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Social Cognitive Career Theory (SCCT) has been extensively employed to elucidate the enduring gender differences in mathematics-intensive fields, with a particular emphasis on the complex interplay of motivational factors and extra-personal…
This paper provides an overview of the applications of sheaf theory in deep learning, data science, and computer science in general. The primary text of this work serves as a friendly introduction to applied and computational sheaf theory…
Few models have been more ubiquitous in their respective fields than Bayesian knowledge tracing and item response theory. Both of these models were developed to analyze data on learners. However, the study designs that these models are…
In many modern applications, there is interest in analyzing enormous data sets that cannot be easily moved across computers or loaded into memory on a single computer. In such settings, it is very common to be interested in clustering.…
The sole aim of this book is to give a self-contained introduction to concepts and mathematical tools in Bayesian matrix decomposition in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent…
Several recently proposed methods aim to learn conceptual space representations from large text collections. These learned representations asso- ciate each object from a given domain of interest with a point in a high-dimensional Euclidean…
As the amount of economic and other data generated worldwide increases vastly, a challenge for future generations of econometricians will be to master efficient algorithms for inference in empirical models with large information sets. This…
The idea that the brain is a probabilistic (Bayesian) inference machine, continuously trying to figure out the hidden causes of its inputs, has become very influential in cognitive (neuro)science over recent decades. Here I present a…
We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is…
Artificial Intelligence (AI), and in particular, the explainability thereof, has gained phenomenal attention over the last few years. Whilst we usually do not question the decision-making process of these systems in situations where only…
A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for specifying and reasoning about algorithms that manipulate mathematical…
As a result of the increased emphasis on mis- and over-use of $p$-values in scientific research and the rise in popularity of Bayesian statistics, Bayesian education is becoming more important at the undergraduate level. With the advances…
A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the…
Knowledge graphs are increasingly used in a plethora of downstream tasks or in the augmentation of statistical models to improve factuality. However, social biases are engraved in these representations and propagate downstream. We conducted…
Using a diagrammatic reformulation of Bayes' theorem, we provide a necessary and sufficient condition for the existence of Bayesian inference in the setting of finite-dimensional $C^*$-algebras. In other words, we prove an analogue of…
Text Document classification aims in associating one or more predefined categories based on the likelihood suggested by the training set of labeled documents. Many machine learning algorithms play a vital role in training the system with…
Bayesian forecasting is developed in multivariate time series analysis for causal inference. Causal evaluation of sequentially observed time series data from control and treated units focuses on the impacts of interventions using…
Deep learning based visual-linguistic multimodal models such as Contrastive Language Image Pre-training (CLIP) have become increasingly popular recently and are used within text-to-image generative models such as DALL-E and Stable…
Bayes nets are relatively recent innovations. As a result, most of their theoretical development has focused on the simplest class of single-author models. The introduction of more sophisticated multiple-author settings raises a variety of…
Bayesian Filtering for plan and activity recognition is challenging for scenarios that contain many observation equivalent entities (i.e. entities that produce the same observations). This is due to the combinatorial explosion in the number…