Related papers: Knowledge Spaces and Learning Spaces
We describe the algorithms used by the ALEKS computer learning system for manipulating combinatorial descriptions of human learners' states of knowledge, generating all states that are possible according to a description of a learning space…
We study the data space $D$ of any given data set $X$ and explain how functions and relations are defined over $D$. From $D$ and for a specific domain $\Delta$ we construct the information space $I$ of $X$ by interpreting variables,…
Learning Spaces are certain set systems that are applied in the mathematical modeling of education. We propose a suitable compression (without loss of information) of such set systems to facilitate their logical and statistical analysis.…
Using the previously developed concepts of semantic spacetime, I explore the interpretation of knowledge representations, and their structure, as a semantic system, within the framework of promise theory. By assigning interpretations to…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous…
To answer complex queries on knowledge graphs, logical reasoning over incomplete knowledge is required due to the open-world assumption. Learning-based methods are essential because they are capable of generalizing over unobserved…
We consider the fundamental question: how a legacy "student" Artificial Intelligent (AI) system could learn from a legacy "teacher" AI system or a human expert without complete re-training and, most importantly, without requiring…
Active learning is a practical field of machine learning that automates the process of selecting which data to label. Current methods are effective in reducing the burden of data labeling but are heavily model-reliant. This has led to the…
Recent research has proposed neural architectures for solving combinatorial problems in structured output spaces. In many such problems, there may exist multiple solutions for a given input, e.g. a partially filled Sudoku puzzle may have…
We propose a theory of learning aimed to formalize some ideas underlying Coquand's game semantics and Krivine's realizability of classical logic. We introduce a notion of knowledge state together with a new topology, capturing finite…
In domains with high knowledge distribution a natural objective is to create principle foundations for collaborative interactive learning environments. We present a first mathematical characterization of a collaborative learning group, a…
Knowledge tracing is the task of predicting a learner's future performance based on the history of the learner's performance. Current knowledge tracing models are built based on an extensive set of data that are collected from multiple…
With the long term accumulation of high quality educational data, artificial intelligence has shown excellent performance in knowledge tracing. However, due to the lack of interpretability and transparency of some algorithms, this approach…
Computational models of human learning can play a significant role in enhancing our knowledge about nuances in theoretical and qualitative learning theories and frameworks. There are many existing frameworks in educational settings that…
A major problem in machine learning is that of inductive bias: how to choose a learner's hypothesis space so that it is large enough to contain a solution to the problem being learnt, yet small enough to ensure reliable generalization from…
An S-approximation space is a novel approach to study systems with uncertainty that are not expressible in terms of inclusion relations. In this work, we further examined these spaces, mostly from a topological point of view by a…
As the quantity of human knowledge increasing rapidly, it is harder and harder to evaluate a knowledge worker's knowledge quantitatively. There are lots of demands for evaluating a knowledge worker's knowledge. For example, accurately…
Lifelong learning can be viewed as a continuous transfer learning procedure over consecutive tasks, where learning a given task depends on accumulated knowledge --- the so-called knowledge base. Most published work on lifelong learning…
In modern machine learning, pattern recognition replaces realtime semantic reasoning. The mapping from input to output is learned with fixed semantics by training outcomes deliberately. This is an expensive and static approach which depends…