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Human Aspects of Machine Learning

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Empirical Inference Ph.D. Thesis Modeling the polygenic architecture of complex traits Rakitsch, B. Eberhard Karls Universität Tübingen, November 2014 BibTeX

Empirical Inference Conference Paper Curiosity-driven learning with Context Tree Weighting Peng, Z., Braun, D. 366-367, IEEE, Piscataway, NJ, USA, 4th Joint IEEE International Conference on Development and Learning and on Epigenetic Robotics (IEEE ICDL-EPIROB 2014), October 2014
In the first simulation, the intrinsic motivation of the agent was given by measuring learning progress through reduction in informational surprise (Figure 1 A-C). This way the agent should first learn the action that is easiest to learn (a1), and then switch to other actions that still allow for learning (a2) and ignore actions that cannot be learned at all (a3). This is exactly what we found in our simple environment. Compared to the original developmental learning algorithm based on learning progress proposed by Oudeyer [2], our Context Tree Weighting approach does not require local experts to do prediction, rather it learns the conditional probability distribution over observations given action in one structure. In the second simulation, the intrinsic motivation of the agent was given by measuring compression progress through improvement in compressibility (Figure 1 D-F). The agent behaves similarly: the agent first concentrates on the action with the most predictable consequence and then switches over to the regular action where the consequence is more difficult to predict, but still learnable. Unlike the previous simulation, random actions are also interesting to some extent because the compressed symbol strings use 8-bit representations, while only 2 bits are required for our observation space. Our preliminary results suggest that Context Tree Weighting might provide a useful representation to study problems of development.
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Perceiving Systems Empirical Inference Conference Paper Human Pose Estimation with Fields of Parts Kiefel, M., Gehler, P. In Computer Vision – ECCV 2014, LNCS 8693:331-346, Lecture Notes in Computer Science, (Editors: Fleet, David and Pajdla, Tomas and Schiele, Bernt and Tuytelaars, Tinne), Springer, 13th European Conference on Computer Vision, September 2014
This paper proposes a new formulation of the human pose estimation problem. We present the Fields of Parts model, a binary Conditional Random Field model designed to detect human body parts of articulated people in single images. The Fields of Parts model is inspired by the idea of Pictorial Structures, it models local appearance and joint spatial configuration of the human body. However the underlying graph structure is entirely different. The idea is simple: we model the presence and absence of a body part at every possible position, orientation, and scale in an image with a binary random variable. This results into a vast number of random variables, however, we show that approximate inference in this model is efficient. Moreover we can encode the very same appearance and spatial structure as in Pictorial Structures models. This approach allows us to combine ideas from segmentation and pose estimation into a single model. The Fields of Parts model can use evidence from the background, include local color information, and it is connected more densely than a kinematic chain structure. On the challenging Leeds Sports Poses dataset we improve over the Pictorial Structures counterpart by 5.5% in terms of Average Precision of Keypoints (APK).
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Perceiving Systems Empirical Inference Probabilistic Numerics Conference Paper Probabilistic Progress Bars Kiefel, M., Schuler, C., Hennig, P. In Conference on Pattern Recognition (GCPR), 8753:331-341, Lecture Notes in Computer Science, (Editors: Jiang, X., Hornegger, J., and Koch, R.), Springer, GCPR, September 2014
Predicting the time at which the integral over a stochastic process reaches a target level is a value of interest in many applications. Often, such computations have to be made at low cost, in real time. As an intuitive example that captures many features of this problem class, we choose progress bars, a ubiquitous element of computer user interfaces. These predictors are usually based on simple point estimators, with no error modelling. This leads to fluctuating behaviour confusing to the user. It also does not provide a distribution prediction (risk values), which are crucial for many other application areas. We construct and empirically evaluate a fast, constant cost algorithm using a Gauss-Markov process model which provides more information to the user.
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Empirical Inference Article Information-Theoretic Bounded Rationality and ϵ-Optimality Braun, D., Ortega, P. Entropy, 16(8):4662-4676, August 2014
Bounded rationality concerns the study of decision makers with limited information processing resources. Previously, the free energy difference functional has been suggested to model bounded rational decision making, as it provides a natural trade-off between an energy or utility function that is to be optimized and information processing costs that are measured by entropic search costs. The main question of this article is how the information-theoretic free energy model relates to simple \(\epsilon\)-optimality models of bounded rational decision making, where the decision maker is satisfied with any action in an \(\epsilon\)-neighborhood of the optimal utility. We find that the stochastic policies that optimize the free energy trade-off comply with the notion of \(\epsilon\)-optimality. Moreover, this optimality criterion even holds when the environment is adversarial. We conclude that the study of bounded rationality based on \(\epsilon\)-optimality criteria that abstract away from the particulars of the information processing constraints is compatible with the information-theoretic free energy model of bounded rationality.
DOI BibTeX

Empirical Inference Conference Paper Monte Carlo methods for exact & efficient solution of the generalized optimality equations Ortega, P., Braun, D., Tishby, N. 4322-4327, IEEE, Piscataway, NJ, USA, IEEE International Conference on Robotics and Automation (ICRA 2014), July 2014
Previous work has shown that classical sequential decision making rules, including expectimax and minimax, are limit cases of a more general class of bounded rational planning problems that trade off the value and the complexity of the solution, as measured by its information divergence from a given reference. This allows modeling a range of novel planning problems having varying degrees of control due to resource constraints, risk-sensitivity, trust and model uncertainty. However, so far it has been unclear in what sense information constraints relate to the complexity of planning. In this paper, we introduce Monte Carlo methods to solve the generalized optimality equations in an efficient \& exact way when the inverse temperatures in a generalized decision tree are of the same sign. These methods highlight a fundamental relation between inverse temperatures and the number of Monte Carlo proposals. In particular, it is seen that the number of proposals is essentially independent of the size of the decision tree.
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Empirical Inference Conference Paper Seeing the Arrow of Time Pickup, L., Zheng, P., Donglai, W., YiChang, S., Changshui, Z., Zisserman, A., Schölkopf, B., Freeman, W. Computer Vision and Pattern Recognition (CVPR), 2014 IEEE Conference on, 2043-2050, IEEE, CVPR, June 2014 (Published) DOI BibTeX

Perceiving Systems Empirical Inference Probabilistic Numerics Conference Paper Probabilistic Solutions to Differential Equations and their Application to Riemannian Statistics Hennig, P., Hauberg, S. In Proceedings of the 17th International Conference on Artificial Intelligence and Statistics, 33:347-355, JMLR: Workshop and Conference Proceedings, (Editors: S Kaski and J Corander), Microtome Publishing, Brookline, MA, AISTATS, April 2014
We study a probabilistic numerical method for the solution of both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Such methods have concrete value in the statistics on Riemannian manifolds, where non-analytic ordinary differential equations are involved in virtually all computations. The probabilistic formulation permits marginalising the uncertainty of the numerical solution such that statistics are less sensitive to inaccuracies. This leads to new Riemannian algorithms for mean value computations and principal geodesic analysis. Marginalisation also means results can be less precise than point estimates, enabling a noticeable speed-up over the state of the art. Our approach is an argument for a wider point that uncertainty caused by numerical calculations should be tracked throughout the pipeline of machine learning algorithms.
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Empirical Inference Conference Paper A Visual Analytics Approach to Study Anatomic Covariation Hermann, M., Schunke, A., Schultz, T., Klein, R. In Proceedings of IEEE Pacific Visualization 2014, 161-168, March 2014 (Published)
Gaining insight into anatomic covariation helps the understanding of organismic shape variability in general and is of particular interest for delimiting morphological modules. Generation of hypotheses on structural covariation is undoubtedly a highly creative process, and as such, requires an exploratory approach. In this work we propose a new local anatomic covariance tensor which enables interactive visualizations to explore covariation at different levels of detail, stimulating rapid formation and (qualitative) evaluation of hypotheses. The effectiveness of the presented approach is demonstrated on a muCT dataset of mouse mandibles for which results from the literature are successfully reproduced, while providing a more detailed representation of covariation compared to state-of-the-art methods.
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Empirical Inference Article Assessing randomness and complexity in human motion trajectories through analysis of symbolic sequences Peng, Z., Genewein, T., Braun, D. Frontiers in Human Neuroscience, 8(168):1-13, March 2014
Complexity is a hallmark of intelligent behavior consisting both of regular patterns and random variation. To quantitatively assess the complexity and randomness of human motion, we designed a motor task in which we translated subjects' motion trajectories into strings of symbol sequences. In the first part of the experiment participants were asked to perform self-paced movements to create repetitive patterns, copy pre-specified letter sequences, and generate random movements. To investigate whether the degree of randomness can be manipulated, in the second part of the experiment participants were asked to perform unpredictable movements in the context of a pursuit game, where they received feedback from an online Bayesian predictor guessing their next move. We analyzed symbol sequences representing subjects' motion trajectories with five common complexity measures: predictability, compressibility, approximate entropy, Lempel-Ziv complexity, as well as effective measure complexity. We found that subjects’ self-created patterns were the most complex, followed by drawing movements of letters and self-paced random motion. We also found that participants could change the randomness of their behavior depending on context and feedback. Our results suggest that humans can adjust both complexity and regularity in different movement types and contexts and that this can be assessed with information-theoretic measures of the symbolic sequences generated from movement trajectories.
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Empirical Inference Article Generalized Thompson sampling for sequential decision-making and causal inference Ortega, P., Braun, D. Complex Adaptive Systems Modeling, 2(2):1-23, March 2014
Purpose Sampling an action according to the probability that the action is believed to be the optimal one is sometimes called Thompson sampling. Methods Although mostly applied to bandit problems, Thompson sampling can also be used to solve sequential adaptive control problems, when the optimal policy is known for each possible environment. The predictive distribution over actions can then be constructed by a Bayesian superposition of the policies weighted by their posterior probability of being optimal. Results Here we discuss two important features of this approach. First, we show in how far such generalized Thompson sampling can be regarded as an optimal strategy under limited information processing capabilities that constrain the sampling complexity of the decision-making process. Second, we show how such Thompson sampling can be extended to solve causal inference problems when interacting with an environment in a sequential fashion. Conclusion In summary, our results suggest that Thompson sampling might not merely be a useful heuristic, but a principled method to address problems of adaptive sequential decision-making and causal inference.
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Empirical Inference Article A Brain-Computer Interface Based on Self-Regulation of Gamma-Oscillations in the Superior Parietal Cortex Grosse-Wentrup, M., Schölkopf, B. Journal of Neural Engineering, 11(5):056015, 2014
Objective. Brain–computer interface (BCI) systems are often based on motor- and/or sensory processes that are known to be impaired in late stages of amyotrophic lateral sclerosis (ALS). We propose a novel BCI designed for patients in late stages of ALS that only requires high-level cognitive processes to transmit information from the user to the BCI. Approach. We trained subjects via EEG-based neurofeedback to self-regulate the amplitude of gamma-oscillations in the superior parietal cortex (SPC). We argue that parietal gamma-oscillations are likely to be associated with high-level attentional processes, thereby providing a communication channel that does not rely on the integrity of sensory- and/or motor-pathways impaired in late stages of ALS. Main results. Healthy subjects quickly learned to self-regulate gamma-power in the SPC by alternating between states of focused attention and relaxed wakefulness, resulting in an average decoding accuracy of 70.2%. One locked-in ALS patient (ALS-FRS-R score of zero) achieved an average decoding accuracy significantly above chance-level though insufficient for communication (55.8%). Significance. Self-regulation of gamma-power in the SPC is a feasible paradigm for brain–computer interfacing and may be preserved in late stages of ALS. This provides a novel approach to testing whether completely locked-in ALS patients retain the capacity for goal-directed thinking.
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Empirical Inference Master Thesis A Novel Causal Inference Method for Time Series Shajarisales, N. Eberhard Karls Universität Tübingen, Germany, Eberhard Karls Universität Tübingen, Germany, 2014 (Published) PDF BibTeX

Empirical Inference Conference Paper A Permutation-Based Kernel Conditional Independence Test Doran, G., Muandet, K., Zhang, K., Schölkopf, B. In Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence (UAI2014), 132-141, (Editors: Nevin L. Zhang and Jin Tian), AUAI Press Corvallis, Oregon, UAI2014, 2014 PDF BibTeX

Empirical Inference Article A few extreme events dominate global interannual variability in gross primary production Zscheischler, J., Mahecha, M., v Buttlar, J., Harmeling, S., Jung, M., Rammig, A., Randerson, J., Schölkopf, B., Seneviratne, S., Tomelleri, E., Zaehle, S., Reichstein, M. Environmental Research Letters, 9(3):035001, 2014 PDF Web DOI BibTeX

Empirical Inference Conference Paper A unifying view of representer theorems Argyriou, A., Dinuzzo, F. In Proceedings of the 31th International Conference on Machine Learning, 32:748-756, (Editors: Xing, E. P. and Jebera, T.), ICML, 2014 PDF PDF BibTeX

Empirical Inference Probabilistic Numerics Conference Paper Active Learning of Linear Embeddings for Gaussian Processes Garnett, R., Osborne, M., Hennig, P. In Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, 230-239, (Editors: NL Zhang and J Tian), AUAI Press , Corvallis, Oregon, UAI2014, 2014, another link: http://arxiv.org/abs/1310.6740 PDF Web BibTeX

Empirical Inference Conference Paper Active Reward Learning Daniel, C., Viering, M., Metz, J., Kroemer, O., Peters, J. In Proceedings of Robotics: Science & Systems, (Editors: Fox, D., Kavraki, LE., and Kurniawati, H.), RSS, 2014 (Published) PDF BibTeX

Empirical Inference Conference Paper An Experimental Comparison of Bayesian Optimization for Bipedal Locomotion Calandra, R., Seyfarth, A., Peters, J., Deisenroth, M. In Proceedings of 2014 IEEE International Conference on Robotics and Automation, 1951-1958, IEEE, ICRA, 2014 (Published) PDF DOI BibTeX

Empirical Inference Ph.D. Thesis Analysis of Distance Functions in Graphs Alamgir, M. University of Hamburg, Germany, University of Hamburg, Germany, 2014 BibTeX

Empirical Inference Article Assessing attention and cognitive function in completely locked-in state with event-related brain potentials and epidural electrocorticography Bensch, M., Martens, S., Halder, S., Hill, J., Nijboer, F., Ramos, A., Birbaumer, N., Bodgan, M., Kotchoubey, B., Rosenstiel, W., Schölkopf, B., Gharabaghi, A. Journal of Neural Engineering, 11(2):026006, 2014 (Published)
Objective. Patients in the completely locked-in state (CLIS), due to, for example, amyotrophic lateral sclerosis (ALS), no longer possess voluntary muscle control. Assessing attention and cognitive function in these patients during the course of the disease is a challenging but essential task for both nursing staff and physicians. Approach. An electrophysiological cognition test battery, including auditory and semantic stimuli, was applied in a late-stage ALS patient at four different time points during a six-month epidural electrocorticography (ECoG) recording period. Event-related cortical potentials (ERP), together with changes in the ECoG signal spectrum, were recorded via 128 channels that partially covered the left frontal, temporal and parietal cortex. Main results. Auditory but not semantic stimuli induced significant and reproducible ERP projecting to specific temporal and parietal cortical areas. N1/P2 responses could be detected throughout the whole study period. The highest P3 ERP was measured immediately after the patient's last communication through voluntary muscle control, which was paralleled by low theta and high gamma spectral power. Three months after the patient's last communication, i.e., in the CLIS, P3 responses could no longer be detected. At the same time, increased activity in low-frequency bands and a sharp drop of gamma spectral power were recorded. Significance. Cortical electrophysiological measures indicate at least partially intact attention and cognitive function during sparse volitional motor control for communication. Although the P3 ERP and frequency-specific changes in the ECoG spectrum may serve as indicators for CLIS, a close-meshed monitoring will be required to define the exact time point of the transition.
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Empirical Inference Conference Paper Bayesian Gait Optimization for Bipedal Locomotion Calandra, R., Gopalan, N., Seyfarth, A., Peters, J., Deisenroth, M. In Proceedings of the 8th International Conference on Learning and Intelligent Optimization , LNCS 8426:274-290, Lecture Notes in Computer Science, (Editors: Pardalos, PM., Resende, MGC., Vogiatzis, C., and Walteros, JL.), Springer, LION, 2014 (Published) PDF DOI BibTeX

Empirical Inference Master Thesis Causal Discovery in the Presence of Time-Dependent Relations or Small Sample Size Huang, B. Graduate Training Centre of Neuroscience, University of Tübingen, Germany, Graduate Training Centre of Neuroscience, University of Tübingen, Germany, 2014 BibTeX

Empirical Inference Article Causal Discovery with Continuous Additive Noise Models Peters, J., Mooij, J., Janzing, D., Schölkopf, B. Journal of Machine Learning Research, 15:2009-2053, 2014 (Published) PDF Web BibTeX

Empirical Inference Conference Paper Causal and Anti-Causal Learning in Pattern Recognition for Neuroimaging Weichwald, S., Schölkopf, B., Ball, T., Grosse-Wentrup, M. In 4th International Workshop on Pattern Recognition in Neuroimaging (PRNI), IEEE , PRNI, 2014 PDF Arxiv DOI BibTeX

Empirical Inference Poster Cluster analysis of sharp-wave ripple field potential signatures in the macaque hippocampus Ramirez-Villegas, J. F., Logothetis, N. K., Besserve, M. Computational and Systems Neuroscience Meeting (COSYNE 2014), 2014 (Published) BibTeX

Empirical Inference Conference Paper Consistency of Causal Inference under the Additive Noise Model Kpotufe, S., Sgouritsa, E., Janzing, D., Schölkopf, B. In Proceedings of the 31st International Conference on Machine Learning, W&CP 32 (1), 478-495, (Editors: Eric P. Xing and Tony Jebara), JMLR, ICML, 2014 PDF BibTeX

Empirical Inference Article Cost-Sensitive Active Learning With Lookahead: Optimizing Field Surveys for Remote Sensing Data Classification Persello, C., Boularias, A., Dalponte, M., Gobakken, T., Naesset, E., Schölkopf, B. IEEE Transactions on Geoscience and Remote Sensing, 10(52):6652 - 6664, 2014 (Published) DOI BibTeX

Empirical Inference Conference Paper Decoding Index Finger Position from EEG Using Random Forests Weichwald, S., Meyer, T., Schölkopf, B., Ball, T., Grosse-Wentrup, M. In 4th International Workshop on Cognitive Information Processing (CIP), IEEE, CIP, 2014 PDF Arxiv DOI BibTeX

Empirical Inference Thesis Development of advanced methods for improving astronomical images Schmeißer, N. Eberhard Karls Universität Tübingen, Germany, Eberhard Karls Universität Tübingen, Germany, 2014 BibTeX

Empirical Inference Article Diminished White Matter Integrity in Patients with Systemic Lupus Erythematosus Schmidt-Wilcke, T., Cagnoli, P., Wang, P., Schultz, T., Lotz, A., Mccune, W. J., Sundgren, P. C. NeuroImage: Clinical, 5:291-297, 2014 (Published) DOI BibTeX

Empirical Inference Poster Dynamical source analysis of hippocampal sharp-wave ripple episodes Ramirez-Villegas, J. F., Logothetis, N. K., Besserve, M. Bernstein Conference, 2014 (Published) DOI BibTeX

Autonomous Motion Empirical Inference Probabilistic Numerics Conference Paper Efficient Bayesian Local Model Learning for Control Meier, F., Hennig, P., Schaal, S. In Proceedings of the IEEE International Conference on Intelligent Robots and Systems, 2244 - 2249, IROS, 2014, clmc
Model-based control is essential for compliant controland force control in many modern complex robots, like humanoidor disaster robots. Due to many unknown and hard tomodel nonlinearities, analytical models of such robots are oftenonly very rough approximations. However, modern optimizationcontrollers frequently depend on reasonably accurate models,and degrade greatly in robustness and performance if modelerrors are too large. For a long time, machine learning hasbeen expected to provide automatic empirical model synthesis,yet so far, research has only generated feasibility studies butno learning algorithms that run reliably on complex robots.In this paper, we combine two promising worlds of regressiontechniques to generate a more powerful regression learningsystem. On the one hand, locally weighted regression techniquesare computationally efficient, but hard to tune due to avariety of data dependent meta-parameters. On the other hand,Bayesian regression has rather automatic and robust methods toset learning parameters, but becomes quickly computationallyinfeasible for big and high-dimensional data sets. By reducingthe complexity of Bayesian regression in the spirit of local modellearning through variational approximations, we arrive at anovel algorithm that is computationally efficient and easy toinitialize for robust learning. Evaluations on several datasetsdemonstrate very good learning performance and the potentialfor a general regression learning tool for robotics.
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Empirical Inference Conference Paper Efficient Structured Matrix Rank Minimization Yu, A. W., Ma, W., Yu, Y., Carbonell, J., Sra, S. Advances in Neural Information Processing Systems 27, 1350-1358, (Editors: Z. Ghahramani, M. Welling, C. Cortes, N.D. Lawrence and K.Q. Weinberger), Curran Associates, Inc., 28th Annual Conference on Neural Information Processing Systems (NIPS 2014), 2014 (Published) URL BibTeX

Empirical Inference Article Efficient nearest neighbors via robust sparse hashing Cherian, A., Sra, S., Morellas, V., Papanikolopoulos, N. IEEE Transactions on Image Processing, 23(8):3646-3655, 2014 (Published) DOI BibTeX

Empirical Inference Article Epidural electrocorticography for monitoring of arousal in locked-in state Martens, S., Bensch, M., Halder, S., Hill, J., Nijboer, F., Ramos-Murguialday, A., Schölkopf, B., Birbaumer, N., Gharabaghi, A. Frontiers in Human Neuroscience, 8(861), 2014 (Published) DOI BibTeX

Empirical Inference Conference Paper Estimating Causal Effects by Bounding Confounding Geiger, P., Janzing, D., Schölkopf, B. In Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence , 240-249 , (Editors: Nevin L. Zhang and Jin Tian), AUAI Press Corvallis, Oregon , UAI, 2014 PDF BibTeX

Empirical Inference Conference Paper Estimating Diffusion Network Structures: Recovery Conditions, Sample Complexity & Soft-thresholding Algorithm Daneshmand, H., Gomez Rodriguez, M., Song, L., Schölkopf, B. In Proceedings of the 31st International Conference on Machine Learning, W&CP 32 (1), 793-801, (Editors: Eric P. Xing and Tony Jebara), JMLR, ICML, 2014 PDF BibTeX

Empirical Inference Article Evaluation of Positron Emission Tomographic Tracers for Imaging of Papillomavirus-Induced Tumors in Rabbits Probst, S., Wiehr, S., Mantlik, F., Schmidt, H., Kolb, A., Münch, P., Delcuratolo, M., Stubenrauch, F., Pichler, B., Iftner, T. Molecular Imaging, 13(1):1536-0121, 2014 Web BibTeX

Empirical Inference Article Extreme events in gross primary production: a characterization across continents Zscheischler, J., Reichstein, M., Harmeling, S., Rammig, A., Tomelleri, E., Mahecha, M. Biogeosciences, 11:2909-2924, 2014 PDF Web DOI BibTeX

Empirical Inference Poster FID-guided retrospective motion correction based on autofocusing Babayeva, M., Loktyushin, A., Kober, T., Granziera, C., Nickisch, H., Gruetter, R., Krueger, G. Joint Annual Meeting ISMRM-ESMRMB 2014, Milano, Italy, 2014 BibTeX

Empirical Inference Article Factors controlling decomposition rates of fine root litter in temperate forests and grasslands Solly, E., Schöning, I., Boch, S., Kandeler, E., Marhan, S., Michalzik, B., Müller, J., Zscheischler, J., Trumbore, S., Schrumpf, M. Plant and Soil, 2014 PDF DOI BibTeX

Empirical Inference Conference Paper Fast Newton methods for the group fused lasso Wytock, M., Sra, S., Kolter, J. Z. In Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, 888-897, (Editors: Zhang, N. L. and Tian, J.), AUAI Press, UAI, 2014 (Published) URL BibTeX

Empirical Inference Book Chapter Fuzzy Fibers: Uncertainty in dMRI Tractography Schultz, T., Vilanova, A., Brecheisen, R., Kindlmann, G. In Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization, 79-92, 8, Mathematics + Visualization, (Editors: Hansen, C. D., Chen, M., Johnson, C. R., Kaufman, A. E. and Hagen, H.), Springer, 2014 (Published) BibTeX

Empirical Inference Book Chapter Higher-Order Tensors in Diffusion Imaging Schultz, T., Fuster, A., Ghosh, A., Deriche, R., Florack, L., Lim, L. In Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data, 129-161, Mathematics + Visualization, (Editors: Westin, C.-F., Vilanova, A. and Burgeth, B.), Springer, 2014 (Published) BibTeX