13,551 research outputs found
Comment: Boosting Algorithms: Regularization, Prediction and Model Fitting
The authors are doing the readers of Statistical Science a true service with
a well-written and up-to-date overview of boosting that originated with the
seminal algorithms of Freund and Schapire. Equally, we are grateful for
high-level software that will permit a larger readership to experiment with, or
simply apply, boosting-inspired model fitting. The authors show us a world of
methodology that illustrates how a fundamental innovation can penetrate every
nook and cranny of statistical thinking and practice. They introduce the reader
to one particular interpretation of boosting and then give a display of its
potential with extensions from classification (where it all started) to least
squares, exponential family models, survival analysis, to base-learners other
than trees such as smoothing splines, to degrees of freedom and regularization,
and to fascinating recent work in model selection. The uninitiated reader will
find that the authors did a nice job of presenting a certain coherent and
useful interpretation of boosting. The other reader, though, who has watched
the business of boosting for a while, may have quibbles with the authors over
details of the historic record and, more importantly, over their optimism about
the current state of theoretical knowledge. In fact, as much as ``the
statistical view'' has proven fruitful, it has also resulted in some ideas
about why boosting works that may be misconceived, and in some recommendations
that may be misguided. [arXiv:0804.2752]Comment: Published in at http://dx.doi.org/10.1214/07-STS242B the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Optimization Methods for Inverse Problems
Optimization plays an important role in solving many inverse problems.
Indeed, the task of inversion often either involves or is fully cast as a
solution of an optimization problem. In this light, the mere non-linear,
non-convex, and large-scale nature of many of these inversions gives rise to
some very challenging optimization problems. The inverse problem community has
long been developing various techniques for solving such optimization tasks.
However, other, seemingly disjoint communities, such as that of machine
learning, have developed, almost in parallel, interesting alternative methods
which might have stayed under the radar of the inverse problem community. In
this survey, we aim to change that. In doing so, we first discuss current
state-of-the-art optimization methods widely used in inverse problems. We then
survey recent related advances in addressing similar challenges in problems
faced by the machine learning community, and discuss their potential advantages
for solving inverse problems. By highlighting the similarities among the
optimization challenges faced by the inverse problem and the machine learning
communities, we hope that this survey can serve as a bridge in bringing
together these two communities and encourage cross fertilization of ideas.Comment: 13 page
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