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2019


Life Improvement Science: A Manifesto
Life Improvement Science: A Manifesto

Lieder, F.

December 2019 (article) In revision

Abstract
Rapid technological advances present unprecedented opportunities for helping people thrive. This manifesto presents a road map for establishing a solid scientific foundation upon which those opportunities can be realized. It highlights fundamental open questions about the cognitive underpinnings of effective living and how they can be improved, supported, and augmented. These questions are at the core of my proposal for a new transdisciplinary research area called life improvement science. Recent advances have made these questions amenable to scientific rigor, and emerging approaches are paving the way towards practical strategies, clever interventions, and (intelligent) apps for empowering people to reach unprecedented levels of personal effectiveness and wellbeing.

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Life improvement science: a manifesto DOI [BibTex]


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Doing More with Less: Meta-Reasoning and Meta-Learning in Humans and Machines

Griffiths, T. L., Callaway, F., Chang, M. B., Grant, E., Krueger, P. M., Lieder, F.

Current Opinion in Behavioral Sciences, 29, pages: 24-30, October 2019 (article)

Abstract
Artificial intelligence systems use an increasing amount of computation and data to solve very specific problems. By contrast, human minds solve a wide range of problems using a fixed amount of computation and limited experience. We identify two abilities that we see as crucial to this kind of general intelligence: meta-reasoning (deciding how to allocate computational resources) and meta-learning (modeling the learning environment to make better use of limited data). We summarize the relevant AI literature and relate the resulting ideas to recent work in psychology.

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DOI [BibTex]

DOI [BibTex]


Cognitive Prostheses for Goal Achievement
Cognitive Prostheses for Goal Achievement

Lieder, F., Chen, O. X., Krueger, P. M., Griffiths, T. L.

Nature Human Behavior, 3, August 2019 (article)

Abstract
Procrastination and impulsivity take a significant toll on people’s lives and the economy at large. Both can result from the misalignment of an action's proximal rewards with its long-term value. Therefore, aligning immediate reward with long-term value could be a way to help people overcome motivational barriers and make better decisions. Previous research has shown that game elements, such as points, levels, and badges, can be used to motivate people and nudge their decisions on serious matters. Here, we develop a new approach to decision support that leveragesartificial intelligence and game elements to restructure challenging sequential decision problems in such a way that it becomes easier for people to take the right course of action. A series of four increasingly more realistic experiments suggests that this approach can enable people to make better decisions faster, procrastinate less, complete their work on time, and waste less time on unimportant tasks. These findings suggest that our method is a promising step towards developing cognitive prostheses that help people achieve their goals by enhancing their motivation and decision-making in everyday life.

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DOI [BibTex]

DOI [BibTex]


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Resource-rational analysis: Understanding human cognition as the optimal use of limited computational resources

Lieder, F., Griffiths, T. L.

Behavioral and Brain Sciences, 43, E1, Febuary 2019 (article)

Abstract
Modeling human cognition is challenging because there are infinitely many mechanisms that can generate any given observation. Some researchers address this by constraining the hypothesis space through assumptions about what the human mind can and cannot do, while others constrain it through principles of rationality and adaptation. Recent work in economics, psychology, neuroscience, and linguistics has begun to integrate both approaches by augmenting rational models with cognitive constraints, incorporating rational principles into cognitive architectures, and applying optimality principles to understanding neural representations. We identify the rational use of limited resources as a unifying principle underlying these diverse approaches, expressing it in a new cognitive modeling paradigm called resource-rational analysis. The integration of rational principles with realistic cognitive constraints makes resource-rational analysis a promising framework for reverse-engineering cognitive mechanisms and representations. It has already shed new light on the debate about human rationality and can be leveraged to revisit classic questions of cognitive psychology within a principled computational framework. We demonstrate that resource-rational models can reconcile the mind's most impressive cognitive skills with people's ostensive irrationality. Resource-rational analysis also provides a new way to connect psychological theory more deeply with artificial intelligence, economics, neuroscience, and linguistics.

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DOI [BibTex]

DOI [BibTex]


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On the positivity and magnitudes of Bayesian quadrature weights

Karvonen, T., Kanagawa, M., Särkä, S.

Statistics and Computing, 29, pages: 1317-1333, 2019 (article)

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DOI [BibTex]

DOI [BibTex]


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Probabilistic solutions to ordinary differential equations as nonlinear Bayesian filtering: a new perspective

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

Statistics and Computing, 29(6):1297-1315, 2019 (article)

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DOI [BibTex]

DOI [BibTex]


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Co-Contraction facilitates Body Stiffness Modulation during Swimming with Sensory Feedback in a Soft Biorobotic Physical Model

Jusufi, A., Vogt, D., Wood, R. J.

Integrative and Comparative Biology, 59(Supplement 1):E116-E116, Society of Integrative and Comparative Biology, McLean, VA, 2019 (article)

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DOI [BibTex]

DOI [BibTex]


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Dense connectomic reconstruction in layer 4 of the somatosensory cortex

Motta, A., Berning, M., Boergens, K. M., Staffler, B., Beining, M., Loomba, S., Hennig, P., Wissler, H., Helmstaedter, M.

Science, 366(6469):eaay3134, American Association for the Advancement of Science, 2019 (article)

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DOI [BibTex]

DOI [BibTex]


Probabilistic Linear Solvers: A Unifying View
Probabilistic Linear Solvers: A Unifying View

Bartels, S., Cockayne, J., Ipsen, I., Hennig, P.

Statistics and Computing, 29(6):1249-1263, 2019 (article)

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


A Rational Reinterpretation of Dual Process Theories
A Rational Reinterpretation of Dual Process Theories

Milli, S., Lieder, F., Griffiths, T. L.

2019 (article)

Abstract
Highly influential "dual-process" accounts of human cognition postulate the coexistence of a slow accurate system with a fast error-prone system. But why would there be just two systems rather than, say, one or 93? Here, we argue that a dual-process architecture might be neither arbitrary nor irrational, but might instead reflect a rational tradeoff between the cognitive flexibility afforded by multiple systems and the time and effort required to choose between them. We investigate what the optimal set and number of cognitive systems would be depending on the structure of the environment. We find that the optimal number of systems depends on the variability of the environment and the difficulty of deciding when which system should be used. Furthermore, when having two systems is optimal, then the first system is fast but error-prone and the second system is slow but accurate. Our findings thereby provide a rational reinterpretation of dual-process theories.

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DOI [BibTex]

DOI [BibTex]

2017


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]

2017


link (url) Project Page [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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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.

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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)

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link (url) [BibTex]

link (url) [BibTex]

2015


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Probabilistic Interpretation of Linear Solvers

Hennig, P.

SIAM Journal on Optimization, 25(1):234-260, 2015 (article)

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Web PDF link (url) DOI [BibTex]

2015


Web PDF link (url) DOI [BibTex]


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Probabilistic numerics and uncertainty in computations

Hennig, P., Osborne, M. A., Girolami, M.

Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 471(2179), 2015 (article)

Abstract
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.

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PDF DOI [BibTex]

PDF DOI [BibTex]