian White Noise Models

We provide a complete picture of asymptotically minimax estimation of Lr-norms (for any r ≥ 1) of the mean in Gaussian white noise model over Nikolskii-Besov spaces. In this regard, we complement the work of Lepski, Nemirovski and Spokoiny (1999), who considered the cases of r = 1 (with poly-logarithmic gap between upper and lower bounds) and r even (with asymptotically sharp upper and lower bo...

متن کامل

Local Privacy and Minimax Bounds: Sharp Rates for Probability Estimation

We provide a detailed study of the estimation of probability distributions— discrete and continuous—in a stringent setting in which data is kept private even from the statistician. We give sharp minimax rates of convergence for estimation in these locally private settings, exhibiting fundamental trade-offs between privacy and convergence rate, as well as providing tools to allow movement along ...

متن کامل

Accuracy Assessment for High - Dimensional Linear Regression

This paper considers point and interval estimation of the lq loss of an estimator in high-dimensional linear regression with random design. We establish the minimax rate for estimating the lq loss and the minimax expected length of confidence intervals for the lq loss of rate-optimal estimators of the regression vector, including commonly used estimators such as Lasso, scaled Lasso, square-root...

متن کامل

Minimax-optimal Inference from Partial Rankings

This paper studies the problem of rank aggregation under the Plackett-Luce model. The goal is to infer a global ranking and related scores of the items, based on partial rankings provided by multiple users over multiple subsets of items. A question of particular interest is how to optimally assign items to users for ranking and how many item assignments are needed to achieve a target estimation...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Journal of Machine Learning Research

دوره 17  شماره 

صفحات  -

تاریخ انتشار 2015