Figure 2: On the bottom we see a representation oftheproposed regression model that captures all the componentsτi of the mixture of Asymmetric Laplacian distributions (ALD)simultaneously.

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Thistask is challenging because the causal graph is unknown and even there may exist latent confounders.

Thistask is challenging because the causal graph is unknown and even there may exist latent confounders.

Consider the setting of Linear Regression where the observed response variables, in expectation, are linear functions of the p-dimensional covariates. Then to achieve vanishing prediction error, the number of required samples scales faster than pσ2, where σ2 is a bound on the noise variance. In a high-dimensional setting where p is large but the covariates admit a low-dimensional representation (say r p), then Principal Component Regression (PCR), cf.

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Inspired by a two-level theory that unifies agenda setting and ideological framing, we propose supervised hierarchical latent Dirichlet allocation (SHLDA) which jointly captures documents' multi-level topic structure and their polar response variables. Our model extends the nested Chinese restaurant process to discover a tree-structured topic hierarchy and uses both per-topic hierarchical and per-word lexical regression parameters to model the response variables. Experiments in a political domain and on sentiment analysis tasks show that SHLDA improves predictive accuracy while adding a new dimension of insight into how topics under discussion are framed.