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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)

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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.

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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.

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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)

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[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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Community detection, link prediction, and layer interdependence in multilayer networks

De Bacco, C., Power, E. A., Larremore, D. B., Moore, C.

Physical Review E, 95(4):042317, APS, 2017 (article)

pio

Code Preprint link (url) Project Page [BibTex]

Code Preprint link (url) Project Page [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)

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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)

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[BibTex]

[BibTex]

2012


Entropy Search for Information-Efficient Global Optimization
Entropy Search for Information-Efficient Global Optimization

Hennig, P., Schuler, C.

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

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

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PDF Web Project Page [BibTex]

2012


PDF Web Project Page [BibTex]


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Tail-assisted pitch control in lizards, robots and dinosaurs

Libby, T., Moore, T., Chang, E., Li, D., Cohen, D., Jusufi, A., Full, R.

Nature, 2012 (article)

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link (url) [BibTex]

link (url) [BibTex]


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Rapid Inversion: Running Animals and Robots Swing like a Pendulum under Ledges

Mongeau, J., McRae, B., Jusufi, A., Birkmeyer, P., Hoover, A., Fearing, R.

PLoS One, 2012 (article)

bio

link (url) [BibTex]

link (url) [BibTex]


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Burn-in, bias, and the rationality of anchoring

Lieder, F., Griffiths, T. L., Goodman, N. D.

Advances in Neural Information Processing Systems 25, pages: 2699-2707, 2012 (article)

Abstract
Bayesian inference provides a unifying framework for addressing problems in machine learning, artificial intelligence, and robotics, as well as the problems facing the human mind. Unfortunately, exact Bayesian inference is intractable in all but the simplest models. Therefore minds and machines have to approximate Bayesian inference. Approximate inference algorithms can achieve a wide range of time-accuracy tradeoffs, but what is the optimal tradeoff? We investigate time-accuracy tradeoffs using the Metropolis-Hastings algorithm as a metaphor for the mind's inference algorithm(s). We find that reasonably accurate decisions are possible long before the Markov chain has converged to the posterior distribution, i.e. during the period known as burn-in. Therefore the strategy that is optimal subject to the mind's bounded processing speed and opportunity costs may perform so few iterations that the resulting samples are biased towards the initial value. The resulting cognitive process model provides a rational basis for the anchoring-and-adjustment heuristic. The model's quantitative predictions are tested against published data on anchoring in numerical estimation tasks. Our theoretical and empirical results suggest that the anchoring bias is consistent with approximate Bayesian inference.

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link (url) [BibTex]

link (url) [BibTex]

2006


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Die Effektivität von schriftlichen und graphischen Warnhinweisen auf Zigarettenschachteln

Petersen, L., Lieder, F.

Zeitschrift für Sozialpsychologie, 37(4):245-258, Verlag Hans Huber, 2006 (article)

Abstract
In der vorliegenden Studie wurde die Effektivität von furchterregenden Warnhinweisen bei jugendlichen Rauchern und Raucherinnen analysiert. 336 Raucher/-innen (Durchschnittsalter: 15 Jahre) wurden schriftliche oder graphische Warnhinweise auf Zigarettenpackungen präsentiert (Experimentalbedingungen; n = 96, n = 119), oder sie erhielten keine Warnhinweise (Kontrollbedingung; n = 94). Anschließend wurden die Modellfaktoren des revidierten Modells der Schutzmotivation (Arthur & Quester, 2004) erhoben. Die Ergebnisse stützen die Hypothese, dass die Faktoren «Schweregrad der Schädigung» und «Wahrscheinlichkeit der Schädigung» die Verhaltenswahrscheinlichkeit, weniger oder leichtere Zigaretten zu rauchen, vermittelt über den Mediator «Furcht» beeinflussen. Die Verhaltenswahrscheinlichkeit wurde dagegen nicht von den drei experimentellen Bedingungen beeinflusst. Auch konnten die Faktoren «Handlungswirksamkeitserwartungen» und «Selbstwirksamkeitserwartungen» nicht als Moderatoren des Zusammenhangs zwischen Furcht und Verhaltenswahrscheinlichkeit bestätigt werden.

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DOI [BibTex]

2006


DOI [BibTex]