Collective Graphical Models
There are many settings in which we wish to fit a model of the behavior of individuals but where our data consist only of aggregate information (counts or low-dimensional contingency tables). This paper introduces Collective Graphical Models---a framework for modeling and probabilistic inference that operates directly on the sufficient statistics of the individual model. We derive a highly-efficient Gibbs sampling algorithm for sampling from the posterior distribution of the sufficient statistics conditioned on noisy aggregate observations, prove its correctness, and demonstrate its effectiveness experimentally.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Differentially Private Learning of Undirected Graphical Models using Collective Graphical Models
We investigate the problem of learning discrete, undirected graphical models in a differentially private way. We show that the approach of releasing noisy sufficient statistics using the Laplace mechanism achieves a good…
Gaussian Approximation of Collective Graphical Models
The Collective Graphical Model (CGM) models a population of independent and identically distributed individuals when only collective statistics (i.e., counts of individuals) are observed. Exact inference in CGMs is intra…
Probabilistic Optimal Transport based on Collective Graphical Models
Optimal Transport (OT) is being widely used in various fields such as machine learning and computer vision, as it is a powerful tool for measuring the similarity between probability distributions and histograms. In previ…
Robust Collective Classification against Structural Attacks
Collective learning methods exploit relations among data points to enhance classification performance. However, such relations, represented as edges in the underlying graphical model, expose an extra attack surface to th…
Adversarial RobustnessClassificationGeneral ClassificationTransductive LearningBethe Projections for Non-Local Inference
Many inference problems in structured prediction are naturally solved by augmenting a tractable dependency structure with complex, non-local auxiliary objectives. This includes the mean field family of variational infere…
Handwriting RecognitionStructured PredictionVariational Inference