131 research outputs found
The Cost of Uncertainty in Curing Epidemics
Motivated by the study of controlling (curing) epidemics, we consider the
spread of an SI process on a known graph, where we have a limited budget to use
to transition infected nodes back to the susceptible state (i.e., to cure
nodes). Recent work has demonstrated that under perfect and instantaneous
information (which nodes are/are not infected), the budget required for curing
a graph precisely depends on a combinatorial property called the CutWidth. We
show that this assumption is in fact necessary: even a minor degradation of
perfect information, e.g., a diagnostic test that is 99% accurate, drastically
alters the landscape. Infections that could previously be cured in sublinear
time now may require exponential time, or orderwise larger budget to cure. The
crux of the issue comes down to a tension not present in the full information
case: if a node is suspected (but not certain) to be infected, do we risk
wasting our budget to try to cure an uninfected node, or increase our certainty
by longer observation, at the risk that the infection spreads further? Our
results present fundamental, algorithm-independent bounds that tradeoff budget
required vs. uncertainty.Comment: 35 pages, 3 figure
Robustness and Regularization of Support Vector Machines
We consider regularized support vector machines (SVMs) and show that they are
precisely equivalent to a new robust optimization formulation. We show that
this equivalence of robust optimization and regularization has implications for
both algorithms, and analysis. In terms of algorithms, the equivalence suggests
more general SVM-like algorithms for classification that explicitly build in
protection to noise, and at the same time control overfitting. On the analysis
front, the equivalence of robustness and regularization, provides a robust
optimization interpretation for the success of regularized SVMs. We use the
this new robustness interpretation of SVMs to give a new proof of consistency
of (kernelized) SVMs, thus establishing robustness as the reason regularized
SVMs generalize well
A Convex Formulation for Mixed Regression with Two Components: Minimax Optimal Rates
We consider the mixed regression problem with two components, under
adversarial and stochastic noise. We give a convex optimization formulation
that provably recovers the true solution, and provide upper bounds on the
recovery errors for both arbitrary noise and stochastic noise settings. We also
give matching minimax lower bounds (up to log factors), showing that under
certain assumptions, our algorithm is information-theoretically optimal. Our
results represent the first tractable algorithm guaranteeing successful
recovery with tight bounds on recovery errors and sample complexity.Comment: Added results on minimax lower bounds, which match our upper bounds
on recovery errors up to log factors. Appeared in the Conference on Learning
Theory (COLT), 2014. (JMLR W&CP 35 :560-604, 2014
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