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2019


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Semi-supervised learning, causality, and the conditional cluster assumption

von Kügelgen, J., Mey, A., Loog, M., Schölkopf, B.

NeurIPS 2019 Workshop “Do the right thing”: machine learning and causal inference for improved decision making, December 2019 (poster) Accepted

link (url) [BibTex]

2019

link (url) [BibTex]


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Optimal experimental design via Bayesian optimization: active causal structure learning for Gaussian process networks

von Kügelgen, J., Rubenstein, P., Schölkopf, B., Weller, A.

NeurIPS 2019 Workshop “Do the right thing”: machine learning and causal inference for improved decision making, December 2019 (poster) Accepted

link (url) [BibTex]

link (url) [BibTex]


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Perception of temporal dependencies in autoregressive motion

Meding, K., Schölkopf, B., Wichmann, F. A.

European Conference on Visual Perception (ECVP), 2019 (poster)

[BibTex]


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Phenomenal Causality and Sensory Realism

Bruijns, S. A., Meding, K., Schölkopf, B., Wichmann, F. A.

European Conference on Visual Perception (ECVP), 2019 (poster)

[BibTex]

[BibTex]

2015


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Diversity of sharp wave-ripples in the CA1 of the macaque hippocampus and their brain wide signatures

Ramirez-Villegas, J. F., Logothetis, N. K., Besserve, M.

45th Annual Meeting of the Society for Neuroscience (Neuroscience 2015), October 2015 (poster)

link (url) [BibTex]

2015

link (url) [BibTex]


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Causal Inference for Empirical Time Series Based on the Postulate of Independence of Cause and Mechanism

Besserve, M.

53rd Annual Allerton Conference on Communication, Control, and Computing, September 2015 (talk)

[BibTex]

[BibTex]


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Retrospective rigid motion correction of undersampled MRI data

Loktyushin, A., Babayeva, M., Gallichan, D., Krueger, G., Scheffler, K., Kober, T.

23rd Annual Meeting and Exhibition of the International Society for Magnetic Resonance in Medicine, ISMRM, June 2015 (poster)

[BibTex]

[BibTex]


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Improving Quantitative Susceptibility and R2* Mapping by Applying Retrospective Motion Correction

Feng, X., Loktyushin, A., Deistung, A., Reichenbach, J. R.

23rd Annual Meeting and Exhibition of the International Society for Magnetic Resonance in Medicine, ISMRM, June 2015 (poster)

[BibTex]

[BibTex]


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Independence of cause and mechanism in brain networks

Besserve, M.

DALI workshop on Networks: Processes and Causality, April 2015 (talk)

[BibTex]

[BibTex]


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Increasing the sensitivity of Kepler to Earth-like exoplanets

Foreman-Mackey, D., Hogg, D., Schölkopf, B., Wang, D.

Workshop: 225th American Astronomical Society Meeting 2015 , pages: 105.01D, 2015 (poster)

Web link (url) [BibTex]

Web link (url) [BibTex]


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Information-Theoretic Implications of Classical and Quantum Causal Structures

Chaves, R., Majenz, C., Luft, L., Maciel, T., Janzing, D., Schölkopf, B., Gross, D.

18th Conference on Quantum Information Processing (QIP), 2015 (talk)

Web link (url) [BibTex]

Web link (url) [BibTex]


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Calibrating the pixel-level Kepler imaging data with a causal data-driven model

Wang, D., Foreman-Mackey, D., Hogg, D., Schölkopf, B.

Workshop: 225th American Astronomical Society Meeting 2015 , pages: 258.08, 2015 (poster)

Web link (url) [BibTex]

Web link (url) [BibTex]


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Assessment of brain tissue damage in the Sub-Acute Stroke Region by Multiparametric Imaging using [89-Zr]-Desferal-EPO-PET/MRI

Castaneda, S. G., Katiyar, P., Russo, F., Disselhorst, J. A., Calaminus, C., Poli, S., Maurer, A., Ziemann, U., Pichler, B. J.

World Molecular Imaging Conference, 2015 (talk)

[BibTex]

[BibTex]


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Early time point in vivo PET/MR is a promising biomarker for determining efficacy of a novel Db(\alphaEGFR)-scTRAIL fusion protein therapy in a colon cancer model

Divine, M. R., Harant, M., Katiyar, P., Disselhorst, J. A., Bukala, D., Aidone, S., Siegemund, M., Pfizenmaier, K., Kontermann, R., Pichler, B. J.

World Molecular Imaging Conference, 2015 (talk)

[BibTex]

[BibTex]


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Assessment of tumor heterogeneity using unsupervised graph based clustering of multi-modality imaging data

Katiyar, P., Divine, M. R., Pichler, B. J., Disselhorst, J. A.

European Molecular Imaging Meeting, 2015 (poster)

[BibTex]

[BibTex]


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Cosmology from Cosmic Shear with DES Science Verification Data

Abbott, T., Abdalla, F. B., Allam, S., Amara, A., Annis, J., Armstrong, R., Bacon, D., Banerji, M., Bauer, A. H., Baxter, E., others,

arXiv preprint arXiv:1507.05552, 2015 (techreport)

link (url) [BibTex]

link (url) [BibTex]


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The DES Science Verification Weak Lensing Shear Catalogs

Jarvis, M., Sheldon, E., Zuntz, J., Kacprzak, T., Bridle, S. L., Amara, A., Armstrong, R., Becker, M. R., Bernstein, G. M., Bonnett, C., others,

arXiv preprint arXiv:1507.05603, 2015 (techreport)

link (url) [BibTex]

link (url) [BibTex]


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Disparity estimation from a generative light field model

Köhler, R., Schölkopf, B., Hirsch, M.

IEEE International Conference on Computer Vision (ICCV 2015), Workshop on Inverse Rendering, 2015, Note: This work has been presented as a poster and is not included in the workshop proceedings. (poster)

[BibTex]

[BibTex]


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The search for single exoplanet transits in the Kepler light curves

Foreman-Mackey, D., Hogg, D. W., Schölkopf, B.

IAU General Assembly, 22, pages: 2258352, 2015 (talk)

link (url) [BibTex]

link (url) [BibTex]

2013


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Studying large-scale brain networks: electrical stimulation and neural-event-triggered fMRI

Logothetis, N., Eschenko, O., Murayama, Y., Augath, M., Steudel, T., Evrard, H., Besserve, M., Oeltermann, A.

Twenty-Second Annual Computational Neuroscience Meeting (CNS*2013), July 2013, journal = {BMC Neuroscience}, year = {2013}, month = {7}, volume = {14}, number = {Supplement 1}, pages = {A1}, (talk)

Web [BibTex]

2013

Web [BibTex]


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Coupling between spiking activity and beta band spatio-temporal patterns in the macaque PFC

Safavi, S., Panagiotaropoulos, T., Kapoor, V., Logothetis, N., Besserve, M.

43rd Annual Meeting of the Society for Neuroscience (Neuroscience), 2013 (poster)

[BibTex]

[BibTex]


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Gaussian Process Vine Copulas for Multivariate Dependence

Lopez-Paz, D., Hernandez-Lobato, J., Ghahramani, Z.

International Conference on Machine Learning (ICML), 2013 (poster)

PDF [BibTex]

PDF [BibTex]


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Domain Generalization via Invariant Feature Representation

Muandet, K., Balduzzi, D., Schölkopf, B.

30th International Conference on Machine Learning (ICML2013), 2013 (poster)

PDF [BibTex]

PDF [BibTex]


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Analyzing locking of spikes to spatio-temporal patterns in the macaque prefrontal cortex

Safavi, S., Panagiotaropoulos, T., Kapoor, V., Logothetis, N., Besserve, M.

Bernstein Conference, 2013 (poster)

DOI [BibTex]

DOI [BibTex]


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One-class Support Measure Machines for Group Anomaly Detection

Muandet, K., Schölkopf, B.

29th Conference on Uncertainty in Artificial Intelligence (UAI), 2013 (poster)

PDF [BibTex]

PDF [BibTex]


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The Randomized Dependence Coefficient

Lopez-Paz, D., Hennig, P., Schölkopf, B.

Neural Information Processing Systems (NIPS), 2013 (poster)

PDF [BibTex]

PDF [BibTex]


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Characterization of different types of sharp-wave ripple signatures in the CA1 of the macaque hippocampus

Ramirez-Villegas, J., Logothetis, N., Besserve, M.

4th German Neurophysiology PhD Meeting Networks, 2013 (poster)

Web [BibTex]

Web [BibTex]


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Animating Samples from Gaussian Distributions

Hennig, P.

(8), Max Planck Institute for Intelligent Systems, Tübingen, Germany, 2013 (techreport)

PDF [BibTex]

PDF [BibTex]


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Domain Generalization via Invariant Feature Representation

Muandet, K.

30th International Conference on Machine Learning (ICML2013), 2013 (talk)

PDF [BibTex]

PDF [BibTex]


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Maximizing Kepler science return per telemetered pixel: Detailed models of the focal plane in the two-wheel era

Hogg, D. W., Angus, R., Barclay, T., Dawson, R., Fergus, R., Foreman-Mackey, D., Harmeling, S., Hirsch, M., Lang, D., Montet, B. T., Schiminovich, D., Schölkopf, B.

arXiv:1309.0653, 2013 (techreport)

link (url) [BibTex]

link (url) [BibTex]


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Maximizing Kepler science return per telemetered pixel: Searching the habitable zones of the brightest stars

Montet, B. T., Angus, R., Barclay, T., Dawson, R., Fergus, R., Foreman-Mackey, D., Harmeling, S., Hirsch, M., Hogg, D. W., Lang, D., Schiminovich, D., Schölkopf, B.

arXiv:1309.0654, 2013 (techreport)

link (url) [BibTex]

link (url) [BibTex]

2010


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Computationally efficient algorithms for statistical image processing: Implementation in R

Langovoy, M., Wittich, O.

(2010-053), EURANDOM, Technische Universiteit Eindhoven, December 2010 (techreport)

Abstract
In the series of our earlier papers on the subject, we proposed a novel statistical hy- pothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We developed algorithms that allowed to detect objects of unknown shapes in the presence of nonparametric noise of unknown level and of un- known distribution. No boundary shape constraints were imposed on the objects, only a weak bulk condition for the object's interior was required. Our algorithms have linear complexity and exponential accuracy. In the present paper, we describe an implementation of our nonparametric hypothesis testing method. We provide a program that can be used for statistical experiments in image processing. This program is written in the statistical programming language R.

PDF [BibTex]

2010

PDF [BibTex]


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Similarities in resting state and feature-driven activity: Non-parametric evaluation of human fMRI

Shelton, J., Blaschko, M., Gretton, A., Müller, J., Fischer, E., Bartels, A.

NIPS Workshop on Learning and Planning from Batch Time Series Data, December 2010 (poster)

PDF Web [BibTex]

PDF Web [BibTex]


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Fast Convergent Algorithms for Expectation Propagation Approximate Bayesian Inference

Seeger, M., Nickisch, H.

Max Planck Institute for Biological Cybernetics, December 2010 (techreport)

Abstract
We propose a novel algorithm to solve the expectation propagation relaxation of Bayesian inference for continuous-variable graphical models. In contrast to most previous algorithms, our method is provably convergent. By marrying convergent EP ideas from (Opper&Winther 05) with covariance decoupling techniques (Wipf&Nagarajan 08, Nickisch&Seeger 09), it runs at least an order of magnitude faster than the most commonly used EP solver.

Web [BibTex]

Web [BibTex]


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Augmentation of fMRI Data Analysis using Resting State Activity and Semi-supervised Canonical Correlation Analysis

Shelton, JA., Blaschko, MB., Bartels, A.

NIPS Women in Machine Learning Workshop (WiML), December 2010 (poster)

Abstract
Resting state activity is brain activation that arises in the absence of any task, and is usually measured in awake subjects during prolonged fMRI scanning sessions where the only instruction given is to close the eyes and do nothing. It has been recognized in recent years that resting state activity is implicated in a wide variety of brain function. While certain networks of brain areas have different levels of activation at rest and during a task, there is nevertheless significant similarity between activations in the two cases. This suggests that recordings of resting state activity can be used as a source of unlabeled data to augment kernel canonical correlation analysis (KCCA) in a semisupervised setting. We evaluate this setting empirically yielding three main results: (i) KCCA tends to be improved by the use of Laplacian regularization even when no additional unlabeled data are available, (ii) resting state data seem to have a similar marginal distribution to that recorded during the execution of a visual processing task implying largely similar types of activation, and (iii) this source of information can be broadly exploited to improve the robustness of empirical inference in fMRI studies, an inherently data poor domain.

PDF Web [BibTex]

PDF Web [BibTex]


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High frequency phase-spike synchronization of extracellular signals modulates causal interactions in monkey primary visual cortex

Besserve, M., Murayama, Y., Schölkopf, B., Logothetis, N., Panzeri, S.

40(616.2), 40th Annual Meeting of the Society for Neuroscience (Neuroscience), November 2010 (poster)

Abstract
Functional correlates of Rhythms in the gamma band (30-100Hz) are observed in the mammalian brain with a large variety of functional correlates. Nevertheless, their functional role is still debated. One way to disentangle this issue is to go beyond usual correlation analysis and apply causality measures that quantify the directed interactions between the gamma rhythms and other aspects of neural activity. These measures can be further compared with other aspects of neurophysicological signals to find markers of neural interactions. In a recent study, we analyzed extracellular recordings in the primary visual cortex of 4 anesthetized macaques during the presentation of movie stimuli using a causality measure named Transfer Entropy. We found causal interactions between high frequency gamma rhythms (60-100Hz) recorded in different electrodes, involving in particular their phase, and between the gamma phase and spiking activity quantified by the instantaneous envelope of the MUA band (1-3kHz). Here, we further investigate in the same dataset the meaning of these phase-MUA and phase-phase causal interactions by studying the distribution of phases at multiple recording sites at lags around the occurrence of spiking events. First, we found a sharpening of the gamma phase distribution in one electrode when spikes are occurring in other recording site. This phenomena appeared as a form of phase-spike synchronization and was quantified by an information theoretic measure. We found this measure correlates significantly with phase-MUA causal interactions. Additionally, we quantified in a similar way the interplay between spiking and the phase difference between two recording sites (reflecting the well-know concept of phase synchronization). We found that, depending on the couple of recording site, spiking can correlate either with a phase synchronization or with a desynchronization with respect to the baseline. This effect correlates very well with the phase-phase causality measure. These results provide evidence for high frequency phase-spike synchronization to reflect communication between distant neural populations in V1. Conversely, both phase synchronization or desynchronization may favor neural communication between recording sites. This new result, which contrasts with current hypothesis on the role of phase synchronization, could be interpreted as the presence of inhibitory interactions that are suppressed by desynchronization. Finally, our findings give new insights into the role of gamma rhythms in regulating local computation in the visual cortex.

Web [BibTex]

Web [BibTex]


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Attenuation Correction for Whole Body PET/MR: Quantitative Evaluation and Lung Attenuation Estimation with Consistency Information

Bezrukov, I., Hofmann, M., Aschoff, P., Beyer, T., Mantlik, F., Pichler, B., Schölkopf, B.

2010(M13-122), 2010 Nuclear Science Symposium and Medical Imaging Conference (NSS-MIC), November 2010 (poster)

[BibTex]

[BibTex]


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PET/MRI: Observation of Non-Isotropic Positron Distribution in High Magnetic Fields and Its Diagnostic Impact

Kolb, A., Hofmann, M., Sauter, A., Liu, C., Schölkopf, B., Pichler, B.

2010 Nuclear Science Symposium and Medical Imaging Conference, 2010(M18-119):1, November 2010 (poster)

Web [BibTex]

Web [BibTex]


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Comparative Quantitative Evaluation of MR-Based Attenuation Correction Methods in Combined Brain PET/MR

Mantlik, F., Hofmann, M., Bezrukov, I., Kolb, A., Beyer, T., Reimold, M., Pichler, B., Schölkopf, B.

2010(M08-4), 2010 Nuclear Science Symposium and Medical Imaging Conference (NSS-MIC), November 2010 (talk)

Abstract
Combined PET/MR provides at the same time molecular and functional imaging as well as excellent soft tissue contrast. It does not allow one to directly measure the attenuation properties of scanned tissues, despite the fact that accurate attenuation maps are necessary for quantitative PET imaging. Several methods have therefore been proposed for MR-based attenuation correction (MR-AC). So far, they have only been evaluated on data acquired from separate MR and PET scanners. We evaluated several MR-AC methods on data from 10 patients acquired on a combined BrainPET/MR scanner. This allowed the consideration of specific PET/MR issues, such as the RF coil that attenuates and scatters 511 keV gammas. We evaluated simple MR thresholding methods as well as atlas and machine learning-based MR-AC. CT-based AC served as gold standard reference. To comprehensively evaluate the MR-AC accuracy, we used RoIs from 2 anatomic brain atlases with different levels of detail. Visual inspection of the PET images indicated that even the basic FLASH threshold MR-AC may be sufficient for several applications. Using a UTE sequence for bone prediction in MR-based thresholding occasionally led to false prediction of bone tissue inside the brain, causing a significant overestimation of PET activity. Although it yielded a lower mean underestimation of activity, it exhibited the highest variance of all methods. The atlas averaging approach had a smaller mean error, but showed high maximum overestimation on the RoIs of the more detailed atlas. The Nave Bayes and Atlas-Patch MR-AC yielded the smallest variance, and the Atlas-Patch also showed the smallest mean error. In conclusion, Atlas-based AC using only MR information on the BrainPET/MR yields a high level of accuracy that is sufficient for clinical quantitative imaging requirements. The Atlas-Patch approach was superior to alternative atlas-based methods, yielding a quantification error below 10% for all RoIs except very small ones.

[BibTex]

[BibTex]


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Probabilistic Assignment of Chemical Shift Data for Semi-Automatic Amino Acid Recognition

Hooge, J.

11(10):30, 11th Conference of Junior Neuroscientists of T{\"u}bingen (NeNa), October 2010 (poster)

Abstract
manner. First the backbone resonances are assigned. This is usually achieved from sequential information provided by three chemical shifts: CA, CB and C’. Once the sequence is solved, the second assignment step takes place. For this purpose, the CA-CB and HA chemical shifts are used as a start point for assignment of the side chain resonances, thus connecting the backbone resonances to their respective side chains. This strategy is unfortunately limited by the size of the protein due to increasing signal overlap and missing signals. Therefore, amino acid recognition is in many cases not possible as the CA-CB chemical shift pattern is not sufficient to discriminate between the 20 amino acids. As a result, the first step of the strategy described above remains tedious and time consuming. The combination of modern NMR techniques with new spectrometers now provide information that was not always accessible in the past, due to sensitivity problems. These experiments can be applied efficiently to measure a protein size up to 45 kDa and furthermore provide a unique combination of sequential carbon spin system information. The assignment process can thus benefit from a maximum knowledge input, containing âallâ backbone and side chain chemical shifts as well as an immediate amino acid recognition from the side chain spin system. We propose to extend the software PASTA (Protein ASsignment by Threshold Accepting) to achieve a general sequential assignment of backbone and side-chain resonances in a semi- to fullautomatic per-residue approach. PASTA will offer the possibility to achieve the sequential assignment using any kind of chemical shifts (carbons and/or protons) that can provide sequential information combined with an amino acid recognition feature based on carbon spin system analysis.

PDF [BibTex]

PDF [BibTex]


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Generalizing Demonstrated Actions in Manipulation Tasks

Kroemer, O., Detry, R., Piater, J., Peters, J.

IROS 2010 Workshop on Grasp Planning and Task Learning by Imitation, 2010, pages: 1, October 2010 (poster)

Abstract
Programming-by-demonstration promises to significantly reduce the burden of coding robots to perform new tasks. However, service robots will be presented with a variety of different situations that were not specifically demonstrated to it. In such cases, the robot must autonomously generalize its learned motions to these new situations. We propose a system that can generalize movements to new target locations and even new objects. The former is achieved by using a task-specific coordinate system together with dynamical systems motor primitives. Generalizing actions to new objects is a more complex problem, which we solve by treating it as a continuum-armed bandits problem. Using the bandits framework, we can efficiently optimize the learned action for a specific object. The proposed method was implemented on a real robot and succesfully adapted the grasping action to three different objects. Although we focus on grasping as an example of a task, the proposed methods are much more widely applicable to robot manipulation tasks.

PDF Web [BibTex]

PDF Web [BibTex]


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Inhomogeneous Positron Range Effects in High Magnetic Fields might Cause Severe Artefacts in PET/MRI

Kolb, A., Hofmann, M., Sauter, A., Liu, C., Eriksson, L., Pichler, B.

(0305B), 2010 World Molecular Imaging Congress (WMIC), September 2010 (poster)

Abstract
The combination of PET and MRI is an emerging field of current research. It is known that the positron range is shortened in high magnetic fields (MF), leading to an improved resolution in PET images. Interestingly, only the fraction of positron range (PR) orthogonal to the MF is reduced and the fraction along the MF is not affected and yields to a non-isotropic count distribution. We measured the PR effect with PET isotopes like F-18, Cu-64, C-11, N-13 and Ga-68. A piece of paper (1 cm2) was soaked with each isotope and placed in the cFOV of a clinical 3T BrainPET/MR scanner. A polyethylene board (PE) was placed as a positron (β+) stopper with an axial distance of 3 cm from the soaked paper. The area under the peaks of one pixel wide profiles along the z-axis in coronal images was compared. Based on these measurements we confirmed our data in organic tissue. A larynx/trachea and lung of a butchered swine were injected with a mixture of NiSO4 for T1 MRI signals and Ga-68, simulating tumor lesions in the respiratory tract. The trachea/larynx were aligned in 35° to the MF lines and a small mass lesion was inserted to imitate a primary tracheal tumor whereas the larynx was injected submucosally in the lower medial part of the epiglottis. Reconstructed PET data show that the annihilated ratio of β+ at the origin position and in the PE depends on the isotope energy and the direction of the MF. The annihilation ratios of the source and PE are 52.4/47.6 (F-18), 57.5/42.5 (Cu-64), 43.7/56.7 (C-11), 31.1/68.9 (N-13) and 14.9/85.1 (Ga-68). In the swine larynx measurement, an artefact with approximately 39% of the lesion activity formed along MF lines 3cm away from the original injected position (fig.1). The data of the trachea showed two shine artefacts with a symmetric alignment along the MF lines. About 58% of the positrons annihilated at the lesion and 21% formed each artefact. The PR effects areminor in tissue of higher or equal density to water (0.096 cm-1). However, the effect is severe in low density tissue or air and might lead to misinterpretation of clinical data.

Web [BibTex]

Web [BibTex]


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A PAC-Bayesian Analysis of Graph Clustering and Pairwise Clustering

Seldin, Y.

Max Planck Institute for Biological Cybernetics, Tübingen, Germany, September 2010 (techreport)

Abstract
We formulate weighted graph clustering as a prediction problem: given a subset of edge weights we analyze the ability of graph clustering to predict the remaining edge weights. This formulation enables practical and theoretical comparison of different approaches to graph clustering as well as comparison of graph clustering with other possible ways to model the graph. We adapt the PAC-Bayesian analysis of co-clustering (Seldin and Tishby, 2008; Seldin, 2009) to derive a PAC-Bayesian generalization bound for graph clustering. The bound shows that graph clustering should optimize a trade-off between empirical data fit and the mutual information that clusters preserve on the graph nodes. A similar trade-off derived from information-theoretic considerations was already shown to produce state-of-the-art results in practice (Slonim et al., 2005; Yom-Tov and Slonim, 2009). This paper supports the empirical evidence by providing a better theoretical foundation, suggesting formal generalization guarantees, and offering a more accurate way to deal with finite sample issues. We derive a bound minimization algorithm and show that it provides good results in real-life problems and that the derived PAC-Bayesian bound is reasonably tight.

PDF Web [BibTex]

PDF Web [BibTex]


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Sparse nonnegative matrix approximation: new formulations and algorithms

Tandon, R., Sra, S.

(193), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, September 2010 (techreport)

Abstract
We introduce several new formulations for sparse nonnegative matrix approximation. Subsequently, we solve these formulations by developing generic algorithms. Further, to help selecting a particular sparse formulation, we briefly discuss the interpretation of each formulation. Finally, preliminary experiments are presented to illustrate the behavior of our formulations and algorithms.

PDF [BibTex]

PDF [BibTex]


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Robust nonparametric detection of objects in noisy images

Langovoy, M., Wittich, O.

(2010-049), EURANDOM, Technische Universiteit Eindhoven, September 2010 (techreport)

Abstract
We propose a novel statistical hypothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown shapes in the presence of nonparametric noise of unknown level and of unknown distribution. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. In this paper, we develop further the mathematical formalism of our method and explore im- portant connections to the mathematical theory of percolation and statistical physics. We prove results on consistency and algorithmic complexity of our testing procedure. In addition, we address not only an asymptotic behavior of the method, but also a nite sample performance of our test.

PDF [BibTex]

PDF [BibTex]


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Statistical image analysis and percolation theory

Davies, P., Langovoy, M., Wittich, O.

73rd Annual Meeting of the Institute of Mathematical Statistics (IMS), August 2010 (talk)

Abstract
We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of objects of unknown shapes in the case of nonparametric noise. The noise density is unknown and can be heavy-tailed. We view the object detection problem as hypothesis testing for discrete statistical inverse problems. We present an algorithm that allows to detect objects of various shapes in noisy images. We prove results on consistency and algorithmic complexity of our procedures.

Web [BibTex]

Web [BibTex]


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Large Scale Variational Inference and Experimental Design for Sparse Generalized Linear Models

Seeger, M., Nickisch, H.

Max Planck Institute for Biological Cybernetics, August 2010 (techreport)

Abstract
Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We show how higher-order Bayesian decision-making problems, such as optimizing image acquisition in magnetic resonance scanners, can be addressed by querying the SLM posterior covariance, unrelated to the density's mode. We propose a scalable algorithmic framework, with which SLM posteriors over full, high-resolution images can be approximated for the first time, solving a variational optimization problem which is convex iff posterior mode finding is convex. These methods successfully drive the optimization of sampling trajectories for real-world magnetic resonance imaging through Bayesian experimental design, which has not been attempted before. Our methodology provides new insight into similarities and differences between sparse reconstruction and approximate Bayesian inference, and has important implications for compressive sensing of real-world images.

Web [BibTex]