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2012


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Quasi-Newton Methods: A New Direction

Hennig, P., Kiefel, M.

In Proceedings of the 29th International Conference on Machine Learning, pages: 25-32, ICML ’12, (Editors: John Langford and Joelle Pineau), Omnipress, New York, NY, USA, ICML, July 2012 (inproceedings)

Abstract
Four decades after their invention, quasi- Newton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to the objective function. We show that many, including the most popular, quasi-Newton methods can be interpreted as approximations of Bayesian linear regression under varying prior assumptions. This new notion elucidates some shortcomings of classical algorithms, and lights the way to a novel nonparametric quasi-Newton method, which is able to make more efficient use of available information at computational cost similar to its predecessors.

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website+code pdf link (url) [BibTex]

2012


website+code pdf link (url) [BibTex]


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Entropy Search for Information-Efficient Global Optimization

Hennig, P., Schuler, C.

Journal of Machine Learning Research, 13, pages: 1809-1837, -, June 2012 (article)

Abstract
Contemporary global optimization algorithms are based on local measures of utility, rather than a probability measure over location and value of the optimum. They thus attempt to collect low function values, not to learn about the optimum. The reason for the absence of probabilistic global optimizers is that the corresponding inference problem is intractable in several ways. This paper develops desiderata for probabilistic optimization algorithms, then presents a concrete algorithm which addresses each of the computational intractabilities with a sequence of approximations and explicitly adresses the decision problem of maximizing information gain from each evaluation.

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PDF Web Project Page [BibTex]

PDF Web Project Page [BibTex]


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Learning Tracking Control with Forward Models

Bócsi, B., Hennig, P., Csató, L., Peters, J.

In pages: 259 -264, IEEE International Conference on Robotics and Automation (ICRA), May 2012 (inproceedings)

Abstract
Performing task-space tracking control on redundant robot manipulators is a difficult problem. When the physical model of the robot is too complex or not available, standard methods fail and machine learning algorithms can have advantages. We propose an adaptive learning algorithm for tracking control of underactuated or non-rigid robots where the physical model of the robot is unavailable. The control method is based on the fact that forward models are relatively straightforward to learn and local inversions can be obtained via local optimization. We use sparse online Gaussian process inference to obtain a flexible probabilistic forward model and second order optimization to find the inverse mapping. Physical experiments indicate that this approach can outperform state-of-the-art tracking control algorithms in this context.

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PDF Web DOI [BibTex]

PDF Web DOI [BibTex]


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Approximate Gaussian Integration using Expectation Propagation

Cunningham, J., Hennig, P., Lacoste-Julien, S.

In pages: 1-11, -, January 2012 (inproceedings) Submitted

Abstract
While Gaussian probability densities are omnipresent in applied mathematics, Gaussian cumulative probabilities are hard to calculate in any but the univariate case. We offer here an empirical study of the utility of Expectation Propagation (EP) as an approximate integration method for this problem. For rectangular integration regions, the approximation is highly accurate. We also extend the derivations to the more general case of polyhedral integration regions. However, we find that in this polyhedral case, EP's answer, though often accurate, can be almost arbitrarily wrong. These unexpected results elucidate an interesting and non-obvious feature of EP not yet studied in detail, both for the problem of Gaussian probabilities and for EP more generally.

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Web [BibTex]

Web [BibTex]


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Kernel Topic Models

Hennig, P., Stern, D., Herbrich, R., Graepel, T.

In Fifteenth International Conference on Artificial Intelligence and Statistics, 22, pages: 511-519, JMLR Proceedings, (Editors: Lawrence, N. D. and Girolami, M.), JMLR.org, AISTATS , 2012 (inproceedings)

Abstract
Latent Dirichlet Allocation models discrete data as a mixture of discrete distributions, using Dirichlet beliefs over the mixture weights. We study a variation of this concept, in which the documents' mixture weight beliefs are replaced with squashed Gaussian distributions. This allows documents to be associated with elements of a Hilbert space, admitting kernel topic models (KTM), modelling temporal, spatial, hierarchical, social and other structure between documents. The main challenge is efficient approximate inference on the latent Gaussian. We present an approximate algorithm cast around a Laplace approximation in a transformed basis. The KTM can also be interpreted as a type of Gaussian process latent variable model, or as a topic model conditional on document features, uncovering links between earlier work in these areas.

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PDF Web [BibTex]

PDF Web [BibTex]


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Fourier-transform photocurrent spectroscopy using a supercontinuum light source

Petermann, C., Beigang, R., Fischer, P.

APPLIED PHYSICS LETTERS, 100(6), 2012 (article)

Abstract
We demonstrate an implementation of frequency-encoded photocurrent spectroscopy using a super-continuum light source. The spectrally broad light is spatially dispersed and modulated with a special mechanical chopper design that permits a continuous wavelength-dependent modulation. After recombination, the light beam contains a frequency encoded spectrum which enables us to map the spectral response of a given sample in 60 ms and with a lateral resolution of 10 mu m. (C) 2012 American Institute of Physics.

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DOI [BibTex]

DOI [BibTex]


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Eine neue Form von Cavity Enhanced Absorption Spectroscopy

Petermann, C., Fischer, P.

DE Gruyter, 79(1), 2012, Best paper award OPTO 2011 (article)

Abstract
Wir stellen eine Kopplungsmethode für resonatorgestützte Absorptionsmessungen vor, bei der Licht durch einen im Resonator platzierten akustooptischen Modulator aktiv ein- und ausgekoppelt wird. Dies ermöglicht es Cavity-Ring-Down-Spektroskopie (CRDS) mit breitbandigen und zeitlich inkohärenten Lichtquellen niedriger spektraler Leistungsdichte durchzuführen. Das Verfahren wird zum ersten Mal mit einer breitbandigen Superkontinuum-Quelle demonstriert.

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A new coupling scheme for cavity enhanced absorption spectroscopy makes use of an intracavity acousto-optical modulator to actively switch light into (and out of) a resonator. This allows cavity ringdown spectroscopy (CRDS) to be implemented with broadband temporally incoherent light sources with low spectral power densities. The method is demonstrated for the first time using a broadband supercontinuum source. Best paper award OPTO 2011.

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link (url) [BibTex]

link (url) [BibTex]

2011


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Optimal Reinforcement Learning for Gaussian Systems

Hennig, P.

In Advances in Neural Information Processing Systems 24, pages: 325-333, (Editors: J Shawe-Taylor and RS Zemel and P Bartlett and F Pereira and KQ Weinberger), Twenty-Fifth Annual Conference on Neural Information Processing Systems (NIPS), 2011 (inproceedings)

Abstract
The exploration-exploitation trade-off is among the central challenges of reinforcement learning. The optimal Bayesian solution is intractable in general. This paper studies to what extent analytic statements about optimal learning are possible if all beliefs are Gaussian processes. A first order approximation of learning of both loss and dynamics, for nonlinear, time-varying systems in continuous time and space, subject to a relatively weak restriction on the dynamics, is described by an infinite-dimensional partial differential equation. An approximate finitedimensional projection gives an impression for how this result may be helpful.

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PDF Web [BibTex]

2011


PDF Web [BibTex]


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Quantum-Cascade Laser-Based Vibrational Circular Dichroism

Luedeke, S., Pfeifer, M., Fischer, P.

JOURNAL OF THE AMERICAN CHEMICAL SOCIETY, 133(15):5704-5707, 2011 (article)

Abstract
Vibrational circular dichroism (VCD) spectra were recorded with a tunable external-cavity quantum-cascade laser (QCL). In comparison with standard thermal light sources in the IR, QCLs provide orders of magnitude more power and are therefore promising for VCD studies in strongly absorbing solvents. The brightness of this novel light source is demonstrated with VCD and IR absorption measurements of a number of compounds, including proline in water.

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DOI [BibTex]

DOI [BibTex]


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Actively coupled cavity ringdown spectroscopy with low-power broadband sources

Petermann, C., Fischer, P.

OPTICS EXPRESS, 19(11):10164-10173, 2011 (article)

Abstract
We demonstrate a coupling scheme for cavity enhanced absorption spectroscopy that makes use of an intracavity acousto-optical modulator to actively switch light into (and out of) a resonator. This allows cavity ringdown spectroscopy (CRDS) to be implemented with broadband nonlaser light sources with spectral power densities of less than 30 mu W/nm. Although the acousto-optical element reduces the ultimate detection limit by introducing additional losses, it permits absorptivities to be measured with a high dynamic range, especially in lossy environments. Absorption measurements for the forbidden transition of gaseous oxygen in air at similar to 760nm are presented using a low-coherence cw-superluminescent diode. The same setup was electronically configured to cover absorption losses from 1.8 x 10(-8)cm(-1) to 7.5\% per roundtrip. This could be of interest in process analytical applications. (C) 2011 Optical Society of America

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DOI [BibTex]

DOI [BibTex]


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Magnetically actuated propulsion at low Reynolds numbers: towards nanoscale control

Fischer, P., Ghosh, A.

NANOSCALE, 3(2):557-563, 2011 (article)

Abstract
Significant progress has been made in the fabrication of micron and sub-micron structures whose motion can be controlled in liquids under ambient conditions. The aim of many of these engineering endeavors is to be able to build and propel an artificial micro-structure that rivals the versatility of biological swimmers of similar size, e. g. motile bacterial cells. Applications for such artificial ``micro-bots'' are envisioned to range from microrheology to targeted drug delivery and microsurgery, and require full motion-control under ambient conditions. In this Mini-Review we discuss the construction, actuation, and operation of several devices that have recently been reported, especially systems that can be controlled by and propelled with homogenous magnetic fields. We describe the fabrication and associated experimental challenges and discuss potential applications.

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Video - Nanospropellers DOI [BibTex]


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Weak value amplified optical activity measurements

Pfeifer, M., Fischer, P.

Opt. Express, 19(17):16508-16517, OSA, 2011 (article)

Abstract
We present a new form of optical activity measurement based on a modified weak value amplification scheme. It has recently been shown experimentally that the left- and right-circular polarization components refract with slightly different angles of refraction at a chiral interface causing a linearly polarized light beam to split into two. By introducing a polarization modulation that does not give rise to a change in the optical rotation it is possible to differentiate between the two circular polarization components even after post-selection with a linear polarizer. We show that such a modified weak value amplification measurement permits the sign of the splitting and thus the handedness of the optically active medium to be determined. Angular beam separations of Δθ ∼ 1 nanoradian, which corresponds to a circular birefringence of Δn ∼ 1 × 10−9, could be measured with a relative error of less than 1%.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]

2009


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Full phase and amplitude control in computer-generated holography

Fratz, M., Fischer, P., Giel, D. M.

OPTICS LETTERS, 34(23):3659-3661, 2009 (article)

Abstract
We report what we believe to be the first realization of a computer-generated complex-valued hologram recorded in a single film of photoactive polymer. Complex-valued holograms give rise to a diffracted optical field with control over its amplitude and phase. The holograms are generated by a one-step direct laser writing process in which a spatial light modulator (SLM) is imaged onto a polymer film. Temporal modulation of the SLM during exposure controls both the strength of the induced birefringence and the orientation of the fast axis. We demonstrate that complex holograms can be used to impart arbitrary amplitude and phase profiles onto a beam and thereby open new possibilities in the control of optical beams. (C) 2009 Optical Society of America

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[BibTex]

2009


[BibTex]


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Digital polarization holograms with defined magnitude and orientation of each pixel’s birefringence

Fratz, M., Giel, D. M., Fischer, P.

OPTICS LETTERS, 34(8):1270-1272, 2009 (article)

Abstract
A new form of digital polarization holography is demonstrated that permits both the amplitude and the phase of a diffracted beam to be independently controlled. This permits two independent intensity images to be stored in the same hologram. To fabricate the holograms, a birefringence with defined retardance and orientation of the fast axis is recorded into a photopolymer film. The holograms are selectively read out by choosing the polarization state of the read beam. Polarization holograms of this kind increase the data density in holographic data storage and allow higher quality diffractive optical elements to be written. (C) 2009 Optical Society of America

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[BibTex]


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Controlled Propulsion of Artificial Magnetic Nanostructured Propellers

Ghosh, A., Fischer, P.

NANO LETTERS, 9(6):2243-2245, 2009, Featured highlight ‘Nanotechnology: The helix that delivers’ Nature 459, 13 (2009). (article)

Abstract
For biomedical applications, such as targeted drug delivery and microsurgery, it is essential to develop a system of swimmers that can be propelled wirelessly in fluidic environments with good control. Here, we report the construction and operation of chiral colloidal propellers that can be navigated in water with micrometer-level precision using homogeneous magnetic fields. The propellers are made via nanostructured surfaces and can be produced in large numbers. The nanopropellers can carry chemicals, push loads, and act as local probes in rheological measurements.

Featured highlight ‘Nanotechnology: The helix that delivers’ Nature 459, 13 (2009).

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Video - Nanospropellers DOI [BibTex]

Video - Nanospropellers DOI [BibTex]


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Absolute Asymmetric Reduction Based on the Relative Orientation of Achiral Reactants

Kuhn, A., Fischer, P.

ANGEWANDTE CHEMIE-INTERNATIONAL EDITION, 48(37):6857-6860, 2009 (article)

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DOI [BibTex]

DOI [BibTex]

2003


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New electro-optic effect: Sum-frequency generation from optically active liquids in the presence of a dc electric field

Fischer, P., Buckingham, A., Beckwitt, K., Wiersma, D., Wise, F.

PHYSICAL REVIEW LETTERS, 91(17), 2003 (article)

Abstract
We report the observation of sum-frequency signals that depend linearly on an applied electrostatic field and that change sign with the handedness of an optically active solute. This recently predicted chiral electro-optic effect exists in the electric-dipole approximation. The static electric field gives rise to an electric-field-induced sum-frequency signal (an achiral third-order process) that interferes with the chirality-specific sum-frequency at second order. The cross-terms linear in the electrostatic field constitute the effect and may be used to determine the absolute sign of second- and third-order nonlinear-optical susceptibilities in isotropic media.

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DOI [BibTex]

2003


DOI [BibTex]


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Chiral and achiral contributions to sum-frequency generation from optically active solutions of binaphthol

Fischer, P., Wise, F., Albrecht, A.

JOURNAL OF PHYSICAL CHEMISTRY A, 107(40):8232-8238, 2003 (article)

Abstract
The nonlinear sum- and difference-frequency generation spectroscopies can be probes of molecular chirality in optically active systems. We present a tensorial analysis of the chirality-specific electric-dipolar sum-frequency-generation susceptibility and the achiral electric-quadrupolar and magnetic-dipolar nonlinearities at second order in isotropic media. The chiral and achiral contributions to the sum-frequency signal from the bulk of optically active solutions of 1,1'-bi-2-naphthol (2,2'-dehydroxy-1,1'-binaphthyl) can be distinguished, and the former dominates. Ab initio computations reveal the dramatic resonance enhancement that the isotropic component of the electric-dipolar three-wave mixing hyperpolarizability experiences. Away from resonance its magnitude rapidly decreases, as-unlike the vector component-it is zero in the static limit. The dispersion of the first hyperpolarizability is computed by a configuration interaction singles sum-over-states approach with explicit regard to the Franck-Condon active vibrational substructure for all resonant electronic states.

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DOI [BibTex]

DOI [BibTex]