A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
A new model estimates mixed memberships for categorical data with weighted responses.
An efficient algorithm selects the correct number of latent dimensions in multidimensional probit models.
A new model integrates covariates with grade of membership analysis for better latent structure recovery.
Modern machine learning methods are critical to the development of large-scale personalized learning systems that cater directly to the needs of individual learners. The recently developed SPARse Factor Analysis (SPARFA) framework provides a new statistical model and algorithms for machine learning-based learning analy…
While computer and communication technologies have provided effective means to scale up many aspects of education, the submission and grading of assessments such as homework assignments and tests remains a weak link. In this paper, we study the problem of automatically grading the kinds of open response mathematical qu…
New algorithm speeds up IRT model fitting for large datasets.
Machine learning offers novel ways and means to design personalized learning systems wherein each student's educational experience is customized in real time depending on their background, learning goals, and performance to date. SPARse Factor Analysis (SPARFA) is a novel framework for machine learning-based learning a…
Access to high-quality education at scale is limited by the difficulty of providing student feedback on open-ended assignments in structured domains like computer programming, graphics, and short response questions. This problem has proven to be exceptionally difficult: for humans, it requires large amounts of manual w…
We bring the theory of rough paths to the study of non-parametric statistics on streamed data. We discuss the problem of regression where the input variable is a stream of information, and the dependent response is also (potentially) a stream. A certain graded feature set of a stream, known in the rough path literature…
Aim: To review how machine learning (ML) is applied to imaging biomarkers in neuro-oncology, in particular for diagnosis, prognosis, and treatment response monitoring. Materials and Methods: The PubMed and MEDLINE databases were searched for articles published before September 2018 using relevant search terms. The sear…
Study prenatal PM2.5 exposure and 4th grade reading scores, identifying critical windows of susceptibility.
New method estimates high-dimensional GoM models efficiently.
No-knowledge alarms detect misaligned LLM judges without trusting them.
The recently proposed SPARse Factor Analysis (SPARFA) framework for personalized learning performs factor analysis on ordinal or binary-valued (e.g., correct/incorrect) graded learner responses to questions. The underlying factors are termed "concepts" (or knowledge components) and are used for learning analytics (LA),…
We propose a new probabilistic graphical model that jointly models the difficulties of questions, the abilities of participants and the correct answers to questions in aptitude testing and crowdsourcing settings. We devise an active learning/adaptive testing scheme based on a greedy minimization of expected model entro…
Graded Transformers embed algebraic structure in neural networks through graded transformations.
This paper aims at setting out the basics of -graded manifolds theory. We introduce -graded manifolds from local models and give some of their properties. The requirement to work with a completed graded symmetric algebra to define functions is made clear. Moreover, we define vector fields and ex…
This paper develops a theory of graded manifolds in differential geometry.
Convolutional neural networks improve KL grade prediction from Indian knee radiographs.
Grade prediction for future courses not yet taken by students is important as it can help them and their advisers during the process of course selection as well as for designing personalized degree plans and modifying them based on their performance. One of the successful approaches for accurately predicting a student'…
Proposes new models to predict student grades more accurately.
This is the second in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we extend the classical notion of a dg-algebra to define, in particular, the notion of a differential graded algebra in the wo…
Generative models' evaluation scores can be misleading, leading to inflated grades.
Constructive approach to Lie algebra gradings, computing maximal and enumerating all gradings.
The geometry of graded principal bundles is discussed in the framework of graded manifold theory of Kostant-Berezin-Leites. In particular, we prove that a graded principal bundle is globally trivial if and only if it admits a global graded section and, further, that the sheaf of vertical derivations on such a bundle co…
In massive open online courses (MOOCs), peer grading serves as a critical tool for scaling the grading of complex, open-ended assignments to courses with tens or hundreds of thousands of students. But despite promising initial trials, it does not always deliver accurate results compared to human experts. In this paper,…
Classifies objects in graded skew-gentle algebras using geometric models.
The paper establishes T-duality for 2D σ-models with H-flux.
Paper proposes a fair grading method for randomized exams.
Three definitions of graded vector bundles are shown to be equivalent.
We develop a new model and algorithms for machine learning-based learning analytics, which estimate a learner's knowledge of the concepts underlying a domain, and content analytics, which estimate the relationships among a collection of questions and those concepts. Our model represents the probability that a learner p…
The paper studies graded manifolds and their functorial relationship.
Three new types of graded Lie groups are constructed and analyzed.
In this paper we discuss the question of integrating differential graded Lie algebras (DGLA) to differential graded Lie groups (DGLG). We first recall the classical problem of integration in the context, and present the construction for (non-graded) differential Lie algebras. Then, we define the category of differentia…
We review the concept of a graded bundle as a natural generalisation of a vector bundle. Such geometries are particularly nice examples of more general graded manifolds. With hindsight there are many examples of graded bundles that appear in the existing literature. We start with a discussion of graded spaces, passing …
The paper defines and studies the category of Z-graded manifolds, including their intrinsic structure and formal properties.
MGDL refines deep neural networks by training grades sequentially, improving stability.
Combines generalized and graded geometry to explore new structures.
Framework for fast CAT calibration and administration using AutoML and IRT.
Extends Morse-Novikov Homology to include differential graded coefficients and fibration structures.
The paper examines smoothness in graded skew Clifford algebras.
The paper defines Z-graded hom-Lie superalgebras and explores their properties.
In this paper, we construct a canonical grading on bordered Heegaard Floer homology by homotopy classes of nonvanishing vector fields. This grading is a generalization of our construction of an absolute grading on Heegaard Floer homology and it extends the well-known grading with values in a noncommutative group define…
A pseudo -type Lie algebra naturally gives rise to a conformal pseudo-subriemannian fundamental graded Lie algebras. In this paper we investigate the prolongations of the associated fundamental graded Lie algebra and the associated conformal pseudo-subriemannian fundamental graded Lie algebra. In particular, we show…
Characterizes fundamental groups of disjointly tree-graded spaces.
Unified model for knot polynomials using quantum Heegaard diagrams.
Given a unital associatve graded algebra we construct the graded q-differential algebra by means of a graded q-commutator, where q is a primitive N-th root of unity. The N-th power (N>1) of the differential of this graded q-differential algebra is equal to zero. We use our approach to construct the graded q-differentia…
We propose SPARFA-Trace, a new machine learning-based framework for time-varying learning and content analytics for education applications. We develop a novel message passing-based, blind, approximate Kalman filter for sparse factor analysis (SPARFA), that jointly (i) traces learner concept knowledge over time, (ii) an…