In recent years, the pen and paper RPG market has experienced significant growth. As a result, companies are increasingly exploring the integration of AI technologies to enhance player experience and gain a competitive edge. One of the key challenges faced by publishers is designing new opponents and estimating their challenge level. Currently, there are no automated methods for determining a monster's level; the only approaches used are based on manual testing and expert evaluation. Although these manual methods can provide reasonably accurate estimates, they are time-consuming and resource-intensive. Level prediction can be approached using ordinal regression techniques. This thesis presents an overview and evaluation of state-of-the-art methods for this task. It also details the construction of a dedicated dataset for level estimation. Furthermore, a human-inspired model was developed to serve as a benchmark, allowing comparison between machine learning algorithms and the approach typically employed by pen and paper RPG publishers. In addition, a specialized evaluation procedure, grounded in domain knowledge, was designed to assess model performance and facilitate meaningful comparisons.

Ordinal regression (OR, or called ordinal classification) is the classification of ordinal data in which the underlying target variable is labeled from a categorical ordinal scale that is considered to be equipped with a natural ordinal relation for the underlying explanatory variable, as formalized in Section 2.1. The ordinal scale is typically formed as a graded summary of objective indicators like age groups {'0-9', '10-19',..., '90-99', '100-'} or graded evaluation of subjectivity like human rating {'excellent', 'good', 'average', 'bad', 'terrible'}. OR techniques are employed in a variety of practical applications, for example, age estimation (Niu et al., 2016; Cao et al., 2020), information retrieval (Liu, 2011), movie rating (Yu et al., 2006), and questionnaire survey (Bürkner and Vuorre, 2019). Threshold methods are popular for OR problems as a simple way to capture the ordinal relation of ordinal data, and have been studied vigorously in machine learning research (Shashua and Levin, 2003; Lin and Li, 2006; Chu and Keerthi, 2007; Lin and Li, 2012; Li and Lin, 2007; Pedregosa et al., 2017; Yamasaki, 2023). Those methods learn a one-dimensional transformation (1DT) of the observation of the explanatory variable so that an observation with a larger class label tends to have a larger 1DT value; they then assign a label prediction to the learned 1DT according to the rank of an interval to which the 1DT belongs among intervals on the real line separated by threshold parameters.

Endoscopic Mayo score and Ulcerative Colitis Endoscopic Index of Severity are commonly used scoring systems for the assessment of endoscopic severity of ulcerative colitis. They are based on assigning a score in relation to the disease activity, which creates a rank among the levels, making it an ordinal regression problem. On the other hand, most studies use categorical cross-entropy loss function, which is not optimal for the ordinal regression problem, to train the deep learning models. In this study, we propose a novel loss function called class distance weighted cross-entropy (CDW-CE) that respects the order of the classes and takes the distance of the classes into account in calculation of cost. Experimental evaluations show that CDW-CE outperforms the conventional categorical cross-entropy and CORN framework, which is designed for the ordinal regression problems. In addition, CDW-CE does not require any modifications at the output layer and is compatible with the class activation map visualization techniques.

Ordinal regression predicts the objects' labels that exhibit a natural ordering, which is important to many managerial problems such as credit scoring and clinical diagnosis. In these problems, the ability to explain how the attributes affect the prediction is critical to users. However, most, if not all, existing ordinal regression models simplify such explanation in the form of constant coefficients for the main and interaction effects of individual attributes. Such explanation cannot characterize the contributions of attributes at different value scales. To address this challenge, we propose a new explainable ordinal regression model, namely, the Explainable Ordinal Factorization Model (XOFM). XOFM uses the piece-wise linear functions to approximate the actual contributions of individual attributes and their interactions. Moreover, XOFM introduces a novel ordinal transformation process to assign each object the probabilities of belonging to multiple relevant classes, instead of fixing boundaries to differentiate classes. XOFM is based on the Factorization Machines to handle the potential sparsity problem as a result of discretizing the attribute scales. Comprehensive experiments with benchmark datasets and baseline models demonstrate that the proposed XOFM exhibits superior explainability and leads to state-of-the-art prediction accuracy.

We address the problem of general supervised learning when data can only be accessed through an (indefinite) similarity function between data points. Existing work on learning with indefinite kernels has concentrated solely on binary/multi-class classification problems. We propose a model that is generic enough to handle any supervised learning task and also subsumes the model previously proposed for classification. We give a "goodness" criterion for similarity functions w.r.t. a given supervised learning task and then adapt a well-known landmarking technique to provide efficient algorithms for supervised learning using "good" similarity functions. We demonstrate the effectiveness of our model on three important super-vised learning problems: a) real-valued regression, b) ordinal regression and c) ranking where we show that our method guarantees bounded generalization error. Furthermore, for the case of real-valued regression, we give a natural goodness definition that, when used in conjunction with a recent result in sparse vector recovery, guarantees a sparse predictor with bounded generalization error. Finally, we report results of our learning algorithms on regression and ordinal regression tasks using non-PSD similarity functions and demonstrate the effectiveness of our algorithms, especially that of the sparse landmark selection algorithm that achieves significantly higher accuracies than the baseline methods while offering reduced computational costs.

We present a reduction framework from ordinal regression to binary classification based on extended examples. The framework consists of three steps: extracting extended examples from the original examples, learning a binary classifier on the extended examples with any binary classification algorithm, and constructing a ranking rule from the binary classifier. A weighted 0/1 loss of the binary classifier would then bound the mislabeling cost of the ranking rule. Our framework allows not only to design good ordinal regression algorithms based on well-tuned binary classification approaches, but also to derive new generalization bounds for ordinal regression from known bounds for binary classification.