In science, technology, and engineering, creating models of the environment to predict future events has always been a key component. The models could be everything from how the friction of a tire depends on the wheels slip to how a pathogen is spread throughout society. As more data becomes available, the use of data-driven black-box models becomes more attractive. In many areas they have shown promising results, but for them to be used widespread in safety-critical applications such as autonomous driving some notion of uncertainty in the prediction is required. An example of such a black-box model is neural networks (NNs). This thesis aims to increase the usefulness of NNs by presenting an method where uncertainty in the prediction is obtained by linearization of the model. In system identification and sensor fusion, under the condition that the model structure is identifiable, this is a commonly used approach to get uncertainty in the prediction from a nonlinear model. If the model structure is not identifiable, such as for NNs, the ambiguities that cause this have to be taken care of in order to make the approach applicable. This is handled in the first part of the thesis where NNs are analyzed from a system identification perspective, and sources of uncertainty are discussed. Another problem with data-driven black-box models is that it is difficult to know how flexible the model needs to be in order to correctly model the true system. One solution to this problem is to use a model that is more flexible than necessary to make sure that the model is flexible enough. But how would that extra flexibility affect the uncertainty in the prediction? This is handled in the later part of the thesis where it is shown that the uncertainty in the prediction is bounded from below by the uncertainty in the prediction of the model with lowest flexibility required for representing true system accurately. In the literature, many other approaches to handle the uncertainty in predictions by NNs have been suggested, of which some are summarized in this work. Furthermore, a simulation and an experimental studies inspired by autonomous driving are conducted. In the simulation study, different sources of uncertainty are investigated, as well as how large the uncertainty in the predictions by NNs are in areas without training data. In the experimental study, the uncertainty in predictions done by different models are investigated. The results show that, compared to existing methods, the linearization method produces similar results for the uncertainty in predictions by NNs. An introduction video is available at https://youtu.be/O4ZcUTGXFN0 Inom forskning och utveckling har det har alltid varit centralt att skapa modeller av verkligheten. Dessa modeller har bland annat använts till att förutspå framtida händelser eller för att styra ett system till att bete sig som man önskar. Modellerna kan beskriva allt från hur friktionen hos ett bildäck påverkas av hur mycket hjulen glider till hur ett virus kan sprida sig i ett samhälle. I takt med att mer och mer data blir tillgänglig ökar potentialen för datadrivna black-box modeller. Dessa modeller är universella approximationer vilka ska kunna representera vilken godtycklig funktion som helst. Användningen av dessa modeller har haft stor framgång inom många områden men för att verkligen kunna etablera sig inom säkerhetskritiska områden såsom självkörande farkoster behövs en förståelse för osäkerhet i prediktionen från modellen. Neuronnät är ett exempel på en sådan black-box modell. I denna avhandling kommer olika sätt att tillförskaffa sig kunskap om osäkerhet i prediktionen av neuronnät undersökas. En metod som bygger på linjärisering av modellen för att tillförskaffa sig osäkerhet i prediktionen av neuronnätet kommer att presenteras. Denna metod är välbeprövad inom systemidentifiering och sensorfusion under antagandet att modellen är identifierbar. För modeller såsom neuronnät, vilka inte är identifierbara behövs det att det tas hänsyn till tvetydigheterna i modellen. En annan utmaning med datadrivna black-box modeller, är att veta om den valda modellmängden är tillräckligt generell för att kunna modellera det sanna systemet. En lösning på detta problem är att använda modeller som har mer flexibilitet än vad som behövs, det vill säga en överparameteriserad modell. Men hur påverkas osäkerheten i prediktionen av detta? Detta är något som undersöks i denna avhandling, vilken visar att osäkerheten i den överparameteriserad modellen kommer att vara begränsad underifrån av modellen med minst flexibilitet som ändå är tillräckligt generell för att modellera det sanna systemet. Som avslutning kommer dessa resultat att demonstreras i både en simuleringsstudie och en experimentstudie inspirerad av självkörande farkoster. Fokuset i simuleringsstudien är hur osäkerheten hos modellen är i områden med och utan tillgång till träningsdata medan experimentstudien fokuserar på jämförelsen mellan osäkerheten i olika typer av modeller.Resultaten från dessa studier visar att metoden som bygger på linjärisering ger liknande resultat för skattningen av osäkerheten i prediktionen av neuronnät, jämfört med existerande metoder.

This book constitutes the proceedings of the 12th IFIP TC 8 International Conference, CISIM 2013, held in Cracow, Poland, in September 2013. The 44 papers presented in this volume were carefully reviewed and selected from over 60 submissions. They are organized in topical sections on biometric and biomedical applications; pattern recognition and image processing; various aspects of computer security, networking, algorithms, and industrial applications. The book also contains full papers of a keynote speech and the invited talk.

Artificial "neural networks" are widely used as flexible models for classification and regression applications, but questions remain about how the power of these models can be safely exploited when training data is limited. This book demonstrates how Bayesian methods allow complex neural network models to be used without fear of the "overfitting" that can occur with traditional training methods. Insight into the nature of these complex Bayesian models is provided by a theoretical investigation of the priors over functions that underlie them. A practical implementation of Bayesian neural network learning using Markov chain Monte Carlo methods is also described, and software for it is freely available over the Internet. Presupposing only basic knowledge of probability and statistics, this book should be of interest to researchers in statistics, engineering, and artificial intelligence.

Computer vision has been successful in several important applications recently. Vision techniques can now be used to build very good models of buildings from pictures quickly and easily, to overlay operation planning data on a neuros- geon’s view of a patient, and to recognise some of the gestures a user makes to a computer. Object recognition remains a very di cult problem, however. The key questions to understand in recognition seem to be: (1) how objects should be represented and (2) how to manage the line of reasoning that stretches from image data to object identity. An important part of the process of recognition { perhaps, almost all of it { involves assembling bits of image information into helpful groups. There is a wide variety of possible criteria by which these groups could be established { a set of edge points that has a symmetry could be one useful group; others might be a collection of pixels shaded in a particular way, or a set of pixels with coherent colour or texture. Discussing this process of grouping requires a detailed understanding of the relationship between what is seen in the image and what is actually out there in the world.

This book constitutes the refereed proceedings of the First International Workshop on Uncertainty for Safe Utilization of Machine Learning in Medical Imaging, UNSURE 2019, and the 8th International Workshop on Clinical Image-Based Procedures, CLIP 2019, held in conjunction with MICCAI 2019, in Shenzhen, China, in October 2019. For UNSURE 2019, 8 papers from 15 submissions were accepted for publication. They focus on developing awareness and encouraging research in the field of uncertainty modelling to enable safe implementation of machine learning tools in the clinical world. CLIP 2019 accepted 11 papers from the 15 submissions received. The workshops provides a forum for work centred on specific clinical applications, including techniques and procedures based on comprehensive clinical image and other data.

Probability is the bedrock of machine learning. You cannot develop a deep understanding and application of machine learning without it. Cut through the equations, Greek letters, and confusion, and discover the topics in probability that you need to know. Using clear explanations, standard Python libraries, and step-by-step tutorial lessons, you will discover the importance of probability to machine learning, Bayesian probability, entropy, density estimation, maximum likelihood, and much more.

Recent advances in machine learning or artificial intelligence for vision and natural language processing that have enabled the development of new technologies such as personal assistants or self-driving cars have brought machine learning and artificial intelligence to the forefront of popular culture. The accumulation of these algorithmic advances along with the increasing availability of large data sets and readily available high performance computing has played an important role in bringing machine learning applications to such a wide range of disciplines. Given the emphasis in the chemical sciences on the relationship between structure and function, whether in biochemistry or in materials chemistry, adoption of machine learning by chemistsderivations where they are important