25,232 research outputs found
On Correcting Inputs: Inverse Optimization for Online Structured Prediction
Algorithm designers typically assume that the input data is correct, and then
proceed to find "optimal" or "sub-optimal" solutions using this input data.
However this assumption of correct data does not always hold in practice,
especially in the context of online learning systems where the objective is to
learn appropriate feature weights given some training samples. Such scenarios
necessitate the study of inverse optimization problems where one is given an
input instance as well as a desired output and the task is to adjust the input
data so that the given output is indeed optimal. Motivated by learning
structured prediction models, in this paper we consider inverse optimization
with a margin, i.e., we require the given output to be better than all other
feasible outputs by a desired margin. We consider such inverse optimization
problems for maximum weight matroid basis, matroid intersection, perfect
matchings, minimum cost maximum flows, and shortest paths and derive the first
known results for such problems with a non-zero margin. The effectiveness of
these algorithmic approaches to online learning for structured prediction is
also discussed.Comment: Conference version to appear in FSTTCS, 201
Streaming Verification of Graph Properties
Streaming interactive proofs (SIPs) are a framework for outsourced
computation. A computationally limited streaming client (the verifier) hands
over a large data set to an untrusted server (the prover) in the cloud and the
two parties run a protocol to confirm the correctness of result with high
probability. SIPs are particularly interesting for problems that are hard to
solve (or even approximate) well in a streaming setting. The most notable of
these problems is finding maximum matchings, which has received intense
interest in recent years but has strong lower bounds even for constant factor
approximations.
In this paper, we present efficient streaming interactive proofs that can
verify maximum matchings exactly. Our results cover all flavors of matchings
(bipartite/non-bipartite and weighted). In addition, we also present streaming
verifiers for approximate metric TSP. In particular, these are the first
efficient results for weighted matchings and for metric TSP in any streaming
verification model.Comment: 26 pages, 2 figure, 1 tabl
Quantum Error Correction with the Toric-GKP Code
We examine the performance of the single-mode GKP code and its concatenation
with the toric code for a noise model of Gaussian shifts, or displacement
errors. We show how one can optimize the tracking of errors in repeated noisy
error correction for the GKP code. We do this by examining the
maximum-likelihood problem for this setting and its mapping onto a 1D Euclidean
path-integral modeling a particle in a random cosine potential. We demonstrate
the efficiency of a minimum-energy decoding strategy as a proxy for the path
integral evaluation. In the second part of this paper, we analyze and
numerically assess the concatenation of the GKP code with the toric code. When
toric code measurements and GKP error correction measurements are perfect, we
find that by using GKP error information the toric code threshold improves from
to . When only the GKP error correction measurements are perfect
we observe a threshold at . In the more realistic setting when all error
information is noisy, we show how to represent the maximum likelihood decoding
problem for the toric-GKP code as a 3D compact QED model in the presence of a
quenched random gauge field, an extension of the random-plaquette gauge model
for the toric code. We present a new decoder for this problem which shows the
existence of a noise threshold at shift-error standard deviation for toric code measurements, data errors and GKP ancilla errors.
If the errors only come from having imperfect GKP states, this corresponds to
states with just 4 photons or more. Our last result is a no-go result for
linear oscillator codes, encoding oscillators into oscillators. For the
Gaussian displacement error model, we prove that encoding corresponds to
squeezing the shift errors. This shows that linear oscillator codes are useless
for quantum information protection against Gaussian shift errors.Comment: 50 pages, 14 figure
Combinatorial RNA Design: Designability and Structure-Approximating Algorithm
In this work, we consider the Combinatorial RNA Design problem, a minimal
instance of the RNA design problem which aims at finding a sequence that admits
a given target as its unique base pair maximizing structure. We provide
complete characterizations for the structures that can be designed using
restricted alphabets. Under a classic four-letter alphabet, we provide a
complete characterization of designable structures without unpaired bases. When
unpaired bases are allowed, we provide partial characterizations for classes of
designable/undesignable structures, and show that the class of designable
structures is closed under the stutter operation. Membership of a given
structure to any of the classes can be tested in linear time and, for positive
instances, a solution can be found in linear time. Finally, we consider a
structure-approximating version of the problem that allows to extend bands
(helices) and, assuming that the input structure avoids two motifs, we provide
a linear-time algorithm that produces a designable structure with at most twice
more base pairs than the input structure.Comment: CPM - 26th Annual Symposium on Combinatorial Pattern Matching, Jun
2015, Ischia Island, Italy. LNCS, 201
Optimal Recombination in Genetic Algorithms
This paper surveys results on complexity of the optimal recombination problem
(ORP), which consists in finding the best possible offspring as a result of a
recombination operator in a genetic algorithm, given two parent solutions. We
consider efficient reductions of the ORPs, allowing to establish polynomial
solvability or NP-hardness of the ORPs, as well as direct proofs of hardness
results
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