Related papers: On the Structure of Ordered Latent Trait Models
In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic…
Mechanistic interpretability aims to understand how neural networks generalize beyond their training data by reverse-engineering their internal structures. We introduce patterning as the dual problem: given a desired form of generalization,…
An agent-based model for financial markets has to incorporate two aspects: decision making and price formation. We introduce a simple decision model and consider its implications in two different pricing schemes. First, we study its…
A structural time series model additively decomposes into generative, semantically-meaningful components, each of which depends on a vector of parameters. We demonstrate that considering each generative component together with its vector of…
The Bradley-Terry (BT) model is a common and successful practice in reward modeling for Large Language Model (LLM) alignment. However, it remains unclear why this model -- originally developed for multi-player stochastic game matching --…
It is reasonable to consider, in many cases, that individuals' latent traits have a hierarchical structure such that more general traits are a suitable composition of more specific ones. Existing item response models that account for such…
Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the…
Human beings learn causal models and constantly use them to transfer knowledge between similar environments. We use this intuition to design a transfer-learning framework using object-oriented representations to learn the causal…
In model-based reinforcement learning, generative and temporal models of environments can be leveraged to boost agent performance, either by tuning the agent's representations during training or via use as part of an explicit planning…
A burgeoning literature in economics studies how people form beliefs about the causal structures linking economic variables, and what happens when those beliefs are mistaken. We survey this research and connect it to a rich literature in…
With a growing number of BERTology work analyzing different components of pre-trained language models, we extend this line of research through an in-depth analysis of discourse information in pre-trained and fine-tuned language models. We…
Probabilistic graphical models (PGMs) are widely used to discover latent structure in data, but their success hinges on selecting an appropriate model design. In practice, model specification is difficult and often requires iterative…
Predictive models that are developed in a regulated industry or a regulated application, like determination of credit worthiness, must be interpretable and rational (e.g., meaningful improvements in basic credit behavior must result in…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
As the use of machine learning models has increased, numerous studies have aimed to enhance fairness. However, research on the intersection of fairness and explainability remains insufficient, leading to potential issues in gaining the…
Decision analysis deals with modeling and enhancing decision processes. A principal challenge in improving behavior is in obtaining a transparent description of existing behavior in the first place. In this paper, we develop an expressive,…
Our goal is to show that the standard model-theoretic concept of types can be applied in the study of order-invariant properties, i.e., properties definable in a logic in the presence of an auxiliary order relation, but not actually…
We study individual decision-making behavioral on generic view. Using a formal mathematical model, we investigate the action mechanism of decision behavioral under subjective perception changing of task attributes. Our model is built on…
Compositional, structured models are appealing because they explicitly decompose problems and provide interpretable intermediate outputs that give confidence that the model is not simply latching onto data artifacts. Learning these models…
Written to be contributed as the "mathematical modeling" chapter of a book, edited by Elaine Landry, to be titled "Categories for the Working Philosopher". In this chapter, category theory is presented as a mathematical modeling framework…