The paper shows that the application of the fixed-effect multiple linear regression model to an overparameterized dataset is equivalent to fitting the data with a hyper-curve parameterized by a single scalar parameter. This equivalence allows for a predictor-focused approach, where each predictor is described by a function of the chosen parameter. It is proven that a linear model will produce exact predictions even in the presence of nonlinear dependencies that violate the model assumptions. Parameterization in terms of the dependent variable and the monomial basis in the predictor function space are applied here to both synthetic and experimental data. The hyper-curve approach is especially suited for the regularization of problems with noise in predictor variables and can be used to remove noisy and "improper" predictors from the model.

Catastrophe (CAT) bonds have become increasingly vital in managing and transferring catastrophic risk. These bonds offer a source of capital to cover losses arising from natural disasters, allowing investors to diversify their portfolios while helping issuers mitigate potentially devastating financial consequences. Understanding the pricing dynamics of CAT bonds is essential, both for investors seeking informed decisions and for issuers optimizing their risk management strategies. This paper introduces a probabilistic machine-learning-based predictive framework for the pricing of CAT bonds, aiming to enhance empirical pricing accuracy and discover previously undetected nonlinear dependence between the key risk factors and CAT bond spreads. Early research by Lane (2000) laid the groundwork for CAT bond pricing literature, proposing a log-linear regression model employing conditional expected loss and probability of first loss as predictors. Subsequent studies expanded on this linear framework, incorporating additional predictors and examining pricing under diverse conditions. Gürtler et al. (2016) incorporated bond characteristics like trigger type and bond rating, while Braun (2016) integrated market condition indices, such as the Lane Synthetic Rate on Line index and the BB corporate bond spread. Götze and Gürtler (2020a) explored sponsor-related pricing inefficiencies across different market conditions, and Morana and Sbrana (2019) focused on the impact of climate change on CAT bond returns. Further extending the research scope, Zhao and Yu (2020) utilized actual catastrophe data to forecast CAT bond prices using market-based methods, Braun et al. (2022) developed factor pricing models for cross-sectional CAT bond returns, and Herrmann and Hibbeln (2023) investigated liquidity premiums in the secondary market.

Many explainable AI (XAI) techniques strive for interpretability by providing concise salient information, such as sparse linear factors. However, users either only see inaccurate global explanations, or highly-varying local explanations. We propose to provide more detailed explanations by leveraging the human cognitive capacity to accumulate knowledge by incrementally receiving more details. Focusing on linear factor explanations (factors $\times$ values = outcome), we introduce Incremental XAI to automatically partition explanations for general and atypical instances by providing Base + Incremental factors to help users read and remember more faithful explanations. Memorability is improved by reusing base factors and reducing the number of factors shown in atypical cases. In modeling, formative, and summative user studies, we evaluated the faithfulness, memorability and understandability of Incremental XAI against baseline explanation methods. This work contributes towards more usable explanation that users can better ingrain to facilitate intuitive engagement with AI.

Racial diversity has become increasingly discussed within the AI The utilization of racial and ethnic categories in the development and algorithmic fairness literature, yet little attention is focused on of datasets and models facilitates the inclusion and documentation justifying the choices of racial categories and understanding how of diverse perspectives. Racial and ethnic categories are especially people are racialized into these chosen racial categories. Even less crucial for datasets and models in which race and ethnicity attention is given to how racial categories shift and how the racialization serve as relevant factors, may act as confounding variables, or enable process changes depending on the context of a dataset or the ability to audit for fairness using race and ethnicity for model. An unclear understanding of who comprises the racial categories fairness purposes. For example, understanding the racial and/or chosen and how people are racialized into these categories ethnic target of hate speech is crucial for understanding the impact can lead to varying interpretations of these categories. These varying of hate speech, as hate speech can differ based on the race interpretations can lead to harm when the understanding of and/or ethnicity of the target[48]. Similarly, in health, race is correlated racial categories and the racialization process is misaligned from with health outcomes[6], and knowledge of a patient's race the actual racialization process and racial categories used. Harm and ethnicity can help contextualize the patient's experience and can also arise if the racialization process and racial categories used health history[53]. In algorithmic fairness settings, knowledge of are irrelevant ordonot exist inthecontext they areapplied.

In this work the decision trees are used for explanation of support vector regression model. The decision trees act as a global technique as well as a local technique. They are compared against the popular technique of LIME which is a local explanatory technique and with multi linear regression. It is observed that decision trees give a lower RMSE value when fitted to support vector regression as compared to LIME in 87% of the runs over 5 datasets. The comparison of results is statistically significant. Multi linear regression also gives a lower RMSE value when fitted to support vector regression model as compared to LIME in 73% of the runs over 5 datasets but the comparison of results is not statistically significant. Also, when used as a local explanatory technique, decision trees give better performance than LIME and the comparison of results is statistically significant.

A new knowledge-based and machine learning hybrid modeling approach, called conditional Gaussian neural stochastic differential equation (CGNSDE), is developed to facilitate modeling complex dynamical systems and implementing analytic formulae of the associated data assimilation (DA). In contrast to the standard neural network predictive models, the CGNSDE is designed to effectively tackle both forward prediction tasks and inverse state estimation problems. The CGNSDE starts by exploiting a systematic causal inference via information theory to build a simple knowledge-based nonlinear model that nevertheless captures as much explainable physics as possible. Then, neural networks are supplemented to the knowledge-based model in a specific way, which not only characterizes the remaining features that are challenging to model with simple forms but also advances the use of analytic formulae to efficiently compute the nonlinear DA solution. These analytic formulae are used as an additional computationally affordable loss to train the neural networks that directly improve the DA accuracy. This DA loss function promotes the CGNSDE to capture the interactions between state variables and thus advances its modeling skills. With the DA loss, the CGNSDE is more capable of estimating extreme events and quantifying the associated uncertainty. Furthermore, crucial physical properties in many complex systems, such as the translate-invariant local dependence of state variables, can significantly simplify the neural network structures and facilitate the CGNSDE to be applied to high-dimensional systems. Numerical experiments based on chaotic systems with intermittency and strong non-Gaussian features indicate that the CGNSDE outperforms knowledge-based regression models, and the DA loss further enhances the modeling skills of the CGNSDE.

Portfolio management is one of the unresponded problems of the Motion Pictures Industry (MPI). To design an optimal portfolio for an MPI distributor, it is essential to predict the box office of each project. Moreover, for an accurate box office prediction, it is critical to consider the effect of the celebrities involved in each MPI project, which was impossible with any precedent expert-based method. Additionally, the asymmetric characteristic of MPI data decreases the performance of any predictive algorithm. In this paper, firstly, the fame score of the celebrities is determined using a large language model. Then, to tackle the asymmetric character of MPI's data, projects are classified. Furthermore, the box office prediction takes place for each class of projects. Finally, using a hybrid multi-attribute decision-making technique, the preferability of each project for the distributor is calculated, and benefiting from a bi-objective optimization model, the optimal portfolio is designed.

These notes expound the recent use of the signature transform and rough path theory in data science and machine learning. We develop the core theory of the signature from first principles and then survey some recent popular applications of this approach, including signature-based kernel methods and neural rough differential equations. The notes are based on a course given by the two authors at Imperial College London.

Thyroid cancer is an increasing global health concern that requires advanced diagnostic methods. The application of AI and radiomics to thyroid cancer diagnosis is examined in this review. A review of multiple databases was conducted in compliance with PRISMA guidelines until October 2023. A combination of keywords led to the discovery of an English academic publication on thyroid cancer and related subjects. 267 papers were returned from the original search after 109 duplicates were removed. Relevant studies were selected according to predetermined criteria after 124 articles were eliminated based on an examination of their abstract and title. After the comprehensive analysis, an additional six studies were excluded. Among the 28 included studies, radiomics analysis, which incorporates ultrasound (US) images, demonstrated its effectiveness in diagnosing thyroid cancer. Various results were noted, some of the studies presenting new strategies that outperformed the status quo. The literature has emphasized various challenges faced by AI models, including interpretability issues, dataset constraints, and operator dependence. The synthesized findings of the 28 included studies mentioned the need for standardization efforts and prospective multicenter studies to address these concerns. Furthermore, approaches to overcome these obstacles were identified, such as advances in explainable AI technology and personalized medicine techniques. The review focuses on how AI and radiomics could transform the diagnosis and treatment of thyroid cancer. Despite challenges, future research on multidisciplinary cooperation, clinical applicability validation, and algorithm improvement holds the potential to improve patient outcomes and diagnostic precision in the treatment of thyroid cancer.

We show that common choices of kernel functions for a highly accurate and massively scalable nearest-neighbour based GP regression model (GPnn: \cite{GPnn}) exhibit gradual convergence to asymptotic behaviour as dataset-size $n$ increases. For isotropic kernels such as Mat\'{e}rn and squared-exponential, an upper bound on the predictive MSE can be obtained as $O(n^{-\frac{p}{d}})$ for input dimension $d$, $p$ dictated by the kernel (and $d>p$) and fixed number of nearest-neighbours $m$ with minimal assumptions on the input distribution. Similar bounds can be found under model misspecification and combined to give overall rates of convergence of both MSE and an important calibration metric. We show that lower bounds on $n$ can be given in terms of $m$, $l$, $p$, $d$, a tolerance $\varepsilon$ and a probability $\delta$. When $m$ is chosen to be $O(n^{\frac{p}{p+d}})$ minimax optimal rates of convergence are attained. Finally, we demonstrate empirical performance and show that in many cases convergence occurs faster than the upper bounds given here.