Models of eye-movement control during reading, developed largely within psychology, usually focus on visual, attentional, lexical, and motor processes but neglect post-lexical language processing; by contrast, models of sentence comprehension processes, developed largely within psycholinguistics, generally focus only on post-lexical language processes. We present a model that combines these two research threads, by integrating eye-movement control and sentence processing. Developing such an integrated model is extremely challenging and computationally demanding, but such an integration is an important step toward complete mathematical models of natural language comprehension in reading. We combine the SWIFT model of eye-movement control (Seelig et al., 2020, doi:10.1016/j.jmp.2019.102313) with key components of the Lewis and Vasishth sentence processing model (Lewis & Vasishth, 2005, doi:10.1207/s15516709cog0000_25). This integration becomes possible, for the first time, due in part to recent advances in successful parameter identification in dynamical models, which allows us to investigate profile log-likelihoods for individual model parameters. We present a fully implemented proof-of-concept model demonstrating how such an integrated model can be achieved; our approach includes Bayesian model inference with Markov Chain Monte Carlo (MCMC) sampling as a key computational tool. The integrated Sentence-Processing and Eye-Movement Activation-Coupled Model (SEAM) can successfully reproduce eye movement patterns that arise due to similarity-based interference in reading. To our knowledge, this is the first-ever integration of a complete process model of eye-movement control with linguistic dependency completion processes in sentence comprehension. In future work, this proof of concept model will need to be evaluated using a comprehensive set of benchmark data.

Accurate uncertainty quantification is necessary to enhance the reliability of deep learning models in real-world applications. In the case of regression tasks, prediction intervals (PIs) should be provided along with the deterministic predictions of deep learning models. Such PIs are useful or "high-quality" as long as they are sufficiently narrow and capture most of the probability density. In this paper, we present a method to learn prediction intervals for regression-based neural networks automatically in addition to the conventional target predictions. In particular, we train two companion neural networks: one that uses one output, the target estimate, and another that uses two outputs, the upper and lower bounds of the corresponding PI. Our main contribution is the design of a novel loss function for the PI-generation network that takes into account the output of the target-estimation network and has two optimization objectives: minimizing the mean prediction interval width and ensuring the PI integrity using constraints that maximize the prediction interval probability coverage implicitly. Furthermore, we introduce a self-adaptive coefficient that balances both objectives within the loss function, which alleviates the task of fine-tuning. Experiments using a synthetic dataset, eight benchmark datasets, and a real-world crop yield prediction dataset showed that our method was able to maintain a nominal probability coverage and produce significantly narrower PIs without detriment to its target estimation accuracy when compared to those PIs generated by three state-of-the-art neural-network-based methods. In other words, our method was shown to produce higher-quality PIs.

Transfer learning is a burgeoning concept in statistical machine learning that seeks to improve inference and/or predictive accuracy on a domain of interest by leveraging data from related domains. While the term "transfer learning" has garnered much recent interest, its foundational principles have existed for years under various guises. Prior literature reviews in computer science and electrical engineering have sought to bring these ideas into focus, primarily surveying general methodologies and works from these disciplines. This article highlights Bayesian approaches to transfer learning, which have received relatively limited attention despite their innate compatibility with the notion of drawing upon prior knowledge to guide new learning tasks. Our survey encompasses a wide range of Bayesian transfer learning frameworks applicable to a variety of practical settings. We discuss how these methods address the problem of finding the optimal information to transfer between domains, which is a central question in transfer learning. We illustrate the utility of Bayesian transfer learning methods via a simulation study where we compare performance against frequentist competitors.

However, training and sampling from EBMs continue to pose significant challenges. The widely-used Denoising Score Matching (DSM) method [40] for scalable EBM training suffers from inconsistency issues, causing the energy model to learn a'noisy' data distribution. In this work, we propose an efficient sampling framework, (pseudo)-Gibbs sampling with moment matching, which enables effective sampling from the underlying clean model when given a'noisy' model that has been well-trained via DSM. We explore the benefits of our approach compared to related methods and demonstrate how to scale the method to high-dimensional datasets.

While generalized linear mixed models (GLMMs) are a fundamental tool in applied statistics, many specifications -- such as those involving categorical factors with many levels or interaction terms -- can be computationally challenging to estimate due to the need to compute or approximate high-dimensional integrals. Variational inference (VI) methods are a popular way to perform such computations, especially in the Bayesian context. However, naive VI methods can provide unreliable uncertainty quantification. We show that this is indeed the case in the GLMM context, proving that standard VI (i.e. mean-field) dramatically underestimates posterior uncertainty in high-dimensions. We then show how appropriately relaxing the mean-field assumption leads to VI methods whose uncertainty quantification does not deteriorate in high-dimensions, and whose total computational cost scales linearly with the number of parameters and observations. Our theoretical and numerical results focus on GLMMs with Gaussian or binomial likelihoods, and rely on connections to random graph theory to obtain sharp high-dimensional asymptotic analysis. We also provide generic results, which are of independent interest, relating the accuracy of variational inference to the convergence rate of the corresponding coordinate ascent variational inference (CAVI) algorithm for Gaussian targets. Our proposed partially-factorized VI (PF-VI) methodology for GLMMs is implemented in the R package vglmer, see https://github.com/mgoplerud/vglmer . Numerical results with simulated and real data examples illustrate the favourable computation cost versus accuracy trade-off of PF-VI.

The selection of the assumed effect size (AES) critically determines the duration of an experiment, and hence its accuracy and efficiency. Traditionally, experimenters determine AES based on domain knowledge. However, this method becomes impractical for online experimentation services managing numerous experiments, and a more automated approach is hence of great demand. We initiate the study of data-driven AES selection in for online experimentation services by introducing two solutions. The first employs a three-layer Gaussian Mixture Model considering the heteroskedasticity across experiments, and it seeks to estimate the true expected effect size among positive experiments. The second method, grounded in utility theory, aims to determine the optimal effect size by striking a balance between the experiment's cost and the precision of decision-making. Through comparisons with baseline methods using both simulated and real data, we showcase the superior performance of the proposed approaches.

This dissertation reports some first steps towards a compositional account of active inference and the Bayesian brain. Specifically, we use the tools of contemporary applied category theory to supply functorial semantics for approximate inference. To do so, we define on the `syntactic' side the new notion of Bayesian lens and show that Bayesian updating composes according to the compositional lens pattern. Using Bayesian lenses, and inspired by compositional game theory, we define fibrations of statistical games and classify various problems of statistical inference as corresponding sections: the chain rule of the relative entropy is formalized as a strict section, while maximum likelihood estimation and the free energy give lax sections. In the process, we introduce a new notion of `copy-composition'. On the `semantic' side, we present a new formalization of general open dynamical systems (particularly: deterministic, stochastic, and random; and discrete- and continuous-time) as certain coalgebras of polynomial functors, which we show collect into monoidal opindexed categories (or, alternatively, into algebras for multicategories of generalized polynomial functors). We use these opindexed categories to define monoidal bicategories of cilia: dynamical systems which control lenses, and which supply the target for our functorial semantics. Accordingly, we construct functors which explain the bidirectional compositional structure of predictive coding neural circuits under the free energy principle, thereby giving a formal mathematical underpinning to the bidirectionality observed in the cortex. Along the way, we explain how to compose rate-coded neural circuits using an algebra for a multicategory of linear circuit diagrams, showing subsequently that this is subsumed by lenses and polynomial functors.

The theory of belief functions [162, 67] is a modelling language for representing and combining elementary items of evidence, which do not necessarily come in the form of sharp statements, with the goal of maintaining a mathematical representation of an agent's beliefs about those aspects of the world which the agent is unable to predict with reasonable certainty. While arguably a more appropriate mathematical description of uncertainty than classical probability theory, for the reasons we have thoroughly explored in [50], the theory of evidence is relatively simple to understand and implement, and does not require one to abandon the notion of an event, as is the case, for instance, for Walley's imprecise probability theory [193]. It is grounded in the beautiful mathematics of random sets, and exhibits strong relationships with many other theories of uncertainty. As mathematical objects, belief functions have fascinating properties in terms of their geometry, algebra [207] and combinatorics. Despite initial concerns about the computational complexity of a naive implementation of the theory of evidence, evidential reasoning can actually be implemented on large sample spaces [156] and in situations involving the combination of numerous pieces of evidence [74]. Elementary items of evidence often induce simple belief functions, which can be combined very efficiently with complexity O(n + 1).

We consider a combinatorial Gaussian process semi-bandit problem with time-varying arm availability. Each round, an agent is provided a set of available base arms and must select a subset of them to maximize the long-term cumulative reward. Assuming the expected rewards are sampled from a Gaussian process (GP) over the arm space, the agent can efficiently learn. We study the Bayesian setting and provide novel Bayesian regret bounds for three GP-based algorithms: GP-UCB, Bayes-GP-UCB and GP-TS. Our bounds extend previous results for GP-UCB and GP-TS to a combinatorial setting with varying arm availability and to the best of our knowledge, we provide the first Bayesian regret bound for Bayes-GP-UCB. Time-varying arm availability encompasses other widely considered bandit problems such as contextual bandits. We formulate the online energy-efficient navigation problem as a combinatorial and contextual bandit and provide a comprehensive experimental study on synthetic and real-world road networks with detailed simulations. The contextual GP model obtains lower regret and is less dependent on the informativeness of the prior compared to the non-contextual Bayesian inference model. In addition, Thompson sampling obtains lower regret than Bayes-UCB for both the contextual and non-contextual model.

Background: We are witnessing an increasing adoption of machine learning (ML), especially deep learning (DL) algorithms in many software systems, including safety-critical systems such as health care systems or autonomous driving vehicles. Ensuring the software quality of these systems is yet an open challenge for the research community, mainly due to the inductive nature of ML software systems. Traditionally, software systems were constructed deductively, by writing down the rules that govern the behavior of the system as program code. However, for ML software, these rules are inferred from training data. Few recent research advances in the quality assurance of ML systems have adapted different concepts from traditional software testing, such as mutation testing, to help improve the reliability of ML software systems. However, it is unclear if any of these proposed testing techniques from research are adopted in practice. There is little empirical evidence about the testing strategies of ML engineers. Aims: To fill this gap, we perform the first fine-grained empirical study on ML testing practices in the wild, to identify the ML properties being tested, the followed testing strategies, and their implementation throughout the ML workflow. Method: First, we systematically summarized the different testing strategies (e.g., Oracle Approximation), the tested ML properties (e.g., Correctness, Bias, and Fairness), and the testing methods (e.g., Unit test) from the literature. Then, we conducted a study to understand the practices of testing ML software. Results: In our findings: 1) we identified four (4) major categories of testing strategy including Grey-box, White-box, Black-box, and Heuristic-based techniques that are used by the ML engineers to find software bugs. 2) We identified 16 ML properties that are tested in the ML workflow.