Scalable Learning of Item Response Theory Models: Coresets for Efficient Computation

Основні поняття

The author presents a method to efficiently learn Item Response Theory models using coresets, enabling scalable computations from large datasets.

Анотація

The content discusses the challenges of learning IRT models from large datasets and introduces the concept of coresets to facilitate efficient computation. By leveraging similarities to logistic regression, the author demonstrates how coresets can be used in alternating optimization algorithms for IRT models.
Classical psychometric assessments with a small number of examinees and items contrast with modern global assessments like PISA, leading to scalability challenges. In Machine Learning contexts, where algorithms act as examinees and data problems as items, efficiency becomes crucial. Coresets are introduced as a solution to handle large data efficiently by approximating logistic regression problems within IRT models.
The paper provides theoretical guarantees for constructing coresets for both 2PL and 3PL IRT models. Experimental results show significant computational savings and comparable parameter estimation accuracy between full datasets and coresets. The approach offers a promising solution for handling large-scale IRT computations effectively.

Статистика

"n ≈ 600 000 examinees are being tested regularly."
"m ≈ 10 − 30 items in each category."
"μ-complexity ranges between 2 and 20."

Цитати

"There exists a weighted set K ∈ Rk×2 of size k ∈ O( µ3 ε4 (log(n)4 + log(m)), that is a (1 + ε)-coreset simultaneously for all X(i), i ∈ [m] for the 2PL IRT problem."
"Let each X(j) = (−YijαT i )i∈[m] ∈ Rm×2. Let X′(j) contain the rows i of X(j) where Yij = −1 and let X′′(j) comprise the rows with Yij = 1."
"The accuracy clearly improves with increasing coreset size."

Ключові висновки, отримані з

Scalable Learning of Item Response Theory Models

by Susa... о arxiv.org 03-04-2024

https://arxiv.org/pdf/2403.00680.pdf

Глибші Запити

How can the concept of coresets be applied to other machine learning algorithms beyond IRT models

Coresets can be applied to various machine learning algorithms beyond Item Response Theory (IRT) models to enhance scalability and efficiency. One key application is in clustering algorithms, where large datasets can be subsampled using coresets to represent the original data accurately while reducing computational complexity. This approach can significantly speed up clustering processes without compromising the quality of the results. Additionally, coresets can be utilized in regression analysis to handle massive datasets by creating smaller representative subsets that maintain statistical accuracy.

What potential limitations or biases may arise when using coresets in parameter estimation for non-convex problems

When using coresets for parameter estimation in non-convex problems, several limitations and biases may arise. One potential limitation is related to the choice of sampling probabilities for constructing the coreset. Biases may occur if certain parts of the data are overrepresented or underrepresented in the coreset due to incorrect weighting schemes or sensitivity estimates. In non-convex optimization problems, there is a risk of getting stuck in local optima even with coreset-based approaches, leading to suboptimal solutions. Moreover, inaccuracies in estimating sensitivities or VC dimension bounds could introduce errors into parameter estimates.

How might advancements in coreset construction impact the scalability of machine learning applications in various industries

Advancements in coreset construction have significant implications for enhancing scalability in machine learning applications across various industries. By improving the efficiency of handling large-scale datasets through coresets, machine learning models can process vast amounts of information more quickly and cost-effectively. This scalability enables real-time decision-making based on extensive data analysis, benefiting sectors such as finance, healthcare, e-commerce, and cybersecurity. With optimized coreset techniques, organizations can leverage complex machine learning algorithms on big data sets without overwhelming computational resources or sacrificing model accuracy.