Probabilistic programming in Python using PyMC3

Salvatier, John; Wiecki, Thomas V.; Fonnesbeck, Christopher

doi:10.7287/peerj.preprints.1686

Cited by 597 publications

(696 citation statements)

References 3 publications

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“…Despite this complication, it is relatively straightforward to fit the RSM as a Bayesian model using a probabilistic programming framework, such as BUGS, JAGS, or Stan. For the models in this paper, we used the PyMC3 Python package (Patil et al, 2010; Salvatier et al, 2015), which is built on the Theano deep learning package (Bastien et al, 2012; Bergstra et al, 2010; version 0.9.0.dev2) and implements the state-of-the-art No U-Turn MCMC Sampler (Hoffman & Gelman, 2014). An alpha version of our NiPyMC analysis package is available online (https://github.com/PsychoinformaticsLab/nipymc; DOI, 10.5281/zenodo.168087; Yarkoni & Westfall, 2016).…”

Section: Methodsmentioning

confidence: 99%

Fixing the stimulus-as-fixed-effect fallacy in task fMRI

Westfall¹,

Nichols²,

Yarkoni³

2016

Wellcome Open Res

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Most functional magnetic resonance imaging (fMRI) experiments record the brain’s responses to samples of stimulus materials (e.g., faces or words). Yet the statistical modeling approaches used in fMRI research universally fail to model stimulus variability in a manner that affords population generalization, meaning that researchers’ conclusions technically apply only to the precise stimuli used in each study, and cannot be generalized to new stimuli. A direct consequence of this stimulus-as-fixed-effect fallacy is that the majority of published fMRI studies have likely overstated the strength of the statistical evidence they report. Here we develop a Bayesian mixed model (the random stimulus model; RSM) that addresses this problem, and apply it to a range of fMRI datasets. Results demonstrate considerable inflation (50-200% in most of the studied datasets) of test statistics obtained from standard “summary statistics”-based approaches relative to the corresponding RSM models. We demonstrate how RSMs can be used to improve parameter estimates, properly control false positive rates, and test novel research hypotheses about stimulus-level variability in human brain responses.

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Section: Methodsmentioning

confidence: 99%

Fixing the stimulus-as-fixed-effect fallacy in task fMRI

Westfall¹,

Nichols²,

Yarkoni³

2016

Wellcome Open Res

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“…Hence, in total, there are three-level comparisons in our experiment, i.e., model comparison; prior comparison; and uncertainty comparison. The entire experiment is written in Python, using Theano [34], and Pymc3 [35] libraries. The partial code to produce this study is available from: https://github.com/LeonBai/Uncertainty-Flow.…”

Section: Methodsmentioning

confidence: 99%

Uncertainty Flow Facilitates Zero-Shot Multi-Label Learning in Affective Facial Analysis

2018

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Featured Application: The proposed Uncertainty Flow framework may benefit the facial analysis with its promised elevation in discriminability in multi-label affective classification tasks. Moreover, this framework also allows the efficient model training and between tasks knowledge transfer. The applications that rely heavily on continuous prediction on emotional valance, e.g., to monitor prisoners' emotional stability in jail, can be directly benefited from our framework. Abstract:To lower the single-label dependency on affective facial analysis, it urges the fruition of multi-label affective learning. The impediment to practical implementation of existing multi-label algorithms pertains to scarcity of scalable multi-label training datasets. To resolve this, an inductive transfer learning based framework, i.e., Uncertainty Flow, is put forward in this research to allow knowledge transfer from a single labelled emotion recognition task to a multi-label affective recognition task. I.e., the model uncertainty-which can be quantified in Uncertainty Flow-is distilled from a single-label learning task. The distilled model uncertainty ensures the later efficient zero-shot multi-label affective learning. On the theoretical perspective, within our proposed Uncertainty Flow framework, the feasibility of applying weakly informative priors, e.g., uniform and Cauchy prior, is fully explored in this research. More importantly, based on the derived weight uncertainty, three sets of prediction related uncertainty indexes, i.e., soft-max uncertainty, pure uncertainty and uncertainty plus are proposed to produce reliable and accurate multi-label predictions. Validated on our manual annotated evaluation dataset, i.e., the multi-label annotated FER2013, our proposed Uncertainty Flow in multi-label facial expression analysis exhibited superiority to conventional multi-label learning algorithms and multi-label compatible neural networks. The success of our proposed Uncertainty Flow provides a glimpse of future in continuous, uncertain, and multi-label affective computing.

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“…It was simulated in PyMC3 using the Automatic Differentiation Variational Inference (ADVI) algorithm with 100,000 draws, which is stable and converges on the posterior distribution in 10.76 s on a middle-range laptop computer. Although the mathematical notation may seem intimidating to practitioners who are not used to it, writing this in the probabilistic Python programming package PyMC3 [43] demonstrates the intuitive nature of such a model: It is important to note that no probability statements about the values inside the frequentist interval can be made, nor can one fit a distribution to the interval. The distribution indicated is strictly a Bayesian one.…”

Section: Bayesian Solutionmentioning

confidence: 99%

Bayesian Energy Measurement and Verification Analysis

2018

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Energy Measurement and Verification (M&V) aims to make inferences about the savings achieved in energy projects, given the data and other information at hand. Traditionally, a frequentist approach has been used to quantify these savings and their associated uncertainties. We demonstrate that the Bayesian paradigm is an intuitive, coherent, and powerful alternative framework within which M&V can be done. Its advantages and limitations are discussed, and two examples from the industry-standard International Performance Measurement and Verification Protocol (IPMVP) are solved using the framework. Bayesian analysis is shown to describe the problem more thoroughly and yield richer information and uncertainty quantification results than the standard methods while not sacrificing model simplicity. We also show that Bayesian methods can be more robust to outliers. Bayesian alternatives to standard M&V methods are listed, and examples from literature are cited.

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Probabilistic programming in Python using PyMC3

Cited by 597 publications

References 3 publications

Fixing the stimulus-as-fixed-effect fallacy in task fMRI

Fixing the stimulus-as-fixed-effect fallacy in task fMRI

Uncertainty Flow Facilitates Zero-Shot Multi-Label Learning in Affective Facial Analysis

Bayesian Energy Measurement and Verification Analysis

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