Embodied agents, be they animals or robots, acquire information about the world through their senses. Embodied agents, however, do not simply lose this information once it passes by, but rather process and store it for future use. The most general theory of how an agent can combine stored knowledge with new observations is Bayesian inference. In this dissertation I present a theory of how embodied agents can learn to implement Bayesian inference with neural networks. By neural network I mean both artificial and biological neural networks, and in my dissertation I address both kinds. On one hand, I develop theory for implementing Bayesian inference in deep generative models, and I show how to train multilayer perceptrons to compute approximate predictions for Bayesian filtering. On the other hand, I show that several models in computational neuroscience are special cases of the general theory that I develop in this dissertation, and I use this theory to model and explain several phenomena in neuroscience. The key contributions of this dissertation can be summarized as follows: - I develop a class of graphical model called nth-order harmoniums. An nth-order harmonium is an n-tuple of random variables, where the conditional distribution of each variable given all the others is always an element of the same exponential family. I show that harmoniums have a recursive structure which allows them to be analyzed at coarser and finer levels of detail. - I define a class of harmoniums called rectified harmoniums, which are constrained to have priors which are conjugate to their posteriors. As a consequence of this, rectified harmoniums afford efficient sampling and learning. - I develop deep harmoniums, which are harmoniums which can be represented by hierarchical, undirected graphs. I develop the theory of rectification for deep harmoniums, and develop a novel algorithm for training deep generative models. - I show how to implement a variety of optimal and near-optimal Bayes filters by combining the solution to Bayes' rule provided by rectified harmoniums, with predictions computed by a recurrent neural network. I then show how to train a neural network to implement Bayesian filtering when the transition and emission distributions are unknown. - I show how some well-established models of neural activity are special cases of the theory I present in this dissertation, and how these models can be generalized with the theory of rectification. - I show how the theory that I present can model several neural phenomena including proprioception and gain-field modulation of tuning curves. - I introduce a library for the programming language Haskell, within which I have implemented all the simulations presented in this dissertation. This library uses concepts from Riemannian geometry to provide a rigorous and efficient environment for implementing complex numerical simulations. I also use the results presented in this dissertation to argue for the fundamental role of neural computation in embodied cognition. I argue, in other words, that before we will be able to build truly intelligent robots, we will need to truly understand biological brains.

The objective of this paper is to retrospectively evaluate forecast models for polling data, to be used prospectively for the Swedish general election in 2022. One of the simplest ways of forecasting an election result is through opinion polls, and using the latest observation as the forecast. This paper considers five different forecasting models on polling data which are evaluated based on different error measures and the results are compared to previous research done on the same topic. The data in this paper consists of time series data of party-preference polls from Statistics Sweden. When forecasting polling data, the naive forecasting model was the most accurate, but forecasting the election in 2018 resulted in the forecast combinations model being the most accurate. Finally, the models are used to make forecasts on the Swedish general election taking place in September of 2022.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第19129号 / 情博第575号 / 新制||情||101(附属図書館) / 32080 / 京都大学大学院情報学研究科通信情報システム専攻 / (主査)教授 岩間 一雄, 教授 髙木 直史, 教授 五十嵐 淳 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第20516号 / 情博第644号 / 新制||情||111(附属図書館) / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 永持 仁, 教授 太田 快人, 教授 山下 信雄 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

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In this report we will plunge down in the fascinating world of the generating functions. Generating functions showcase the "power of power series", giving more depth to the word "power" in power series. We start off small to get a good understanding of the generating function and what it does. Also, off course, explaining why it works and why we can do some of the things we do with them. We will see alot of examples throughout the text that helps the reader to grasp the mathematical object that is the generating function. We will look at several kinds of generating functions, the main focus when we establish our understanding of these will be the "ordinary power series" generating function ("ops") that we discuss before moving on to the "exponential generating function" ("egf"). During our discussion on ops we will see a "first time in literature" derivation of the generating function for a recurrence relation regarding "branched coverings". After finishing the discussion regarding egf we move on the Hermite polynomials and show how we derive their generating function. Which is a generating function that generates functions. Lastly we will have a quick look at the "moment generating function".

Cyber-Physical System (CPS) becomes more and more importance from industrial application (e.g., aircraft control, automation management) to societal challenges (e.g. health caring, environment monitoring). It has traditionally been designed to one specific application domain and to be managed by a single entity, implemented communication between physical world and computational world. However, it still just work within its domain, and not be interoperability. How to make it into scalable? How to make it reusing? These questions become more and more necessary. In this paper, we are trying to developing a common CPS infrastructure, let it be an innovative CPS crossing multiple domains to broad use sensors and actuators. Here, we implement a technique for automatically build a model according to the sensor data in different domains. And based on our approach under continuous situation, it could identify the sensor values right now or estimate next few time step, which we call spatial model or temporal model.

This dissertation focuses on the development of adaptive time-stepping and high-order parallel stages exponential Runge–Kutta methods for discretizing stiff partial differential equations (PDEs). The design of exponential Runge–Kutta methods relies heavily on the existing stiff order conditions available in the literature, primarily up to order 5. It is well-known that constructing higher-order efficient methods that strictly satisfy all the stiff order conditions is challenging. Typically, methods up to order 5 have been derived by relaxing one or more order conditions, depending on the desired accuracy level. Our approach will be based on a comprehensive investigation of these conditions. We will derive novel and efficient exponential Runge–Kutta schemes of orders up to 5, which not only fulfill the stiff order conditions in a strict sense but also support the implementation of variable step sizes. Furthermore, we develop the first-ever sixth-order exponential Runge–Kutta schemes by leveraging the exponential B-series theory. Notably, all the newly derived schemes allow the efficient computation of multiple stages, either simultaneously or in parallel. To establish the convergence properties of the proposed methods, we perform an analysis within an abstract Banach space in the context of semigroup theory. Our numerical experiments are given on parabolic PDEs to confirm the accuracy and efficiency of the newly constructed methods.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24393号 / 理博第4892号 / 新制||理||1699(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 長谷川 真人, 教授 牧野 和久, 准教授 照井 一成 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM