高效序列Gibbs采样法：大规模认知诊断模型
需积分: 14 11 浏览量
更新于2024-07-15
收藏 362KB PDF 举报
"这篇论文提出了一种用于处理大量属性的认知诊断模型的Sequential Gibbs采样算法，解决了当属性数量（K）较大时，传统Markov Chain Monte Carlo (MCMC)算法计算复杂度过高的问题。通过将时间复杂度从O(2^K)降低到O(K)，该方法显著提高了效率。在DINA模型和GDINA模型上进行了实验，并在仿真数据、分数减法数据集以及TIMMS 2007实际数据集上验证了其性能。对于K=15，I=2000，J=30的参数设置，模型在3000次迭代中仅需170秒，显示了高效性。关键词包括Gibbs采样、GDINA、参数估计和认知诊断。"
认知诊断模型(Cognitive Diagnosis Models, CDMs)是统计学中一种强大的工具，它们能够提供有关干预和学习的深入信息。在教育和心理学等领域，CDMs被广泛应用于评估个体的知识掌握程度和能力结构。其中，DINA模型（Diagnostic Model for Multiple Attributes）和GDINA（Generalized DINA）模型是两种常用模型，分别代表了不同的假设和复杂度。
传统的MCMC算法是估计和推断CDMs的常见方法，但在属性数量大时，由于需要计算每个属性配置的条件分布，其时间复杂度高，导致计算效率低下。为了克服这个问题，作者提出了一个序列Gibbs采样方法。这种新方法通过减少计算量，使得每次采样属性配置仅需O(K)的计算，极大地提升了效率。
在模拟数据和真实数据实验中，Sequential Gibbs采样展示出了良好的有限样本性能，并且在处理大规模属性集时比现有方法具有优势。例如，当K=15，I=2000，J=30的条件下，模型在3000次迭代中只需170秒，这表明新算法在处理大问题时的计算速度显著快于传统方法。
这篇论文提出的Sequential Gibbs采样算法为解决CDMs的大规模属性估计问题提供了一个高效解决方案，对于需要快速处理大量数据的领域，如大规模在线学习评估，具有重要的实践意义。
2.2 Priors of Measurement Models’ Parameters
The population proportion parameter π includes t he saturated information about the
attribute profile distribution in CDMs. The Dirichlet distribution is commonly used as
a conjugated prio r for π, such as Culpepper (2015), Culpepper and Hudson (2018) and
Zhan et al. (2019). The specific form of the Dirichlet prior for π is
p(π) = p(π
1
, · · · , π
C
) = Dirichlet(δ
1
, · · · , δ
C
).
Let the notation δ = (δ, · · · , δ
C
)
′
represent a C-dimensional hyper-par ameter vector of π,
and we denote the prior p(π) by Dir ichlet(δ). The Dirichlet prior implies the generation
of attribute profiles, i.e., δ determines π and π determines α.
In different CDMs, item parameters will be presented in the different f orms: g
j
and
s
j
are item parameters in the DINA model, respectively, and λ
j
is the item parameter
in the GDINA model. For the DINA model, independent Beta distributions, Beta(a
g
, b
g
)
and Beta(a
s
, b
s
), are often used as the prio r s for guessing and slipping parameters, respec-
tively. We may also constraint 0 ≤ g
j
< 1 − s
j
≤ 1, to ensure the mo del identifiability
(Junker and Sijtsma, 2001; Chen et al., 2018; Xu and Zhang , 2016; Gu and Xu, 2019).
For the GDINA model, the item parameters λ are r egr ession coefficients. The normal
distributions are often taken as priors for the item parameters (e.g., Zhan et a l., 2019).
Specifically, two types of pr iors are often chosen for item parameters, the one is a multi-
variate normal distribution, λ
j
∼ N(µ
λ
j
, Σ
λ
j
), as a general choice; the other is a truncated
multivariate normal distribution, λ
j
∼ N(µ
λ
j
, Σ
λ
j
)I
{λ
j
∈T }
, which is used to ensure cer-
tain monotonicity assumption of the item resp onse function. Particularly, assuming the
dimension of λ
j
is M, T = { T
1
, · · · , T
M
} and each set T
m
represents some pr e-specified
constraint of the m-th element of λ
j
. For instance, we may r estrict the main effect terms
in λ
j
to be positive to ensure the monotonicity assumption. For the indicator function
I
{λ
j
∈T }
, I
{λ
j
∈T }
= 1 if λ
jm
∈ T
m
for m = 1, · · · , M and I
{λ
j
∈T }
= 0 otherwise.
As discussed in the introduction, for a large K, the existing MCMC algorithms with
Dirichlet prior for π often suffer from the increasing computationa l cost of sampling
each latent attribute profile α
i
from its conditiona l distribution, which is a categorical
distribution with 2
K
different categories. Therefore, it needs to evaluate 2
K
posterior
probabilities of each possible profile candidate to sample each α
i
, and the corresponding
7
剩余36页未读，继续阅读
2010-03-11 上传
2020-10-28 上传
2023-03-05 上传
2021-02-21 上传
2019-04-11 上传
2021-02-21 上传
2024-09-13 上传
maerdym
- 粉丝: 307
- 资源: 20
我的内容管理
展开
最新资源
- 天池大数据比赛：伪造人脸图像检测技术
- ADS1118数据手册中英文版合集
- Laravel 4/5包增强Eloquent模型本地化功能
- UCOSII 2.91版成功移植至STM8L平台
- 蓝色细线风格的PPT鱼骨图设计
- 基于Python的抖音舆情数据可视化分析系统
- C语言双人版游戏设计：别踩白块儿
- 创新色彩搭配的PPT鱼骨图设计展示
- SPICE公共代码库：综合资源管理
- 大气蓝灰配色PPT鱼骨图设计技巧
- 绿色风格四原因分析PPT鱼骨图设计
- 恺撒密码：古老而经典的替换加密技术解析
- C语言超市管理系统课程设计详细解析
- 深入分析：黑色因素的PPT鱼骨图应用
- 创新彩色圆点PPT鱼骨图制作与分析
- C语言课程设计：吃逗游戏源码分享
