Sparse Conjoint Analysis Through Maximum Likelihood Estimation
Sparse Conjoint Analysis Through Maximum Likelihood Estimation
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DOI：
10.1109/tsp.2013.2278529
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发表时间：
2013-11
影响因子：
5.4
通讯作者：
Efthimios E. Tsakonas;J. Jaldén;N. Sidiropoulos;B. Ottersten
中科院分区：
文献类型：
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作者：
Efthimios E. Tsakonas;J. Jaldén;N. Sidiropoulos;B. Ottersten
联合分析（CA）是偏好评估中使用的经典工具，其目标是基于表达的偏好数据来估计个体或群体的效用函数。一个例子是用于消费者分析的基于选择的CA，即，揭示消费者效用函数仅仅基于产品之间的选择。本文研究了一种基于选择的CA统计模型。与最近的分类为基础的方法，稀疏感知高斯最大似然（ML）制定提出了估计模型参数。借鉴相关的强大的简约建模方法，该模型使用稀疏约束来考虑离群值，并检测影响决策的显着特征。贡献包括统计可识别性的条件，推导相关的Cramér-Rao下限（CRLB），以及拟议的稀疏非线性模型的ML一致性条件。建议的ML方法自然适合于基于交替方向乘法器（ADMM）的非常适合分布式实现的M1型凸松弛。一个特定的分解主张绕过明显需要离群通信，从而保持可扩展性。所提出的ML方法的性能通过与相关的CRLB和现有的最先进的合成和真实的数据集进行比较来证明。
Conjoint analysis (CA) is a classical tool used in preference assessment, where the objective is to estimate the utility function of an individual, or a group of individuals, based on expressed preference data. An example is choice-based CA for consumer profiling, i.e., unveiling consumer utility functions based solely on choices between products. A statistical model for choice-based CA is investigated in this paper. Unlike recent classification-based approaches, a sparsity-aware Gaussian maximum likelihood (ML) formulation is proposed to estimate the model parameters. Drawing from related robust parsimonious modeling approaches, the model uses sparsity constraints to account for outliers and to detect the salient features that influence decisions. Contributions include conditions for statistical identifiability, derivation of the pertinent Cramér-Rao Lower Bound (CRLB), and ML consistency conditions for the proposed sparse nonlinear model. The proposed ML approach lends itself naturally to ℓ1-type convex relaxations which are well-suited for distributed implementation, based on the alternating direction method of multipliers (ADMM). A particular decomposition is advocated which bypasses the apparent need for outlier communication, thus maintaining scalability. The performance of the proposed ML approach is demonstrated by comparing against the associated CRLB and prior state-of-the-art using both synthetic and real data sets.