Topic: Text as Data

Abstract: Professor Wedeking will give a summary of three projects that he has been involved in using text as data (1 is published, 1 is under review, and 1 is ongoing). Specifically, for each of the 3 projects, He will:  (1) describe the method he's using, what it generally is used for;  (2) the motivation for the project-e.g., the substantive research question and relevant background information;  (3) a brief description of the data; and  (4) the results of the method and the substantive conclusions.  The three projects are: (1) measuring how legal issues are framed (e.g., free speech vs. right to privacy, etc) and how that helps parties win; (2) uncovering the clarity of texts using readability formulas; and (3) scaling justices with texts- uncovering their ideological positions (how liberal or conservative they are) using their words.

Abstract:

We present a Multivariate Decomposition Method (MDM) for approximating integrals of functions with countably many variables. We assume that the integrands have mixed first order partial derivatives bounded in a γ = {γ_u }u⊂N+ -weighted Lp norm. We also assume that the integrands can be evaluated only at points with finitely many (d) coordinates different than zero and that the cost of such a sampling is equal to $(d) for a given cost function $. We show that MDM can approximate the integrals with the worst case error bounded by ε at cost proportional to −1+|O(ln(1/ε)/ ln(ln(1/ε)))| ε even if the cost function is exponential in d, i.e., $(d) = e^{O(d)}.  This is an almost optimal method since all algorithms for univariate functions (d = 1) from this space have the cost bounded from below by Ω(1/ε).