This paper presents Tyche, a Python library to facilitate probabilistic reasoning in uncertain worlds through the construction, querying, and learning of belief models. Tyche uses aleatoric description logic (ADL), which provides computational advantages in its evaluation over other description logics. Tyche belief models can be succinctly created by defining classes of individuals, the probabilistic beliefs about them (concepts), and the probabilistic relationships between them (roles). We also introduce a method of observation propagation to facilitate learning from complex ADL observations. A demonstration of Tyche to predict the author of anonymised messages, and to extract author writing tendencies from anonymised messages, is provided. Tyche has the potential to assist in the development of expert systems, knowledge extraction systems, and agents to play games with incomplete and probabilistic information.

Node classification using Graph Neural Networks (GNNs) has been widely applied in various real-world scenarios. However, in recent years, compelling evidence emerges that the performance of GNN-based node classification may deteriorate substantially by topological perturbation, such as random connections or adversarial attacks. Various solutions, such as topological denoising methods and mechanism design methods, have been proposed to develop robust GNN-based node classifiers but none of these works can fully address the problems related to topological perturbations. Recently, the Bayesian label transition model is proposed to tackle this issue but its slow convergence may lead to inferior performance. In this work, we propose a new label inference model, namely LInDT, which integrates both Bayesian label transition and topology-based label propagation for improving the robustness of GNNs against topological perturbations. LInDT is superior to existing label transition methods as it improves the label prediction of uncertain nodes by utilizing neighborhood-based label propagation leading to better convergence of label inference. Besides, LIndT adopts asymmetric Dirichlet distribution as a prior, which also helps it to improve label inference. Extensive experiments on five graph datasets demonstrate the superiority of LInDT for GNN-based node classification under three scenarios of topological perturbations.

Variational Bayes (VB) applied to latent Dirichlet allocation (LDA) has become the most popular algorithm for aspect modeling. While sufficiently successful in text topic extraction from large corpora, VB is less successful in identifying aspects in the presence of limited data. We present a novel variational message passing algorithm as applied to Latent Dirichlet Allocation (LDA) and compare it with the gold standard VB and collapsed Gibbs sampling. In situations where marginalisation leads to non-conjugate messages, we use ideas from sampling to derive approximate update equations. In cases where conjugacy holds, Loopy Belief update (LBU) (also known as Lauritzen-Spiegelhalter) is used. Our algorithm, ALBU (approximate LBU), has strong similarities with Variational Message Passing (VMP) (which is the message passing variant of VB). To compare the performance of the algorithms in the presence of limited data, we use data sets consisting of tweets and news groups. Using coherence measures we show that ALBU learns latent distributions more accurately than does VB, especially for smaller data sets.

Of late, in order to have better acceptability among various domain, researchers have argued that machine intelligence algorithms must be able to provide explanations that humans can understand causally. This aspect, also known as'causability' achieves a specific level of human-level explainability. A specific class of algorithms known as counterfactuals may be able to provide causability. In statistics, causality has been studied and applied for many years, but not in great detail in artificial intelligence (AI). In a first-of-its-kind study, we employed the principles of causal inference to provide explainability for solving the analytical customer relationship management (ACRM) problems. In the context of banking and insurance, current research on interpretability tries to address causality-related questions like why did this model make such decisions, and was the model's choice influenced by a particular factor? We propose a solution in the form of an intervention, wherein the effect of changing the distribution of features of ACRM datasets is studied on the target feature. Subsequently, a set of counterfactuals is also obtained that may be furnished to any customer who demands an explanation of the decision taken by the bank/insurance company. Except for the credit card churn prediction dataset, good quality counterfactuals were generated for the loan default, insurance fraud detection, and credit card fraud detection datasets, where changes in no more than three features are observed.

Recent progress in machine learning methods, and the emerging availability of programmable interfaces for scanning probe microscopes (SPMs), have propelled automated and autonomous microscopies to the forefront of attention of the scientific community. However, enabling automated microscopy requires the development of task-specific machine learning methods, understanding the interplay between physics discovery and machine learning, and fully defined discovery workflows. This, in turn, requires balancing the physical intuition and prior knowledge of the domain scientist with rewards that define experimental goals and machine learning algorithms that can translate these to specific experimental protocols. Here, we discuss the basic principles of Bayesian active learning and illustrate its applications for SPM. We progress from the Gaussian Process as a simple data-driven method and Bayesian inference for physical models as an extension of physics-based functional fits to more complex deep kernel learning methods, structured Gaussian Processes, and hypothesis learning. These frameworks allow for the use of prior data, the discovery of specific functionalities as encoded in spectral data, and exploration of physical laws manifesting during the experiment. The discussed framework can be universally applied to all techniques combining imaging and spectroscopy, SPM methods, nanoindentation, electron microscopy and spectroscopy, and chemical imaging methods, and can be particularly impactful for destructive or irreversible measurements.

Given a learning problem with real-world tradeoffs, which cost function should the model be trained to optimize? This is the metric selection problem in machine learning. Despite its practical interest, there is limited formal guidance on how to select metrics for machine learning applications. This thesis outlines metric elicitation as a principled framework for selecting the performance metric that best reflects implicit user preferences. Once specified, the evaluation metric can be used to compare and train models. In this manuscript, we formalize the problem of Metric Elicitation and devise novel strategies for eliciting classification performance metrics using pairwise preference feedback over classifiers. Specifically, we provide novel strategies for eliciting linear and linear-fractional metrics for binary and multiclass classification problems, which are then extended to a framework that elicits group-fair performance metrics in the presence of multiple sensitive groups. All the elicitation strategies that we discuss are robust to both finite sample and feedback noise, thus are useful in practice for real-world applications. Using the tools and the geometric characterizations of the feasible confusion statistics sets from the binary, multiclass, and multiclass-multigroup classification setups, we further provide strategies to elicit from a wider range of complex, modern multiclass metrics defined by quadratic functions of confusion statistics by exploiting their local linear structure. From application perspective, we also propose to use the metric elicitation framework in optimizing complex black box metrics that is amenable to deep network training. Lastly, to bring theory closer to practice, we conduct a preliminary real-user study that shows the efficacy of the metric elicitation framework in recovering the users' preferred performance metric in a binary classification setup.

Normalizing Flows (NFs) are flexible explicit generative models that have been shown to accurately model complex real-world data distributions. However, their invertibility constraint imposes limitations on data distributions that reside on lower dimensional manifolds embedded in higher dimensional space. Practically, this shortcoming is often bypassed by adding noise to the data which impacts the quality of the generated samples. In contrast to prior work, we approach this problem by generating samples from the original data distribution given full knowledge about the perturbed distribution and the noise model. To this end, we establish that NFs trained on perturbed data implicitly represent the manifold in regions of maximum likelihood. Then, we propose an optimization objective that recovers the most likely point on the manifold given a sample from the perturbed distribution. Finally, we focus on 3D point clouds for which we utilize the explicit nature of NFs, i.e. surface normals extracted from the gradient of the log-likelihood and the log-likelihood itself, to apply Poisson surface reconstruction to refine generated point sets.

Sharing medical data between institutions is difficult in practice due to data protection laws and official procedures within institutions. Therefore, most existing algorithms are trained on relatively small electroencephalogram (EEG) data sets which is likely to be detrimental to prediction accuracy. In this work, we simulate a case when the data can not be shared by splitting the publicly available data set into disjoint sets representing data in individual institutions. We propose to train a (local) detector in each institution and aggregate their individual predictions into one final prediction. Four aggregation schemes are compared, namely, the majority vote, the mean, the weighted mean and the Dawid-Skene method. The method was validated on an independent data set using only a subset of EEG channels. The ensemble reaches accuracy comparable to a single detector trained on all the data when sufficient amount of data is available in each institution. The weighted mean aggregation scheme showed best performance, it was only marginally outperformed by the Dawid--Skene method when local detectors approach performance of a single detector trained on all available data.

Bonus-Malus Systems (BMSs) are nowadays widely employed in automobile insurance to dynamically adjust a premium based on a customer's claims experience. The intuition behind these posterior ratemaking systems is that as we observe more claiming behavior, we learn more about the underlying risk profile. These systems are therefore a commercially attractive form of experience rating, in which we correct the prior premium for past claims to reflect our updated beliefs about a customer's risk profile. Moreover, they traditionally consider a customer's number of claims irrespective of their sizes and thus implicitly assume independence between the claim counts and sizes (Hey, 1970; Denuit et al., 2007; Boucher and Inoussa, 2014; Verschuren, 2021). Alternative Bayesian forms of experience rating typically depend only on the frequency component as well or consider the two components separately (see, e.g., Denuit and Lang (2004); Bühlmann and Gisler (2005); Mahmoudvand and Hassani (2009); Bermúdez and Karlis (2011, 2017)).

Causal discovery has become a vital tool for scientists and practitioners wanting to discover causal relationships from observational data. While most previous approaches to causal discovery have implicitly assumed that no expert domain knowledge is available, practitioners can often provide such domain knowledge from prior experience. Recent work has incorporated domain knowledge into constraint-based causal discovery. The majority of such constraint-based methods, however, assume causal faithfulness, which has been shown to be frequently violated in practice. Consequently, there has been renewed attention towards exact-search score-based causal discovery methods, which do not assume causal faithfulness, such as A*-based methods. However, there has been no consideration of these methods in the context of domain knowledge. In this work, we focus on efficiently integrating several types of domain knowledge into A*-based causal discovery. In doing so, we discuss and explain how domain knowledge can reduce the graph search space and then provide an analysis of the potential computational gains. We support these findings with experiments on synthetic and real data, showing that even small amounts of domain knowledge can dramatically speed up A*-based causal discovery and improve its performance and practicality.