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Ya'acov Ritov

Publications and source records attributed to Ya'acov Ritov.

47 records · Page 3Linked to original sources
arXiv2011

A Random Walk with Drift: Interview with Peter J. Bickel

I met Peter J. Bickel for the first time in 1981. He came to Jerusalem for a year; I had just started working on my Ph.D. studies. Yossi Yahav, who was my advisor at this time, busy as the Dean of Social Sciences, brought us together. Peter became my chief thesis advisor. A year and a half later I came to Berkeley as a post-doc. Since then we have continued to work together. Peter was first my advisor, then a teacher, and now he is also a friend. It is appropriate that this interview took place in two cities. We spoke together first in Jerusalem, at Mishkenot Shaananim and the Center for Research of Rationality, and then at the University of California at Berkeley. These conversations were not formal interviews, but just questions that prompted Peter to tell his story.

stat.ME↗
arXiv2010

Simultaneous analysis of Lasso and Dantzig selector

We exhibit an approximate equivalence between the Lasso estimator and Dantzig selector. For both methods we derive parallel oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the $\ell_p$ estimation loss for $1\le p\le 2$ in the linear model when the number of variables can be much larger than the sample size.

math.ST↗
arXiv2010

The Best Linear Unbiased Estimator for Continuation of a Function

We show how to construct the best linear unbiased predictor (BLUP) for the continuation of a curve in a spline-function model. We assume that the entire curve is drawn from some smooth random process and that the curve is given up to some cut point. We demonstrate how to compute the BLUP efficiently. Confidence bands for the BLUP are discussed. Finally, we apply the proposed BLUP to real-world call center data. Specifically, we forecast the continuation of both the call arrival counts and the workload process at the call center of a commercial bank.

stat.AP↗
arXiv2010

On the trasductive arguments in statistics

The paper argues that a part of the current statistical discussion is not based on the standard firm foundations of the field. Among the examples we consider are prediction into the future, semi-supervised classification, and causality inference based on observational data.

math.ST↗
arXiv2010

Sparse Empirical Bayes Analysis (SEBA)

We consider a joint processing of $n$ independent sparse regression problems. Each is based on a sample $(y_{i1},x_{i1})...,(y_{im},x_{im})$ of $m$ \iid observations from $y_{i1}=x_{i1}\tβ_i+\eps_{i1}$, $y_{i1}\in \R$, $x_{i 1}\in\R^p$, $i=1,...,n$, and $\eps_{i1}\dist N(0,\sig^2)$, say. $p$ is large enough so that the empirical risk minimizer is not consistent. We consider three possible extensions of the lasso estimator to deal with this problem, the lassoes, the group lasso and the RING lasso, each utilizing a different assumption how these problems are related. For each estimator we give a Bayesian interpretation, and we present both persistency analysis and non-asymptotic error bounds based on restricted eigenvalue - type assumptions.

stat.ML↗
arXiv2008

LLE with low-dimensional neighborhood representation

The local linear embedding algorithm (LLE) is a non-linear dimension-reducing technique, widely used due to its computational simplicity and intuitive approach. LLE first linearly reconstructs each input point from its nearest neighbors and then preserves these neighborhood relations in the low-dimensional embedding. We show that the reconstruction weights computed by LLE capture the high-dimensional structure of the neighborhoods, and not the low-dimensional manifold structure. Consequently, the weight vectors are highly sensitive to noise. Moreover, this causes LLE to converge to a linear projection of the input, as opposed to its non-linear embedding goal. To overcome both of these problems, we propose to compute the weight vectors using a low-dimensional neighborhood representation. We prove theoretically that this straightforward and computationally simple modification of LLE reduces LLE's sensitivity to noise. This modification also removes the need for regularization when the number of neighbors is larger than the dimension of the input. We present numerical examples demonstrating both the perturbation and linear projection problems, and the improved outputs using the low-dimensional neighborhood representation.

stat.ML↗
arXiv2008

Asymptotic efficiency of simple decisions for the compound decision problem

We consider the compound decision problem of estimating a vector of $n$ parameters, known up to a permutation, corresponding to $n$ independent observations, and discuss the difference between two symmetric classes of estimators. The first and larger class is restricted to the set of all permutation invariant estimators. The second class is restricted further to simple symmetric procedures. That is, estimators such that each parameter is estimated by a function of the corresponding observation alone. We show that under mild conditions, the minimal total squared error risks over these two classes are asymptotically equivalent up to essentially O(1) difference.

math.ST↗
arXiv2008

Hierarchical selection of variables in sparse high-dimensional regression

We study a regression model with a huge number of interacting variables. We consider a specific approximation of the regression function under two ssumptions: (i) there exists a sparse representation of the regression function in a suggested basis, (ii) there are no interactions outside of the set of the corresponding main effects. We suggest an hierarchical randomized search procedure for selection of variables and of their interactions. We show that given an initial estimator, an estimator with a similar prediction loss but with a smaller number of non-zero coordinates can be found.

math.ST↗
arXiv2006

Tailor-made tests for goodness of fit to semiparametric hypotheses

We introduce a new framework for constructing tests of general semiparametric hypotheses which have nontrivial power on the $n^{-1/2}$ scale in every direction, and can be tailored to put substantial power on alternatives of importance. The approach is based on combining test statistics based on stochastic processes of score statistics with bootstrap critical values.

math.ST↗