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.

For robotic decision-making under uncertainty, the balance between exploitation and exploration of available options must be carefully taken into account. In this study, we introduce a new variant of contextual multi-armed bandits called observation-augmented CMABs (OA-CMABs) wherein a decision-making agent can utilize extra outcome observations from an external information source. CMABs model the expected option outcomes as a function of context features and hidden parameters, which are inferred from previous option outcomes. In OA-CMABs, external observations are also a function of context features and thus provide additional evidence about the hidden parameters. Yet, if an external information source is error-prone, the resulting posterior updates can harm decision-making performance unless the presence of errors is considered. To this end, we propose a robust Bayesian inference process for OA-CMABs that is based on the concept of probabilistic data validation. Our approach handles complex mixture model parameter priors and hybrid observation likelihoods for semantic data sources, allowing us to develop validation algorithms based on recently develop probabilistic semantic data association techniques. Furthermore, to more effectively cope with the combined sources of uncertainty in OA-CMABs, we derive a new active inference algorithm for option selection based on expected free energy minimization. This generalizes previous work on active inference for bandit-based robotic decision-making by accounting for faulty observations and non-Gaussian inference. Our approaches are demonstrated on a simulated asynchronous search site selection problem for space exploration. The results show that even if incorrect observations are provided by external information sources, efficient decision-making and robust parameter inference are still achieved in a wide variety of experimental conditions.

Decision trees remain one of the most popular machine learning models today, largely due to their out-of-the-box performance and interpretability. In this work, we present a Bayesian approach to decision tree induction via maximum a posteriori inference of a posterior distribution over trees. We first demonstrate a connection between maximum a posteriori inference of decision trees and AND/OR search. Using this connection, we propose an AND/OR search algorithm, dubbed MAPTree, which is able to recover the maximum a posteriori tree. Lastly, we demonstrate the empirical performance of the maximum a posteriori tree both on synthetic data and in real world settings. On 16 real world datasets, MAPTree either outperforms baselines or demonstrates comparable performance but with much smaller trees. On a synthetic dataset, MAPTree also demonstrates greater robustness to noise and better generalization than existing approaches. Finally, MAPTree recovers the maxiumum a posteriori tree faster than existing sampling approaches and, in contrast with those algorithms, is able to provide a certificate of optimality. The code for our experiments is available at https://github.com/ThrunGroup/maptree.

Deep learning has seen rapid growth in recent years and achieved state-of-the-art performance in a wide range of applications. However, training models typically requires expensive and time-consuming collection of large quantities of labeled data. This is particularly true within the scope of medical imaging analysis (MIA), where data are limited and labels are expensive to be acquired. Thus, label-efficient deep learning methods are developed to make comprehensive use of the labeled data as well as the abundance of unlabeled and weak-labeled data. In this survey, we extensively investigated over 300 recent papers to provide a comprehensive overview of recent progress on label-efficient learning strategies in MIA. We first present the background of label-efficient learning and categorize the approaches into different schemes. Next, we examine the current state-of-the-art methods in detail through each scheme. Specifically, we provide an in-depth investigation, covering not only canonical semi-supervised, self-supervised, and multi-instance learning schemes, but also recently emerged active and annotation-efficient learning strategies. Moreover, as a comprehensive contribution to the field, this survey not only elucidates the commonalities and unique features of the surveyed methods but also presents a detailed analysis of the current challenges in the field and suggests potential avenues for future research.

One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly available and can be approximated conventionally by finite differences. However, the discrete approximations of time derivatives may result in a poor estimation when state data are scarce and/or corrupted by noise, thus compromising the predictiveness of the learned dynamical models. To overcome this technical hurdle, we propose a new method that learns nonlinear dynamics through a Bayesian inference of characterizing model parameters. This method leverages a Gaussian process representation of states, and constructs a likelihood function using the correlation between state data and their derivatives, yet prevents explicit evaluations of time derivatives. Through a Bayesian scheme, a probabilistic estimate of the model parameters is given by the posterior distribution, and thus a quantification is facilitated for uncertainties from noisy state data and the learning process. Specifically, we will discuss the applicability of the proposed method to two typical scenarios for dynamical systems: parameter identification and estimation with an affine structure of the system, and nonlinear parametric approximation without prior knowledge.

Traditional social learning frameworks consider environments with a homogeneous state, where each agent receives observations conditioned on that true state of nature. In this work, we relax this assumption and study the distributed hypothesis testing problem in a heterogeneous environment, where each agent can receive observations conditioned on their own personalized state of nature (or truth). This situation arises in many scenarios, such as when sensors are spatially distributed, or when individuals in a social network have differing views or opinions. In these heterogeneous contexts, the graph topology admits a block structure. We study social learning under personalized (or multitask) models and examine their convergence behavior.