[latexpage]I recently read the paper “Variational Inference for Crowdsourcing,” by Qiang Liu, Jian Peng, and Alexander Ihler. They present an approach using belief propagation to deal with reliability when using crowdsourcing to collect labeled data. This post is based on their exposition. Crowdsourcing (via services such as Amazon Mechanical Turk) has been used as a cheap way to amass large quantities of labeled data. However, the labels are likely to be noisy. To deal with this, a common strategy is to employ redundancy: each task is labeled by multiple workers. For simplicity, suppose there are $N$ tasks and $M$ workers, and assume that the possible labels are $\{\pm 1\}$. Define the $N \times M$ matrix $L$ so that $L_{ij}$ is …

## Discriminative (supervised) Learning

Often the goal of inference and learning is to use the inferred marginal distributions for prediction or classification purposes. In such scenarios, finding the correct “model structure” or the true “model parameters”, via maximum-likelihood (ML) estimation or (generalized) expectation-maximization (EM), is secondary to the final objective of minimizing a prediction or a classification cost function. Recently, I came across a few interesting papers on learning and inference in graphical models by direct optimization of a cost function of the inferred marginal distributions (or normalized beliefs) [1, 2, 3, 4]: , where f is a differentiable function that maps the beliefs (bs) to the outcomes/labels of interest, is a set of model parameters, and C is a differentiable cost function that penalizes for incorrect …