161 research outputs found
A companion for the Kiefer--Wolfowitz--Blum stochastic approximation algorithm
A stochastic algorithm for the recursive approximation of the location
of a maximum of a regression function was introduced by Kiefer and
Wolfowitz [Ann. Math. Statist. 23 (1952) 462--466] in the univariate framework,
and by Blum [Ann. Math. Statist. 25 (1954) 737--744] in the multivariate case.
The aim of this paper is to provide a companion algorithm to the
Kiefer--Wolfowitz--Blum algorithm, which allows one to simultaneously
recursively approximate the size of the maximum of the regression
function. A precise study of the joint weak convergence rate of both algorithms
is given; it turns out that, unlike the location of the maximum, the size of
the maximum can be approximated by an algorithm which converges at the
parametric rate. Moreover, averaging leads to an asymptotically efficient
algorithm for the approximation of the couple .Comment: Published in at http://dx.doi.org/10.1214/009053606000001451 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Estimation of the parameters of sampled-data systems by stochastic approximation
Parameter estimation of sampled data control systems by stochastic approximatio
Stochastic Approximation and Modern Model-Based Designs for Dose-Finding Clinical Trials
In 1951 Robbins and Monro published the seminal article on stochastic
approximation and made a specific reference to its application to the
"estimation of a quantal using response, nonresponse data." Since the 1990s,
statistical methodology for dose-finding studies has grown into an active area
of research. The dose-finding problem is at its core a percentile estimation
problem and is in line with what the Robbins--Monro method sets out to solve.
In this light, it is quite surprising that the dose-finding literature has
developed rather independently of the older stochastic approximation
literature. The fact that stochastic approximation has seldom been used in
actual clinical studies stands in stark contrast with its constant application
in engineering and finance. In this article, I explore similarities and
differences between the dose-finding and the stochastic approximation
literatures. This review also sheds light on the present and future relevance
of stochastic approximation to dose-finding clinical trials. Such connections
will in turn steer dose-finding methodology on a rigorous course and extend its
ability to handle increasingly complex clinical situations.Comment: Published in at http://dx.doi.org/10.1214/10-STS334 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
A control algorithm for autonomous optimization of extracellular recordings
This paper develops a control algorithm that can autonomously position an electrode so as to find and then maintain an optimal extracellular recording position. The algorithm was developed and tested in a two-neuron computational model representative of the cells found in cerebral cortex. The algorithm is based on a stochastic optimization of a suitably defined signal quality metric and is shown capable of finding the optimal recording position along representative sampling directions, as well as maintaining the optimal signal quality in the face of modeled tissue movements. The application of the algorithm to acute neurophysiological recording experiments and its potential implications to chronic recording electrode arrays are discussed
On the Determination of the Step Size in Stochastic Quasigradient Methods
For algorithms of the Robbins-Monro type, the best choice (from the asymptotic point of view) for the step-size constants a_n is known to be a/n. From the practical point of view, however, adaptive step-size rules seem more likely to produce quick convergence. In this paper a new adaptive rule for controlling the stepsize is presented and its behavior is studied
Estimating the minimizer and the minimum value of a regression function under passive design
We propose a new method for estimating the minimizer and
the minimum value of a smooth and strongly convex regression function
from the observations contaminated by random noise. Our estimator
of the minimizer is based on a version of
the projected gradient descent with the gradient estimated by a regularized
local polynomial algorithm. Next, we propose a two-stage procedure for
estimation of the minimum value of regression function . At the first
stage, we construct an accurate enough estimator of , which
can be, for example, . At the second stage, we estimate the
function value at the point obtained in the first stage using a rate optimal
nonparametric procedure. We derive non-asymptotic upper bounds for the
quadratic risk and optimization error of , and for the risk
of estimating . We establish minimax lower bounds showing that, under
certain choice of parameters, the proposed algorithms achieve the minimax
optimal rates of convergence on the class of smooth and strongly convex
functions.Comment: 35 page
Event-triggered Learning
The efficient exchange of information is an essential aspect of intelligent
collective behavior. Event-triggered control and estimation achieve some
efficiency by replacing continuous data exchange between agents with
intermittent, or event-triggered communication. Typically, model-based
predictions are used at times of no data transmission, and updates are sent
only when the prediction error grows too large. The effectiveness in reducing
communication thus strongly depends on the quality of the prediction model. In
this article, we propose event-triggered learning as a novel concept to reduce
communication even further and to also adapt to changing dynamics. By
monitoring the actual communication rate and comparing it to the one that is
induced by the model, we detect a mismatch between model and reality and
trigger model learning when needed. Specifically, for linear Gaussian dynamics,
we derive different classes of learning triggers solely based on a statistical
analysis of inter-communication times and formally prove their effectiveness
with the aid of concentration inequalities
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