387 research outputs found
Performance guarantees for greedy maximization of non-submodular controllability metrics
A key problem in emerging complex cyber-physical networks is the design of
information and control topologies, including sensor and actuator selection and
communication network design. These problems can be posed as combinatorial set
function optimization problems to maximize a dynamic performance metric for the
network. Some systems and control metrics feature a property called
submodularity, which allows simple greedy algorithms to obtain provably
near-optimal topology designs. However, many important metrics lack
submodularity and therefore lack provable guarantees for using a greedy
optimization approach. Here we show that performance guarantees can be obtained
for greedy maximization of certain non-submodular functions of the
controllability and observability Gramians. Our results are based on two key
quantities: the submodularity ratio, which quantifies how far a set function is
from being submodular, and the curvature, which quantifies how far a set
function is from being supermodular
Efficient Data Representation by Selecting Prototypes with Importance Weights
Prototypical examples that best summarizes and compactly represents an
underlying complex data distribution communicate meaningful insights to humans
in domains where simple explanations are hard to extract. In this paper we
present algorithms with strong theoretical guarantees to mine these data sets
and select prototypes a.k.a. representatives that optimally describes them. Our
work notably generalizes the recent work by Kim et al. (2016) where in addition
to selecting prototypes, we also associate non-negative weights which are
indicative of their importance. This extension provides a single coherent
framework under which both prototypes and criticisms (i.e. outliers) can be
found. Furthermore, our framework works for any symmetric positive definite
kernel thus addressing one of the key open questions laid out in Kim et al.
(2016). By establishing that our objective function enjoys a key property of
that of weak submodularity, we present a fast ProtoDash algorithm and also
derive approximation guarantees for the same. We demonstrate the efficacy of
our method on diverse domains such as retail, digit recognition (MNIST) and on
publicly available 40 health questionnaires obtained from the Center for
Disease Control (CDC) website maintained by the US Dept. of Health. We validate
the results quantitatively as well as qualitatively based on expert feedback
and recently published scientific studies on public health, thus showcasing the
power of our technique in providing actionability (for retail), utility (for
MNIST) and insight (on CDC datasets) which arguably are the hallmarks of an
effective data mining method.Comment: Accepted for publication in International Conference on Data Mining
(ICDM) 201
Parsimonious Black-Box Adversarial Attacks via Efficient Combinatorial Optimization
Solving for adversarial examples with projected gradient descent has been
demonstrated to be highly effective in fooling the neural network based
classifiers. However, in the black-box setting, the attacker is limited only to
the query access to the network and solving for a successful adversarial
example becomes much more difficult. To this end, recent methods aim at
estimating the true gradient signal based on the input queries but at the cost
of excessive queries. We propose an efficient discrete surrogate to the
optimization problem which does not require estimating the gradient and
consequently becomes free of the first order update hyperparameters to tune.
Our experiments on Cifar-10 and ImageNet show the state of the art black-box
attack performance with significant reduction in the required queries compared
to a number of recently proposed methods. The source code is available at
https://github.com/snu-mllab/parsimonious-blackbox-attack.Comment: Accepted and to appear at ICML 201
Streaming Non-monotone Submodular Maximization: Personalized Video Summarization on the Fly
The need for real time analysis of rapidly producing data streams (e.g.,
video and image streams) motivated the design of streaming algorithms that can
efficiently extract and summarize useful information from massive data "on the
fly". Such problems can often be reduced to maximizing a submodular set
function subject to various constraints. While efficient streaming methods have
been recently developed for monotone submodular maximization, in a wide range
of applications, such as video summarization, the underlying utility function
is non-monotone, and there are often various constraints imposed on the
optimization problem to consider privacy or personalization. We develop the
first efficient single pass streaming algorithm, Streaming Local Search, that
for any streaming monotone submodular maximization algorithm with approximation
guarantee under a collection of independence systems ,
provides a constant approximation guarantee for maximizing a
non-monotone submodular function under the intersection of and
knapsack constraints. Our experiments show that for video summarization, our
method runs more than 1700 times faster than previous work, while maintaining
practically the same performance
- …