20,433 research outputs found
Robust and Efficient Recovery of Rigid Motion from Subspace Constraints Solved using Recursive Identification of Nonlinear Implicit Systems
The problem of estimating rigid motion from projections may be characterized using a nonlinear dynamical system, composed of the rigid motion transformation and the perspective map. The time derivative of the output of such a system, which is also called the "motion field", is bilinear in the motion parameters, and may be used to specify a subspace constraint on either the direction of translation or the inverse depth of the observed points. Estimating motion may then be formulated as an optimization task constrained on such a subspace. Heeger and Jepson [5], who first introduced this constraint, solve the optimization task using an extensive search over the possible directions of translation.
We reformulate the optimization problem in a systems theoretic framework as the the identification of a dynamic system in exterior differential form with parameters on a differentiable manifold, and use techniques which pertain to nonlinear estimation and identification theory to perform the optimization task in a principled manner. The general technique for addressing such identification problems [14] has been used successfully in addressing other problems in computational vision [13, 12].
The application of the general method [14] results in a recursive and pseudo-optimal solution of the motion problem, which has robustness properties far superior to other existing techniques we have implemented.
By releasing the constraint that the visible points lie in front of the observer, we may explain some psychophysical effects on the nonrigid percept of rigidly moving shapes.
Experiments on real and synthetic image sequences show very promising results in terms of robustness, accuracy and computational efficiency
Accelerating delayed-acceptance Markov chain Monte Carlo algorithms
Delayed-acceptance Markov chain Monte Carlo (DA-MCMC) samples from a
probability distribution via a two-stages version of the Metropolis-Hastings
algorithm, by combining the target distribution with a "surrogate" (i.e. an
approximate and computationally cheaper version) of said distribution. DA-MCMC
accelerates MCMC sampling in complex applications, while still targeting the
exact distribution. We design a computationally faster, albeit approximate,
DA-MCMC algorithm. We consider parameter inference in a Bayesian setting where
a surrogate likelihood function is introduced in the delayed-acceptance scheme.
When the evaluation of the likelihood function is computationally intensive,
our scheme produces a 2-4 times speed-up, compared to standard DA-MCMC.
However, the acceleration is highly problem dependent. Inference results for
the standard delayed-acceptance algorithm and our approximated version are
similar, indicating that our algorithm can return reliable Bayesian inference.
As a computationally intensive case study, we introduce a novel stochastic
differential equation model for protein folding data.Comment: 40 pages, 21 figures, 10 table
Computational barriers in minimax submatrix detection
This paper studies the minimax detection of a small submatrix of elevated
mean in a large matrix contaminated by additive Gaussian noise. To investigate
the tradeoff between statistical performance and computational cost from a
complexity-theoretic perspective, we consider a sequence of discretized models
which are asymptotically equivalent to the Gaussian model. Under the hypothesis
that the planted clique detection problem cannot be solved in randomized
polynomial time when the clique size is of smaller order than the square root
of the graph size, the following phase transition phenomenon is established:
when the size of the large matrix , if the submatrix size
for any , computational complexity
constraints can incur a severe penalty on the statistical performance in the
sense that any randomized polynomial-time test is minimax suboptimal by a
polynomial factor in ; if for any
, minimax optimal detection can be attained within
constant factors in linear time. Using Schatten norm loss as a representative
example, we show that the hardness of attaining the minimax estimation rate can
crucially depend on the loss function. Implications on the hardness of support
recovery are also obtained.Comment: Published at http://dx.doi.org/10.1214/14-AOS1300 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
An Efficient Algorithm for Optimizing Adaptive Quantum Metrology Processes
Quantum-enhanced metrology infers an unknown quantity with accuracy beyond
the standard quantum limit (SQL). Feedback-based metrological techniques are
promising for beating the SQL but devising the feedback procedures is difficult
and inefficient. Here we introduce an efficient self-learning
swarm-intelligence algorithm for devising feedback-based quantum metrological
procedures. Our algorithm can be trained with simulated or real-world trials
and accommodates experimental imperfections, losses, and decoherence
Data complexity in machine learning
We investigate the role of data complexity in the context of binary classification problems. The universal data complexity is defined for a data set as the Kolmogorov complexity of the mapping enforced by the data set. It is closely related to several existing principles used in machine learning such as Occam's razor, the minimum description length, and the Bayesian approach. The data complexity can also be defined based on a learning model, which is more realistic for applications. We demonstrate the application of the data complexity in two learning problems, data decomposition and data pruning. In data decomposition, we illustrate that a data set is best approximated by its principal subsets which are Pareto optimal with respect to the complexity and the set size. In data pruning, we show that outliers usually have high complexity contributions, and propose methods for estimating the complexity contribution. Since in practice we have to approximate the ideal data complexity measures, we also discuss the impact of such approximations
Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data
We provide formal definitions and efficient secure techniques for
- turning noisy information into keys usable for any cryptographic
application, and, in particular,
- reliably and securely authenticating biometric data.
Our techniques apply not just to biometric information, but to any keying
material that, unlike traditional cryptographic keys, is (1) not reproducible
precisely and (2) not distributed uniformly. We propose two primitives: a
"fuzzy extractor" reliably extracts nearly uniform randomness R from its input;
the extraction is error-tolerant in the sense that R will be the same even if
the input changes, as long as it remains reasonably close to the original.
Thus, R can be used as a key in a cryptographic application. A "secure sketch"
produces public information about its input w that does not reveal w, and yet
allows exact recovery of w given another value that is close to w. Thus, it can
be used to reliably reproduce error-prone biometric inputs without incurring
the security risk inherent in storing them.
We define the primitives to be both formally secure and versatile,
generalizing much prior work. In addition, we provide nearly optimal
constructions of both primitives for various measures of ``closeness'' of input
data, such as Hamming distance, edit distance, and set difference.Comment: 47 pp., 3 figures. Prelim. version in Eurocrypt 2004, Springer LNCS
3027, pp. 523-540. Differences from version 3: minor edits for grammar,
clarity, and typo
Optimal Quantization for Compressive Sensing under Message Passing Reconstruction
We consider the optimal quantization of compressive sensing measurements
following the work on generalization of relaxed belief propagation (BP) for
arbitrary measurement channels. Relaxed BP is an iterative reconstruction
scheme inspired by message passing algorithms on bipartite graphs. Its
asymptotic error performance can be accurately predicted and tracked through
the state evolution formalism. We utilize these results to design mean-square
optimal scalar quantizers for relaxed BP signal reconstruction and empirically
demonstrate the superior error performance of the resulting quantizers.Comment: 5 pages, 3 figures, submitted to IEEE International Symposium on
Information Theory (ISIT) 2011; minor corrections in v
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
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