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arXiv research

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.

168,982 papers · 148 categories

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48 results for question difficulty

New ensemble models classify mouse movement trajectories to assess survey question difficulty.

problem Assessing survey question difficulty based on respondents' interaction data.
method Ensemble models combining semi-metric-based weak learners to classify multivariate functional data.
result Improved survey data quality through better identification of respondent difficulty.

This study introduces balanced DRPS and OrderedLogitNN for better QDE of discrete-level questions.

problem Lack of ordinal regression methods and fair evaluation metrics for discrete-level QDE.
method Introduces balanced DRPS and OrderedLogitNN, fine-tunes BERT on RACE++ and ARC datasets.
result OrderedLogitNN outperforms other models on complex QDE tasks.

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…

2013-12-19abs ↗pdf ↗

We introduce an invariant linked to some foundational questions in geometric measure theory and provide bounds on this invariant by decomposing an arbitrary cycle into uniformly rectifiable pieces. Our invariant measures the difficulty of cutting a nonorientable closed manifold or mod-2 cycle in Rn\mathbb{R}^n into ori…

2013-12-03abs ↗pdf ↗

The paper explores when to prioritize easy or hard samples in learning tasks.

problem Determining the optimal order of learning easy or hard samples.
method Theoretical analyses and experiments were conducted to propose and validate four priority modes.
result Four priority modes (easy-first, hard-first, medium-first, two-ends-first) can be flexibly applied.

Fast approximate nearest neighbor (NN) search in large databases is becoming popular. Several powerful learning-based formulations have been proposed recently. However, not much attention has been paid to a more fundamental question: how difficult is (approximate) nearest neighbor search in a given data set? And which …

2012-06-27abs ↗pdf ↗

A problem faced by many instructors is that of designing exams that accurately assess the abilities of the students. Typically these exams are prepared several days in advance, and generic question scores are used based on rough approximation of the question difficulty and length. For example, for a recent class taught…

2017-12-24abs ↗pdf ↗

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…

2013-03-22abs ↗pdf ↗

The paper tackles adaptive questioning to classify candidate ability.

problem Designing an optimal sequence of adaptive questions to classify candidate ability.
method Develops lower bounds and geometrical insights for sequential questioning strategies, and arrives at algorithms that match these bounds.
result Asymptotically, any candidate needs to be asked questions at most at two levels, facilitating endogenous exploration.

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),…

2014-12-18abs ↗pdf ↗

This paper poses some basic questions about instances (hard to find) of a special problem in 3-manifold topology. "Important though the general concepts and propositions may be with the modern industrious passion for axiomatizing and generalizing has presented us...nevertheless I am convinced that the special problems …

2013-04-18abs ↗pdf ↗

The study explores how partial observations of network nodes can infer the graph structure.

problem How much information does observing a limited fraction of network nodes provide about the underlying graph structure?
method The article examines the inverse problem of graph learning under partial observability, focusing on decentralized processing strategies and large-scale networks.
result Partial observations of network nodes can still be sufficient to discover the graph linking the probed nodes, despite the presence of unobserved nodes.

A new framework evaluates LLM calibration in open-ended QA.

problem Evaluating LLM calibration in open-ended QA settings.
method Sem-ECE framework: sampling answers, grouping by semantic classes, and using frequencies as confidence.
result Sem-ECE estimators are unbiased and Sem2_2 achieves smaller calibration error.

New research shows deep learning struggles with hard problems due to biased data generation.

problem Deep learning's limitations in solving computationally hard problems.
method Proved that polynomial-time sample generators for NP-hard problems sample from easier sub-problems.
result Machine learning models trained on biased datasets overestimate their accuracy for hard problems.

Deep networks prioritize easier examples over harder ones, leading to faster training.

problem Understanding how deep networks prioritize examples of varying difficulty.
method Investigated the effect of linear vs non-linear learning modes on example difficulty.
result Non-linear dynamics tend to sequentialize the learning of examples of increasing difficulty.

Often, more time is spent on finding a model that works well, rather than tuning the model and working directly with the dataset. Our research began as an attempt to improve upon a simple Recurrent Neural Network for answering "simple" first-order questions (QA-RNN), developed by Ferhan Ture and Oliver Jojic, from Comc…

2018-07-12abs ↗pdf ↗

Optimal ability estimation in adaptive testing with binary responses.

problem Estimating a continuous ability parameter from sequential binary responses.
method Adaptive selection of questions to maximize Fisher information, updating estimate using method-of-moments, and deciding accuracy with a test statistic.
result Fisher-tracking strategy achieves optimal performance in fixed-confidence and fixed-budget regimes.

The question of how to parallelize the stochastic gradient descent (SGD) method has received much attention in the literature. In this paper, we focus instead on batch methods that use a sizeable fraction of the training set at each iteration to facilitate parallelism, and that employ second-order information. In order…

2016-05-19abs ↗pdf ↗

The famous Nash embedding theorem published in 1956 was aiming for the opportunity to use extrinsic help in the study of (intrinsic) Riemannian geometry, if Riemannian manifolds could be regarded as Riemannian submanifolds. However, this hope had not been materialized yet according to \cite{G}. The main reason for this…

2013-07-07abs ↗pdf ↗

The article confirms a conjecture for solvmanifolds with complex commutator.

problem Confirming a conjecture about compact Hermitian manifolds with constant holomorphic sectional curvature.
method Analyzing solvmanifolds with complex commutator, extending results on nilmanifolds.
result The conjecture is confirmed for all solvmanifolds with complex commutator.

Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by finding the values which yield simulated data that resemble the observed data. Thi…

2015-02-19abs ↗pdf ↗

We focus on the distribution regression problem: regressing to a real-valued response from a probability distribution. Although there exist a large number of similarity measures between distributions, very little is known about their generalization performance in specific learning tasks. Learning problems formulated on…

2014-02-07abs ↗pdf ↗

Machine learning uses crowdworkers; determining their status as human subjects is tricky.

problem Determining the appropriate status of ML crowdworkers as human subjects.
method Investigation of natural language processing studies to expose challenges and propose solutions.
result Potential loophole in the U.S. Common Rule for ML research oversight.

Study automorphism groups of geodesic currents and measured laminations on surfaces.

problem Prove Ivanov's meta-conjecture for automorphism groups of geodesic currents.
method Investigate two automorphism groups, Aut(C)Aut(\mathscr{C}) and Aut(ML)Aut(\mathcal{ML}), and compare them to the extended mapping class group.
result Prove Aut(ML)Aut(\mathcal{ML}) is isomorphic to the extended mapping class group for most cases, except a few special cases.

New research shows that binary classification can be done with noisy data, but only if there are clean samples available.

problem Learning binary classification with instance and label dependent label noise.
method Theoretical analysis and empirical risk minimization.
result Empirical risk minimization achieves the optimal excess risk bound without additional assumptions.