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2018


Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective
Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective

Tronarp, F., Kersting, H., Särkkä, S., Hennig, P.

ArXiv preprint 2018, arXiv:1810.03440 [stat.ME], October 2018 (article)

Abstract
We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement sequence to consists of the observations of the difference between the derivative of the GP and the vector field evaluated at the GP---which are all identically zero at the solution of the ODE. When the GP has a state-space representation, the problem can be reduced to a Bayesian state estimation problem and all widely-used approximations to the Bayesian filtering and smoothing problems become applicable. Furthermore, all previous GP-based ODE solvers, which were formulated in terms of generating synthetic measurements of the vector field, come out as specific approximations. We derive novel solvers, both Gaussian and non-Gaussian, from the Bayesian state estimation problem posed in this paper and compare them with other probabilistic solvers in illustrative experiments.

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link (url) Project Page [BibTex]

2018



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Convergence Rates of Gaussian ODE Filters

Kersting, H., Sullivan, T. J., Hennig, P.

arXiv preprint 2018, arXiv:1807.09737 [math.NA], July 2018 (article)

Abstract
A recently-introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems. These methods model the true solution $x$ and its first $q$ derivatives a priori as a Gauss--Markov process $\boldsymbol{X}$, which is then iteratively conditioned on information about $\dot{x}$. We prove worst-case local convergence rates of order $h^{q+1}$ for a wide range of versions of this Gaussian ODE filter, as well as global convergence rates of order $h^q$ in the case of $q=1$ and an integrated Brownian motion prior, and analyse how inaccurate information on $\dot{x}$ coming from approximate evaluations of $f$ affects these rates. Moreover, we present explicit formulas for the steady states and show that the posterior confidence intervals are well calibrated in all considered cases that exhibit global convergence---in the sense that they globally contract at the same rate as the truncation error.

pn

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


Learning 3D Shape Completion under Weak Supervision
Learning 3D Shape Completion under Weak Supervision

Stutz, D., Geiger, A.

Arxiv, May 2018 (article)

Abstract
We address the problem of 3D shape completion from sparse and noisy point clouds, a fundamental problem in computer vision and robotics. Recent approaches are either data-driven or learning-based: Data-driven approaches rely on a shape model whose parameters are optimized to fit the observations; Learning-based approaches, in contrast, avoid the expensive optimization step by learning to directly predict complete shapes from incomplete observations in a fully-supervised setting. However, full supervision is often not available in practice. In this work, we propose a weakly-supervised learning-based approach to 3D shape completion which neither requires slow optimization nor direct supervision. While we also learn a shape prior on synthetic data, we amortize, i.e., learn, maximum likelihood fitting using deep neural networks resulting in efficient shape completion without sacrificing accuracy. On synthetic benchmarks based on ShapeNet and ModelNet as well as on real robotics data from KITTI and Kinect, we demonstrate that the proposed amortized maximum likelihood approach is able to compete with fully supervised baselines and outperforms data-driven approaches, while requiring less supervision and being significantly faster.

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PDF Project Page Project Page [BibTex]


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Rational metareasoning and the plasticity of cognitive control

Lieder, F., Shenhav, A., Musslick, S., Griffiths, T. L.

PLOS Computational Biology, 14(4):e1006043, Public Library of Science, April 2018 (article)

Abstract
The human brain has the impressive capacity to adapt how it processes information to high-level goals. While it is known that these cognitive control skills are malleable and can be improved through training, the underlying plasticity mechanisms are not well understood. Here, we develop and evaluate a model of how people learn when to exert cognitive control, which controlled process to use, and how much effort to exert. We derive this model from a general theory according to which the function of cognitive control is to select and configure neural pathways so as to make optimal use of finite time and limited computational resources. The central idea of our Learned Value of Control model is that people use reinforcement learning to predict the value of candidate control signals of different types and intensities based on stimulus features. This model correctly predicts the learning and transfer effects underlying the adaptive control-demanding behavior observed in an experiment on visual attention and four experiments on interference control in Stroop and Flanker paradigms. Moreover, our model explained these findings significantly better than an associative learning model and a Win-Stay Lose-Shift model. Our findings elucidate how learning and experience might shape people’s ability and propensity to adaptively control their minds and behavior. We conclude by predicting under which circumstances these learning mechanisms might lead to self-control failure.

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Rational metareasoning and the plasticity of cognitive control DOI Project Page Project Page [BibTex]

Rational metareasoning and the plasticity of cognitive control DOI Project Page Project Page [BibTex]


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Over-Representation of Extreme Events in Decision Making Reflects Rational Use of Cognitive Resources

Lieder, F., Griffiths, T. L., Hsu, M.

Psychological Review, 125(1):1-32, January 2018 (article)

Abstract
People’s decisions and judgments are disproportionately swayed by improbable but extreme eventualities, such as terrorism, that come to mind easily. This article explores whether such availability biases can be reconciled with rational information processing by taking into account the fact that decision-makers value their time and have limited cognitive resources. Our analysis suggests that to make optimal use of their finite time decision-makers should over-represent the most important potential consequences relative to less important, put potentially more probable, outcomes. To evaluate this account we derive and test a model we call utility-weighted sampling. Utility-weighted sampling estimates the expected utility of potential actions by simulating their outcomes. Critically, outcomes with more extreme utilities have a higher probability of being simulated. We demonstrate that this model can explain not only people’s availability bias in judging the frequency of extreme events but also a wide range of cognitive biases in decisions from experience, decisions from description, and memory recall.

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DOI [BibTex]

DOI [BibTex]


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Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences

Kanagawa, M., Hennig, P., Sejdinovic, D., Sriperumbudur, B. K.

Arxiv e-prints, arXiv:1805.08845v1 [stat.ML], 2018 (article)

Abstract
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and frequentist kernel methods based on reproducing kernel Hilbert spaces on the other. It is widely known in machine learning that these two formalisms are closely related; for instance, the estimator of kernel ridge regression is identical to the posterior mean of Gaussian process regression. However, they have been studied and developed almost independently by two essentially separate communities, and this makes it difficult to seamlessly transfer results between them. Our aim is to overcome this potential difficulty. To this end, we review several old and new results and concepts from either side, and juxtapose algorithmic quantities from each framework to highlight close similarities. We also provide discussions on subtle philosophical and theoretical differences between the two approaches.

pn ei

arXiv [BibTex]

arXiv [BibTex]


Augmented Reality Meets Computer Vision: Efficient Data Generation for Urban Driving Scenes
Augmented Reality Meets Computer Vision: Efficient Data Generation for Urban Driving Scenes

Alhaija, H., Mustikovela, S., Mescheder, L., Geiger, A., Rother, C.

International Journal of Computer Vision (IJCV), 2018, 2018 (article)

Abstract
The success of deep learning in computer vision is based on the availability of large annotated datasets. To lower the need for hand labeled images, virtually rendered 3D worlds have recently gained popularity. Unfortunately, creating realistic 3D content is challenging on its own and requires significant human effort. In this work, we propose an alternative paradigm which combines real and synthetic data for learning semantic instance segmentation and object detection models. Exploiting the fact that not all aspects of the scene are equally important for this task, we propose to augment real-world imagery with virtual objects of the target category. Capturing real-world images at large scale is easy and cheap, and directly provides real background appearances without the need for creating complex 3D models of the environment. We present an efficient procedure to augment these images with virtual objects. In contrast to modeling complete 3D environments, our data augmentation approach requires only a few user interactions in combination with 3D models of the target object category. Leveraging our approach, we introduce a novel dataset of augmented urban driving scenes with 360 degree images that are used as environment maps to create realistic lighting and reflections on rendered objects. We analyze the significance of realistic object placement by comparing manual placement by humans to automatic methods based on semantic scene analysis. This allows us to create composite images which exhibit both realistic background appearance as well as a large number of complex object arrangements. Through an extensive set of experiments, we conclude the right set of parameters to produce augmented data which can maximally enhance the performance of instance segmentation models. Further, we demonstrate the utility of the proposed approach on training standard deep models for semantic instance segmentation and object detection of cars in outdoor driving scenarios. We test the models trained on our augmented data on the KITTI 2015 dataset, which we have annotated with pixel-accurate ground truth, and on the Cityscapes dataset. Our experiments demonstrate that the models trained on augmented imagery generalize better than those trained on fully synthetic data or models trained on limited amounts of annotated real data.

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pdf Project Page [BibTex]

pdf Project Page [BibTex]


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Counterfactual Mean Embedding: A Kernel Method for Nonparametric Causal Inference

Muandet, K., Kanagawa, M., Saengkyongam, S., Marukata, S.

Arxiv e-prints, arXiv:1805.08845v1 [stat.ML], 2018 (article)

Abstract
This paper introduces a novel Hilbert space representation of a counterfactual distribution---called counterfactual mean embedding (CME)---with applications in nonparametric causal inference. Counterfactual prediction has become an ubiquitous tool in machine learning applications, such as online advertisement, recommendation systems, and medical diagnosis, whose performance relies on certain interventions. To infer the outcomes of such interventions, we propose to embed the associated counterfactual distribution into a reproducing kernel Hilbert space (RKHS) endowed with a positive definite kernel. Under appropriate assumptions, the CME allows us to perform causal inference over the entire landscape of the counterfactual distribution. The CME can be estimated consistently from observational data without requiring any parametric assumption about the underlying distributions. We also derive a rate of convergence which depends on the smoothness of the conditional mean and the Radon-Nikodym derivative of the underlying marginal distributions. Our framework can deal with not only real-valued outcome, but potentially also more complex and structured outcomes such as images, sequences, and graphs. Lastly, our experimental results on off-policy evaluation tasks demonstrate the advantages of the proposed estimator.

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arXiv [BibTex]

arXiv [BibTex]


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Model-based Kernel Sum Rule: Kernel Bayesian Inference with Probabilistic Models

Nishiyama, Y., Kanagawa, M., Gretton, A., Fukumizu, K.

Arxiv e-prints, arXiv:1409.5178v2 [stat.ML], 2018 (article)

Abstract
Kernel Bayesian inference is a powerful nonparametric approach to performing Bayesian inference in reproducing kernel Hilbert spaces or feature spaces. In this approach, kernel means are estimated instead of probability distributions, and these estimates can be used for subsequent probabilistic operations (as for inference in graphical models) or in computing the expectations of smooth functions, for instance. Various algorithms for kernel Bayesian inference have been obtained by combining basic rules such as the kernel sum rule (KSR), kernel chain rule, kernel product rule and kernel Bayes' rule. However, the current framework only deals with fully nonparametric inference (i.e., all conditional relations are learned nonparametrically), and it does not allow for flexible combinations of nonparametric and parametric inference, which are practically important. Our contribution is in providing a novel technique to realize such combinations. We introduce a new KSR referred to as the model-based KSR (Mb-KSR), which employs the sum rule in feature spaces under a parametric setting. Incorporating the Mb-KSR into existing kernel Bayesian framework provides a richer framework for hybrid (nonparametric and parametric) kernel Bayesian inference. As a practical application, we propose a novel filtering algorithm for state space models based on the Mb-KSR, which combines the nonparametric learning of an observation process using kernel mean embedding and the additive Gaussian noise model for a state transition process. While we focus on additive Gaussian noise models in this study, the idea can be extended to other noise models, such as the Cauchy and alpha-stable noise models.

pn

arXiv [BibTex]

arXiv [BibTex]


A probabilistic model for the numerical solution of initial value problems
A probabilistic model for the numerical solution of initial value problems

Schober, M., Särkkä, S., Philipp Hennig,

Statistics and Computing, Springer US, 2018 (article)

Abstract
We study connections between ordinary differential equation (ODE) solvers and probabilistic regression methods in statistics. We provide a new view of probabilistic ODE solvers as active inference agents operating on stochastic differential equation models that estimate the unknown initial value problem (IVP) solution from approximate observations of the solution derivative, as provided by the ODE dynamics. Adding to this picture, we show that several multistep methods of Nordsieck form can be recast as Kalman filtering on q-times integrated Wiener processes. Doing so provides a family of IVP solvers that return a Gaussian posterior measure, rather than a point estimate. We show that some such methods have low computational overhead, nontrivial convergence order, and that the posterior has a calibrated concentration rate. Additionally, we suggest a step size adaptation algorithm which completes the proposed method to a practically useful implementation, which we experimentally evaluate using a representative set of standard codes in the DETEST benchmark set.

pn

PDF Code DOI Project Page [BibTex]


Learning 3D Shape Completion under Weak Supervision
Learning 3D Shape Completion under Weak Supervision

Stutz, D., Geiger, A.

International Journal of Computer Vision (IJCV), 2018, 2018 (article)

Abstract
We address the problem of 3D shape completion from sparse and noisy point clouds, a fundamental problem in computer vision and robotics. Recent approaches are either data-driven or learning-based: Data-driven approaches rely on a shape model whose parameters are optimized to fit the observations; Learning-based approaches, in contrast, avoid the expensive optimization step by learning to directly predict complete shapes from incomplete observations in a fully-supervised setting. However, full supervision is often not available in practice. In this work, we propose a weakly-supervised learning-based approach to 3D shape completion which neither requires slow optimization nor direct supervision. While we also learn a shape prior on synthetic data, we amortize, i.e., learn, maximum likelihood fitting using deep neural networks resulting in efficient shape completion without sacrificing accuracy. On synthetic benchmarks based on ShapeNet and ModelNet as well as on real robotics data from KITTI and Kinect, we demonstrate that the proposed amortized maximum likelihood approach is able to compete with a fully supervised baseline and outperforms the data-driven approach of Engelmann et al., while requiring less supervision and being significantly faster.

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pdf Project Page [BibTex]

pdf Project Page [BibTex]


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The Computational Challenges of Pursuing Multiple Goals: Network Structure of Goal Systems Predicts Human Performance

Reichman, D., Lieder, F., Bourgin, D. D., Talmon, N., Griffiths, T. L.

PsyArXiv, 2018 (article)

Abstract
Extant psychological theories attribute people’s failure to achieve their goals primarily to failures of self-control, insufficient motivation, or lacking skills. We develop a complementary theory specifying conditions under which the computational complexity of making the right decisions becomes prohibitive of goal achievement regardless of skill or motivation. We support our theory by predicting human performance from factors determining the computational complexity of selecting the optimal set of means for goal achievement. Following previous theories of goal pursuit, we express the relationship between goals and means as a bipartite graph where edges between means and goals indicate which means can be used to achieve which goals. This allows us to map two computational challenges that arise in goal achievement onto two classic combinatorial optimization problems: Set Cover and Maximum Coverage. While these problems are believed to be computationally intractable on general networks, their solution can be nevertheless efficiently approximated when the structure of the network resembles a tree. Thus, our initial prediction was that people should perform better with goal systems that are more tree-like. In addition, our theory predicted that people’s performance at selecting means should be a U-shaped function of the average number of goals each means is relevant to and the average number of means through which each goal could be accomplished. Here we report on six behavioral experiments which confirmed these predictions. Our results suggest that combinatorial parameters that are instrumental to algorithm design can also be useful for understanding when and why people struggle to pursue their goals effectively.

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DOI [BibTex]

DOI [BibTex]


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Geckos Race across Water using Multiple Mechanisms

Nirody, J., Jinn, J., Libby, T., Lee, T., Jusufi, A., Hu, D., Full, R.

Current Biology, 2018 (article)

bio

[BibTex]

[BibTex]


Object Scene Flow
Object Scene Flow

Menze, M., Heipke, C., Geiger, A.

ISPRS Journal of Photogrammetry and Remote Sensing, 2018 (article)

Abstract
This work investigates the estimation of dense three-dimensional motion fields, commonly referred to as scene flow. While great progress has been made in recent years, large displacements and adverse imaging conditions as observed in natural outdoor environments are still very challenging for current approaches to reconstruction and motion estimation. In this paper, we propose a unified random field model which reasons jointly about 3D scene flow as well as the location, shape and motion of vehicles in the observed scene. We formulate the problem as the task of decomposing the scene into a small number of rigidly moving objects sharing the same motion parameters. Thus, our formulation effectively introduces long-range spatial dependencies which commonly employed local rigidity priors are lacking. Our inference algorithm then estimates the association of image segments and object hypotheses together with their three-dimensional shape and motion. We demonstrate the potential of the proposed approach by introducing a novel challenging scene flow benchmark which allows for a thorough comparison of the proposed scene flow approach with respect to various baseline models. In contrast to previous benchmarks, our evaluation is the first to provide stereo and optical flow ground truth for dynamic real-world urban scenes at large scale. Our experiments reveal that rigid motion segmentation can be utilized as an effective regularizer for the scene flow problem, improving upon existing two-frame scene flow methods. At the same time, our method yields plausible object segmentations without requiring an explicitly trained recognition model for a specific object class.

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Project Page [BibTex]

Project Page [BibTex]

2017


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Strategy selection as rational metareasoning

Lieder, F., Griffiths, T. L.

Psychological Review, 124, pages: 762-794, American Psychological Association, November 2017 (article)

Abstract
Many contemporary accounts of human reasoning assume that the mind is equipped with multiple heuristics that could be deployed to perform a given task. This raises the question of how the mind determines when to use which heuristic. To answer this question, we developed a rational model of strategy selection, based on the theory of rational metareasoning developed in the artificial intelligence literature. According to our model people learn to efficiently choose the strategy with the best cost–benefit tradeoff by learning a predictive model of each strategy’s performance. We found that our model can provide a unifying explanation for classic findings from domains ranging from decision-making to arithmetic by capturing the variability of people’s strategy choices, their dependence on task and context, and their development over time. Systematic model comparisons supported our theory, and 4 new experiments confirmed its distinctive predictions. Our findings suggest that people gradually learn to make increasingly more rational use of fallible heuristics. This perspective reconciles the 2 poles of the debate about human rationality by integrating heuristics and biases with learning and rationality. (APA PsycInfo Database Record (c) 2017 APA, all rights reserved)

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DOI Project Page [BibTex]

2017


DOI Project Page [BibTex]


Probabilistic Line Searches for Stochastic Optimization
Probabilistic Line Searches for Stochastic Optimization

Mahsereci, M., Hennig, P.

Journal of Machine Learning Research, 18(119):1-59, November 2017 (article)

pn

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


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Empirical Evidence for Resource-Rational Anchoring and Adjustment

Lieder, F., Griffiths, T. L., Huys, Q. J. M., Goodman, N. D.

Psychonomic Bulletin \& Review, 25, pages: 775-784, Springer, May 2017 (article)

Abstract
People’s estimates of numerical quantities are systematically biased towards their initial guess. This anchoring bias is usually interpreted as sign of human irrationality, but it has recently been suggested that the anchoring bias instead results from people’s rational use of their finite time and limited cognitive resources. If this were true, then adjustment should decrease with the relative cost of time. To test this hypothesis, we designed a new numerical estimation paradigm that controls people’s knowledge and varies the cost of time and error independently while allowing people to invest as much or as little time and effort into refining their estimate as they wish. Two experiments confirmed the prediction that adjustment decreases with time cost but increases with error cost regardless of whether the anchor was self-generated or provided. These results support the hypothesis that people rationally adapt their number of adjustments to achieve a near-optimal speed-accuracy tradeoff. This suggests that the anchoring bias might be a signature of the rational use of finite time and limited cognitive resources rather than a sign of human irrationality.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Convergence Analysis of Deterministic Kernel-Based Quadrature Rules in Misspecified Settings

Kanagawa, M., Sriperumbudur, B. K., Fukumizu, K.

Arxiv e-prints, arXiv:1709.00147v1 [math.NA], 2017 (article)

Abstract
This paper presents convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less smooth than a Sobolev RKHS based on which a quadrature rule is constructed. We provide convergence guarantees based on two different assumptions on a quadrature rule: one on quadrature weights, and the other on design points. More precisely, we show that convergence rates can be derived (i) if the sum of absolute weights remains constant (or does not increase quickly), or (ii) if the minimum distance between distance design points does not decrease very quickly. As a consequence of the latter result, we derive a rate of convergence for Bayesian quadrature in misspecified settings. We reveal a condition on design points to make Bayesian quadrature robust to misspecification, and show that, under this condition, it may adaptively achieve the optimal rate of convergence in the Sobolev space of a lesser order (i.e., of the unknown smoothness of a test integrand), under a slightly stronger regularity condition on the integrand.

pn

arXiv [BibTex]

arXiv [BibTex]


Early Stopping Without a Validation Set
Early Stopping Without a Validation Set

Mahsereci, M., Balles, L., Lassner, C., Hennig, P.

arXiv preprint arXiv:1703.09580, 2017 (article)

Abstract
Early stopping is a widely used technique to prevent poor generalization performance when training an over-expressive model by means of gradient-based optimization. To find a good point to halt the optimizer, a common practice is to split the dataset into a training and a smaller validation set to obtain an ongoing estimate of the generalization performance. In this paper we propose a novel early stopping criterion which is based on fast-to-compute, local statistics of the computed gradients and entirely removes the need for a held-out validation set. Our experiments show that this is a viable approach in the setting of least-squares and logistic regression as well as neural networks.

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link (url) Project Page Project Page [BibTex]


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Krylov Subspace Recycling for Fast Iterative Least-Squares in Machine Learning

Roos, F. D., Hennig, P.

arXiv preprint arXiv:1706.00241, 2017 (article)

Abstract
Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time approximations, such as spectral and inducing-point methods, have been suggested and are now in wide use. These are low-rank approximations that choose the low-rank space a priori and do not refine it over time. While this allows linear cost in the data-set size, it also causes a finite, uncorrected approximation error. Authors from numerical linear algebra have explored ways to iteratively refine such low-rank approximations, at a cost of a small number of matrix-vector multiplications. This idea is particularly interesting in the many situations in machine learning where one has to solve a sequence of related symmetric positive definite linear problems. From the machine learning perspective, such deflation methods can be interpreted as transfer learning of a low-rank approximation across a time-series of numerical tasks. We study the use of such methods for our field. Our empirical results show that, on regression and classification problems of intermediate size, this approach can interpolate between low computational cost and numerical precision.

pn

link (url) Project Page [BibTex]


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Fast Bayesian hyperparameter optimization on large datasets

Klein, A., Falkner, S., Bartels, S., Hennig, P., Hutter, F.

Electronic Journal of Statistics, 11, 2017 (article)

pn

[BibTex]

[BibTex]


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Efficiency of analytical and sampling-based uncertainty propagation in intensity-modulated proton therapy

Wahl, N., Hennig, P., Wieser, H. P., Bangert, M.

Physics in Medicine & Biology, 62(14):5790-5807, 2017 (article)

Abstract
The sensitivity of intensity-modulated proton therapy (IMPT) treatment plans to uncertainties can be quantified and mitigated with robust/min-max and stochastic/probabilistic treatment analysis and optimization techniques. Those methods usually rely on sparse random, importance, or worst-case sampling. Inevitably, this imposes a trade-off between computational speed and accuracy of the uncertainty propagation. Here, we investigate analytical probabilistic modeling (APM) as an alternative for uncertainty propagation and minimization in IMPT that does not rely on scenario sampling. APM propagates probability distributions over range and setup uncertainties via a Gaussian pencil-beam approximation into moments of the probability distributions over the resulting dose in closed form. It supports arbitrary correlation models and allows for efficient incorporation of fractionation effects regarding random and systematic errors. We evaluate the trade-off between run-time and accuracy of APM uncertainty computations on three patient datasets. Results are compared against reference computations facilitating importance and random sampling. Two approximation techniques to accelerate uncertainty propagation and minimization based on probabilistic treatment plan optimization are presented. Runtimes are measured on CPU and GPU platforms, dosimetric accuracy is quantified in comparison to a sampling-based benchmark (5000 random samples). APM accurately propagates range and setup uncertainties into dose uncertainties at competitive run-times (GPU ##IMG## [http://ej.iop.org/images/0031-9155/62/14/5790/pmbaa6ec5ieqn001.gif] {$\leqslant {5}$} min). The resulting standard deviation (expectation value) of dose show average global ##IMG## [http://ej.iop.org/images/0031-9155/62/14/5790/pmbaa6ec5ieqn002.gif] {$\gamma_{{3}\% / {3}~{\rm mm}}$} pass rates between 94.2% and 99.9% (98.4% and 100.0%). All investigated importance sampling strategies provided less accuracy at higher run-times considering only a single fraction. Considering fractionation, APM uncertainty propagation and treatment plan optimization was proven to be possible at constant time complexity, while run-times of sampling-based computations are linear in the number of fractions. Using sum sampling within APM, uncertainty propagation can only be accelerated at the cost of reduced accuracy in variance calculations. For probabilistic plan optimization, we were able to approximate the necessary pre-computations within seconds, yielding treatment plans of similar quality as gained from exact uncertainty propagation. APM is suited to enhance the trade-off between speed and accuracy in uncertainty propagation and probabilistic treatment plan optimization, especially in the context of fractionation. This brings fully-fledged APM computations within reach of clinical application.

pn

link (url) [BibTex]

link (url) [BibTex]


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Analytical probabilistic modeling of RBE-weighted dose for ion therapy

Wieser, H., Hennig, P., Wahl, N., Bangert, M.

Physics in Medicine and Biology (PMB), 62(23):8959-8982, 2017 (article)

pn

link (url) [BibTex]

link (url) [BibTex]


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A computerized training program for teaching people how to plan better

Lieder, F., Krueger, P. M., Callaway, F., Griffiths, T. L.

PsyArXiv, 2017 (article)

re

Project Page [BibTex]

Project Page [BibTex]


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Toward a rational and mechanistic account of mental effort

Shenhav, A., Musslick, S., Lieder, F., Kool, W., Griffiths, T., Cohen, J., Botvinick, M.

Annual Review of Neuroscience, 40, pages: 99-124, Annual Reviews, 2017 (article)

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Project Page [BibTex]

Project Page [BibTex]


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The anchoring bias reflects rational use of cognitive resources

Lieder, F., Griffiths, T. L., Huys, Q. J. M., Goodman, N. D.

Psychonomic Bulletin \& Review, 25, pages: 762-794, Springer, 2017 (article)

re

[BibTex]

[BibTex]

2013


Vision meets Robotics: The {KITTI} Dataset
Vision meets Robotics: The KITTI Dataset

Geiger, A., Lenz, P., Stiller, C., Urtasun, R.

International Journal of Robotics Research, 32(11):1231 - 1237 , Sage Publishing, September 2013 (article)

Abstract
We present a novel dataset captured from a VW station wagon for use in mobile robotics and autonomous driving research. In total, we recorded 6 hours of traffic scenarios at 10-100 Hz using a variety of sensor modalities such as high-resolution color and grayscale stereo cameras, a Velodyne 3D laser scanner and a high-precision GPS/IMU inertial navigation system. The scenarios are diverse, capturing real-world traffic situations and range from freeways over rural areas to inner-city scenes with many static and dynamic objects. Our data is calibrated, synchronized and timestamped, and we provide the rectified and raw image sequences. Our dataset also contains object labels in the form of 3D tracklets and we provide online benchmarks for stereo, optical flow, object detection and other tasks. This paper describes our recording platform, the data format and the utilities that we provide.

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pdf DOI [BibTex]

2013


pdf DOI [BibTex]


Quasi-Newton Methods: A New Direction
Quasi-Newton Methods: A New Direction

Hennig, P., Kiefel, M.

Journal of Machine Learning Research, 14(1):843-865, March 2013 (article)

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.

ei ps pn

website+code pdf link (url) [BibTex]

website+code pdf link (url) [BibTex]


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Analytical probabilistic modeling for radiation therapy treatment planning

Bangert, M., Hennig, P., Oelfke, U.

Physics in Medicine and Biology, 58(16):5401-5419, 2013 (article)

ei pn

PDF DOI [BibTex]

PDF DOI [BibTex]


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Modelling trial-by-trial changes in the mismatch negativity

Lieder, F., Daunizeau, J., Garrido, M. I., Friston, K. J., Stephan, K. E.

{PLoS} {C}omputational {B}iology, 9(2):e1002911, Public Library of Science, 2013 (article)

re

[BibTex]

[BibTex]


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A neurocomputational model of the mismatch negativity

Lieder, F., Stephan, K. E., Daunizeau, J., Garrido, M. I., Friston, K. J.

{PLoS Computational Biology}, 9(11):e1003288, Public Library of Science, 2013 (article)

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[BibTex]

[BibTex]