Being Realist about Bayes, and the Predictive Processing Theory of Mind

Some naturalistic philosophers of mind subscribing to the predictive processing theory of mind have adopted a realist attitude towards the results of Bayesian cognitive science. In this paper, we argue that this realist attitude is unwarranted. The Bayesian research program in cognitive science does not possess special epistemic virtues over alternative approaches for explaining mental phenomena involving uncertainty. In particular, the Bayesian approach is not simpler, more unifying, or more rational than alternatives. It is also contentious that the Bayesian approach is overall better supported by the empirical evidence. So, to develop philosophical theories of mind on the basis of a realist interpretation of results from Bayesian cognitive science is unwarranted. Naturalistic philosophers of mind should instead adopt an anti-realist attitude towards these results and remain agnostic as to whether Bayesian models are true. For continuing on with an exclusive focus and praise of Bayes within debates about the predictive processing theory will impede progress in philosophical understanding of scientific practice in computational cognitive science as well as of the architecture of the mind

Bayesian Cognitive Science, Monopoly, and Neglected Frameworks

A widely shared view in the cognitive sciences is that discovering and assessing explanations of cognitive phenomena whose production involves uncertainty should be done in a Bayesian framework. One assumption supporting this modelling choice is that Bayes provides the best approach for representing uncertainty. However, it is unclear that Bayes possesses special epistemic virtues over alternative modelling frameworks, since a systematic comparison has yet to be attempted. Currently, it is then premature to assert that cognitive phenomena involving uncertainty are best explained within the Bayesian framework. As a forewarning, progress in cognitive science may be hindered if too many scientists continue to focus their efforts on Bayesian modelling, which risks to monopolize scientific resources that may be better allocated to alternative approaches

A general framework for ensemble distribution distillation

Ensembles of neural networks have been shown to give better performance than single networks, both in terms of predictions and uncertainty estimation. Additionally, ensembles allow the uncertainty to be decomposed into aleatoric (data) and epistemic (model) components, giving a more complete picture of the predictive uncertainty. Ensemble distillation is the process of compressing an ensemble into a single model, often resulting in a leaner model that still outperforms the individual ensemble members. Unfortunately, standard distillation erases the natural uncertainty decomposition of the ensemble. We present a general framework for distilling both regression and classification ensembles in a way that preserves the decomposition. We demonstrate the desired behaviour of our framework and show that its predictive performance is on par with standard distillation

Contributions to modeling with set-valued data: benefitting from undecided respondents

This dissertation develops a methodological framework and approaches to benefit from undecided survey participants, particularly undecided voters in pre-election polls. As choices can be seen as processes that - in stages - exclude alternatives until arriving at one final element, we argue that in pre-election polls undecided participants can most suitably be represented by the set of their viable options. This consideration set sampling, in contrast to the conventional neglection of the undecided, could reduce nonresponse and collects new and valuable information. We embed the resulting set-valued data in the framework of random sets, which allows for two different interpretations, and develop modeling methods for either one. The first interpretation is called ontic and views the set of options as an entity of its own that most accurately represents the position at the time of the poll, thus as a precise representation of something naturally imprecise. With this, new ways of structural analysis emerge as individuals pondering between particular parties can now be examined. We show how the underlying categorical data structure can be preserved in this formalization process for specific models and how popular methods for categorical data analysis can be broadly transferred. As the set contains the eventual choice, under the second interpretation, the set is seen as a coarse version of an underlying truth, which is called the epistemic view. This imprecise information of something actually precise can then be used to improve predictions or election forecasting. We developed several approaches and a framework of a factorized likelihood to utilize the set-valued information for forecasting. Amongst others, we developed methods addressing the complex uncertainty induced by the undecided, weighting the justifiability of assumptions with the conciseness of the results. To evaluate and apply our approaches, we conducted a pre-election poll for the German federal election of 2021 in cooperation with the polling institute Civey, for the first time regarding undecided voters in a set-valued manner. This provides us with the unique opportunity to demonstrate the advantages of the new approaches based on a state-of-the-art survey

Contributions to reasoning on imprecise data

This thesis contains four contributions which advocate cautious statistical modelling and inference. They achieve it by taking sets of models into account, either directly or indirectly by looking at compatible data situations. Special care is taken to avoid assumptions which are technically convenient, but reduce the uncertainty involved in an unjustified manner. This thesis provides methods for cautious statistical modelling and inference, which are able to exhaust the potential of precise and vague data, motivated by different fields of application, ranging from political science to official statistics. At first, the inherently imprecise Nonparametric Predictive Inference model is involved in the cautious selection of splitting variables in the construction of imprecise classification trees, which are able to describe a structure and allow for a reasonably high predictive power. Dependent on the interpretation of vagueness, different strategies for vague data are then discussed in terms of finite random closed sets: On the one hand, the data to be analysed are regarded as set-valued answers of an item in a questionnaire, where each possible answer corresponding to a subset of the sample space is interpreted as a separate entity. By this the finite random set is reduced to an (ordinary) random variable on a transformed sample space. The context of application is the analysis of voting intentions, where it is shown that the presented approach is able to characterise the undecided in a more detailed way, which common approaches are not able to. Altough the presented analysis, regarded as a first step, is carried out on set-valued data, which are suitably self-constructed with respect to the scientific research question, it still clearly demonstrates that the full potential of this quite general framework is not exhausted. It is capable of dealing with more complex applications. On the other hand, the vague data are produced by set-valued single imputation (imprecise imputation) where the finite random sets are interpreted as being the result of some (unspecified) coarsening. The approach is presented within the context of statistical matching, which is used to gain joint knowledge on features that were not jointly collected in the initial data production. This is especially relevant in data production, e.g. in official statistics, as it allows to fuse the information of already accessible data sets into a new one, without the requirement of actual data collection in the field. Finally, in order to share data, they need to be suitably anonymised. For the specific class of anonymisation techniques of microaggregation, its ability to infer on generalised linear regression models is evaluated. Therefore, the microaggregated data are regarded as a set of compatible, unobserved underlying data situations. Two strategies to follow are proposed. At first, a maximax-like optimisation strategy is pursued, in which the underlying unobserved data are incorporated into the regression model as nuisance parameters, providing a concise yet over-optimistic estimation of the regression coefficients. Secondly, an approach in terms of partial identification, which is inherently more cautious than the previous one, is applied to estimate the set of all regression coefficients that are obtained by performing the estimation on each compatible data situation. Vague data are deemed favourable to precise data as they additionally encompass the uncertainty of the individual observation, and therefore they have a higher informational value. However, to the present day, there are few (credible) statistical models that are able to deal with vague or set-valued data. For this reason, the collection of such data is neglected in data production, disallowing such models to exhaust their full potential. This in turn prevents a throughout evaluation, negatively affecting the (further) development of such models. This situation is a variant of the chicken or egg dilemma. The ambition of this thesis is to break this cycle by providing actual methods for dealing with vague data in relevant situations in practice, to stimulate the required data production.Diese Schrift setzt sich in vier Beiträgen für eine vorsichtige statistische Modellierung und Inferenz ein. Dieses wird erreicht, indem man Mengen von Modellen betrachtet, entweder direkt oder indirekt über die Interpretation der Daten als Menge zugrunde liegender Datensituationen. Besonderer Wert wird dabei darauf gelegt, Annahmen zu vermeiden, die zwar technisch bequem sind, aber die zugrunde liegende Unsicherheit der Daten in ungerechtfertigter Weise reduzieren. In dieser Schrift werden verschiedene Methoden der vorsichtigen Modellierung und Inferenz vorgeschlagen, die das Potential von präzisen und unscharfen Daten ausschöpfen können, angeregt von unterschiedlichen Anwendungsbereichen, die von Politikwissenschaften bis zur amtlichen Statistik reichen. Zuerst wird das Modell der Nonparametrischen Prädiktiven Inferenz, welches per se unscharf ist, in der vorsichtigen Auswahl von Split-Variablen bei der Erstellung von Klassifikationsbäumen verwendet, die auf Methoden der Imprecise Probabilities fußen. Diese Bäume zeichnen sich dadurch aus, dass sie sowohl eine Struktur beschreiben, als auch eine annehmbar hohe Prädiktionsgüte aufweisen. In Abhängigkeit von der Interpretation der Unschärfe, werden dann verschiedene Strategien für den Umgang mit unscharfen Daten im Rahmen von finiten Random Sets erörtert. Einerseits werden die zu analysierenden Daten als mengenwertige Antwort auf eine Frage in einer Fragebogen aufgefasst. Hierbei wird jede mögliche (multiple) Antwort, die eine Teilmenge des Stichprobenraumes darstellt, als eigenständige Entität betrachtet. Somit werden die finiten Random Sets auf (gewöhnliche) Zufallsvariablen reduziert, die nun in einen transformierten Raum abbilden. Im Rahmen einer Analyse von Wahlabsichten hat der vorgeschlagene Ansatz gezeigt, dass die Unentschlossenen mit ihm genauer charakterisiert werden können, als es mit den gängigen Methoden möglich ist. Obwohl die vorgestellte Analyse, betrachtet als ein erster Schritt, auf mengenwertige Daten angewendet wird, die vor dem Hintergrund der wissenschaftlichen Forschungsfrage in geeigneter Weise selbst konstruiert worden sind, zeigt diese dennoch klar, dass die Möglichkeiten dieses generellen Ansatzes nicht ausgeschöpft sind, so dass er auch in komplexeren Situationen angewendet werden kann. Andererseits werden unscharfe Daten durch eine mengenwertige Einfachimputation (imprecise imputation) erzeugt. Hier werden die finiten Random Sets als Ergebnis einer (unspezifizierten) Vergröberung interpretiert. Der Ansatz wird im Rahmen des Statistischen Matchings vorgeschlagen, das verwendet wird, um gemeinsame Informationen über ursprünglich nicht zusammen erhobene Merkmale zur erhalten. Dieses ist insbesondere relevant bei der Datenproduktion, beispielsweise in der amtlichen Statistik, weil es erlaubt, die verschiedenartigen Informationen aus unterschiedlichen bereits vorhandenen Datensätzen zu einen neuen Datensatz zu verschmelzen, ohne dass dafür tatsächlich Daten neu erhoben werden müssen. Zudem müssen die Daten für den Datenaustausch in geeigneter Weise anonymisiert sein. Für die spezielle Klasse der Anonymisierungstechnik der Mikroaggregation wird ihre Eignung im Hinblick auf die Verwendbarkeit in generalisierten linearen Regressionsmodellen geprüft. Hierfür werden die mikroaggregierten Daten als eine Menge von möglichen, unbeobachtbaren zu Grunde liegenden Datensituationen aufgefasst. Es werden zwei Herangehensweisen präsentiert: Als Erstes wird eine maximax-ähnliche Optimisierungsstrategie verfolgt, dabei werden die zu Grunde liegenden unbeobachtbaren Daten als Nuisance Parameter in das Regressionsmodell aufgenommen, was eine enge, aber auch über-optimistische Schätzung der Regressionskoeffizienten liefert. Zweitens wird ein Ansatz im Sinne der partiellen Identifikation angewendet, der per se schon vorsichtiger ist (als der vorherige), indem er nur die Menge aller möglichen Regressionskoeffizienten schätzt, die erhalten werden können, wenn die Schätzung auf jeder zu Grunde liegenden Datensituation durchgeführt wird. Unscharfe Daten haben gegenüber präzisen Daten den Vorteil, dass sie zusätzlich die Unsicherheit der einzelnen Beobachtungseinheit umfassen. Damit besitzen sie einen höheren Informationsgehalt. Allerdings gibt es zur Zeit nur wenige glaubwürdige statistische Modelle, die mit unscharfen Daten umgehen können. Von daher wird die Erhebung solcher Daten bei der Datenproduktion vernachlässigt, was dazu führt, dass entsprechende statistische Modelle ihr volles Potential nicht ausschöpfen können. Dies verhindert eine vollumfängliche Bewertung, wodurch wiederum die (Weiter-)Entwicklung jener Modelle gehemmt wird. Dies ist eine Variante des Henne-Ei-Problems. Diese Schrift will durch Vorschlag konkreter Methoden hinsichtlich des Umgangs mit unscharfen Daten in relevanten Anwendungssituationen Lösungswege aus der beschriebenen Situation aufzeigen und damit die entsprechende Datenproduktion anregen

Uncertainty in Engineering

This open access book provides an introduction to uncertainty quantification in engineering. Starting with preliminaries on Bayesian statistics and Monte Carlo methods, followed by material on imprecise probabilities, it then focuses on reliability theory and simulation methods for complex systems. The final two chapters discuss various aspects of aerospace engineering, considering stochastic model updating from an imprecise Bayesian perspective, and uncertainty quantification for aerospace flight modelling. Written by experts in the subject, and based on lectures given at the Second Training School of the European Research and Training Network UTOPIAE (Uncertainty Treatment and Optimization in Aerospace Engineering), which took place at Durham University (United Kingdom) from 2 to 6 July 2018, the book offers an essential resource for students as well as scientists and practitioners

Uncertainty in Neural Networks; Bayesian Ensembles, Priors & Prediction Intervals

The breakout success of deep neural networks (NNs) in the 2010's marked a new era in the quest to build artificial intelligence (AI). With NNs as the building block of these systems, excellent performance has been achieved on narrow, well-defined tasks where large amounts of data are available. However, these systems lack certain capabilities that are important for broad use in real-world applications. One such capability is the communication of uncertainty in a NN's predictions and decisions. In applications such as healthcare recommendation or heavy machinery prognostics, it is vital that AI systems be aware of and express their uncertainty – this creates safer, more cautious, and ultimately more useful systems. This thesis explores how to engineer NNs to communicate robust uncertainty estimates on their predictions, whilst minimising the impact on usability. One way to encourage uncertainty estimates to be robust is to adopt the Bayesian framework, which offers a principled approach to handling uncertainty. Two of the major contributions in this thesis relate to Bayesian NNs (BNNs). Specifying appropriate priors is an important step in any Bayesian model, yet it is not clear how to do this in BNNs. The first contribution shows that the connection between BNNs and Gaussian Processes (GPs) provides an effective lens to study BNN priors. NN architectures are derived which mirror the combining of GP kernels to create priors tailored to a task. The second major contribution is a novel way to perform approximate Bayesian inference in BNNs using a modified version of ensembling. Novel analysis improves an understanding of a technique known as randomised MAP sampling. It's shown this is particularly effective when strong correlations exist between parameters, making it well suited to NNs. The third major contribution of the thesis is a non-Bayesian technique that trains a NN to directly output prediction intervals for regression tasks through a tailored objective function. This advances over related works that were incompatible with gradient descent, and ignored one source of uncertainty.EPSRC, Alan Turing Institut

A review of probabilistic forecasting and prediction with machine learning

Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and forecasting with machine learning models in academia and industry are becoming more frequent, related concepts and methods have not been formalized and structured under a holistic view of the entire field. Here, we review the topic of predictive uncertainty estimation with machine learning algorithms, as well as the related metrics (consistent scoring functions and proper scoring rules) for assessing probabilistic predictions. The review covers a time period spanning from the introduction of early statistical (linear regression and time series models, based on Bayesian statistics or quantile regression) to recent machine learning algorithms (including generalized additive models for location, scale and shape, random forests, boosting and deep learning algorithms) that are more flexible by nature. The review of the progress in the field, expedites our understanding on how to develop new algorithms tailored to users' needs, since the latest advancements are based on some fundamental concepts applied to more complex algorithms. We conclude by classifying the material and discussing challenges that are becoming a hot topic of research.Comment: 83 pages, 5 figure