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In general insurance, claims are often lower-truncated and right-censored because insurance contracts may involve deductibles and maximal covers. Most classical statistical models are not (directly) suited to model lower-truncated and right-censored claims. A surprisingly flexible family of distributions that can cope with lower-truncated and right-censored claims is the class of MBBEFD distributions that originally has been introduced by Bernegger (1997) for reinsurance pricing, but which has not gained much attention outside the reinsurance literature. Interestingly, in general insurance, we mainly rely on unimodal skewed densities, whereas the reinsurance literature typically proposes monotonically decreasing densities within the MBBEFD class. We show that this class contains both types of densities, and we extend it to a bigger family of distribution functions suitable for modeling lower-truncated and right-censored claims. In addition, we discuss how changes in the deductible or the maximal cover affect the chosen distributions.

Due to their flexibility to represent almost any kind of relational data, graph-based models have enjoyed a tremendous success over the past decades. While graphs are inherently only combinatorial objects, however, many prominent analysis tools are based on the algebraic representation of graphs via matrices such as the graph Laplacian, or on associated graph embeddings. Such embeddings associate to each node a set of coordinates in a vector space, a representation which can then be employed for learning tasks such as the classification or alignment of the nodes of the graph. As the geometric picture provided by embedding methods enables the use of a multitude of methods developed for vector space data, embeddings have thus gained interest both from a theoretical as well as a practical perspective. Inspired by trace-optimization problems, often encountered in the analysis of graph-based data, here we present a method to derive ellipsoidal embeddings of the nodes of a graph, in which each node is assigned a set of coordinates on the surface of a hyperellipsoid. Our method may be seen as an alternative to popular spectral embedding techniques, to which it shares certain similarities we discuss. To illustrate the utility of the embedding we conduct a case study in which we analyse synthetic and real world networks with modular structure, and compare the results obtained with known methods in the literature.

While replacing Gaussian decoders with a conditional diffusion model enhances the perceptual quality of reconstructions in neural image compression, their lack of inductive bias for image data restricts their ability to achieve state-of-the-art perceptual levels. To address this limitation, we adopt a non-isotropic diffusion model at the decoder side. This model imposes an inductive bias aimed at distinguishing between frequency contents, thereby facilitating the generation of high-quality images. Moreover, our framework is equipped with a novel entropy model that accurately models the probability distribution of latent representation by exploiting spatio-channel correlations in latent space, while accelerating the entropy decoding step. This channel-wise entropy model leverages both local and global spatial contexts within each channel chunk. The global spatial context is built upon the Transformer, which is specifically designed for image compression tasks. The designed Transformer employs a Laplacian-shaped positional encoding, the learnable parameters of which are adaptively adjusted for each channel cluster. Our experiments demonstrate that our proposed framework yields better perceptual quality compared to cutting-edge generative-based codecs, and the proposed entropy model contributes to notable bitrate savings.

Preference modelling lies at the intersection of economics, decision theory, machine learning and statistics. By understanding individuals' preferences and how they make choices, we can build products that closely match their expectations, paving the way for more efficient and personalised applications across a wide range of domains. The objective of this tutorial is to present a cohesive and comprehensive framework for preference learning with Gaussian Processes (GPs), demonstrating how to seamlessly incorporate rationality principles (from economics and decision theory) into the learning process. By suitably tailoring the likelihood function, this framework enables the construction of preference learning models that encompass random utility models, limits of discernment, and scenarios with multiple conflicting utilities for both object- and label-preference. This tutorial builds upon established research while simultaneously introducing some novel GP-based models to address specific gaps in the existing literature.

In the field of causal modeling, potential outcomes (PO) and structural causal models (SCMs) stand as the predominant frameworks. However, these frameworks face notable challenges in practically modeling counterfactuals, formalized as parameters of the joint distribution of potential outcomes. Counterfactual reasoning holds paramount importance in contemporary decision-making processes, especially in scenarios that demand personalized incentives based on the joint values of $(Y(0), Y(1))$. This paper begins with an investigation of the PO and SCM frameworks for modeling counterfactuals. Through the analysis, we identify an inherent model capacity limitation, termed as the ``degenerative counterfactual problem'', emerging from the consistency rule that is the cornerstone of both frameworks. To address this limitation, we introduce a novel \textit{distribution-consistency} assumption, and in alignment with it, we propose the Distribution-consistency Structural Causal Models (DiscoSCMs) offering enhanced capabilities to model counterfactuals. To concretely reveal the enhanced model capacity, we introduce a new identifiable causal parameter, \textit{the probability of consistency}, which holds practical significance within DiscoSCM alone, showcased with a personalized incentive example. Furthermore, we provide a comprehensive set of theoretical results about the ``Ladder of Causation'' within the DiscoSCM framework. We hope it opens new avenues for future research of counterfactual modeling, ultimately enhancing our understanding of causality and its real-world applications.

For multivariate data, tandem clustering is a well-known technique aiming to improve cluster identification through initial dimension reduction. Nevertheless, the usual approach using principal component analysis (PCA) has been criticized for focusing solely on inertia so that the first components do not necessarily retain the structure of interest for clustering. To address this limitation, a new tandem clustering approach based on invariant coordinate selection (ICS) is proposed. By jointly diagonalizing two scatter matrices, ICS is designed to find structure in the data while providing affine invariant components. Certain theoretical results have been previously derived and guarantee that under some elliptical mixture models, the group structure can be highlighted on a subset of the first and/or last components. However, ICS has garnered minimal attention within the context of clustering. Two challenges associated with ICS include choosing the pair of scatter matrices and selecting the components to retain. For effective clustering purposes, it is demonstrated that the best scatter pairs consist of one scatter matrix capturing the within-cluster structure and another capturing the global structure. For the former, local shape or pairwise scatters are of great interest, as is the minimum covariance determinant (MCD) estimator based on a carefully chosen subset size that is smaller than usual. The performance of ICS as a dimension reduction method is evaluated in terms of preserving the cluster structure in the data. In an extensive simulation study and empirical applications with benchmark data sets, various combinations of scatter matrices as well as component selection criteria are compared in situations with and without outliers. Overall, the new approach of tandem clustering with ICS shows promising results and clearly outperforms the PCA-based approach.

In systems modelling, a system typically comprises located resources relative to which processes execute. One important use of logic in informatics is in modelling such systems for the purpose of reasoning (perhaps automated) about their behaviour and properties. To this end, one requires an interpretation of logical formulae in terms of the resources and states of the system; such an interpretation is called a resource semantics of the logic. This paper shows how inferentialism -- the view that meaning is given in terms of inferential behaviour -- enables a versatile and expressive framework for resource semantics. Specifically, how inferentialism seamlessly incorporates the assertion-based approach of the logic of Bunched Implications, foundational in program verification (e.g., as the basis of Separation Logic), and the renowned number-of-uses reading of Linear Logic. This integration enables reasoning about shared and separated resources in intuitive and familiar ways, as well as about the composition and interfacing of system components.

Software engineering is a domain characterized by intricate decision-making processes, often relying on nuanced intuition and consultation. Recent advancements in deep learning have started to revolutionize software engineering practices through elaborate designs implemented at various stages of software development. In this paper, we present an innovative paradigm that leverages large language models (LLMs) throughout the entire software development process, streamlining and unifying key processes through natural language communication, thereby eliminating the need for specialized models at each phase. At the core of this paradigm lies ChatDev, a virtual chat-powered software development company that mirrors the established waterfall model, meticulously dividing the development process into four distinct chronological stages: designing, coding, testing, and documenting. Each stage engages a team of agents, such as programmers, code reviewers, and test engineers, fostering collaborative dialogue and facilitating a seamless workflow. The chat chain acts as a facilitator, breaking down each stage into atomic subtasks. This enables dual roles, allowing for proposing and validating solutions through context-aware communication, leading to efficient resolution of specific subtasks. The instrumental analysis of ChatDev highlights its remarkable efficacy in software generation, enabling the completion of the entire software development process in under seven minutes at a cost of less than one dollar. It not only identifies and alleviates potential vulnerabilities but also rectifies potential hallucinations while maintaining commendable efficiency and cost-effectiveness. The potential of ChatDev unveils fresh possibilities for integrating LLMs into the realm of software development.

The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for graph learning. The dissertation begins with a review of the principles over which most of the methods in the field are built, followed by a study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. This framework allows us to consider graphs with discrete and continuous edge features, producing unsupervised embeddings rich enough to reach the state of the art on several classification tasks. Our approach is also amenable to a Bayesian nonparametric extension that automatizes the choice of almost all model's hyper-parameters. Two real-world applications demonstrate the efficacy of deep learning for graphs. The first concerns the prediction of information-theoretic quantities for molecular simulations with supervised neural models. After that, we exploit our Bayesian models to solve a malware-classification task while being robust to intra-procedural code obfuscation techniques. We conclude the dissertation with an attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs.

Effective task management is essential to successful team collaboration. While the past decade has seen considerable innovation in systems that track and manage group tasks, these innovations have typically been outside of the principal communication channels: email, instant messenger, and group chat. Teams formulate, discuss, refine, assign, and track the progress of their collaborative tasks over electronic communication channels, yet they must leave these channels to update their task-tracking tools, creating a source of friction and inefficiency. To address this problem, we explore how bots might be used to mediate task management for individuals and teams. We deploy a prototype bot to eight different teams of information workers to help them create, assign, and keep track of tasks, all within their main communication channel. We derived seven insights for the design of future bots for coordinating work.