## 1 Introduction  
The response rate of a survey, the extent to which submitted surveys are fully completed, and the reliability of the information provided by respondents each greatly depend on the length of time required to take the survey (see, for example, [PERSON] and [PERSON] (1992) [1] and [PERSON] _et al._ (2010) [2]). Shortening a survey without losing important information is quantitatively feasible when past surveys can be analyzed to develop branching rules for future respondents. Branching rules customize the survey experience for each respondent by taking advantage of paths through the survey that are estimated to be highly predictable based on past survey respondents. While individual survey questions are typically not highly predictable over the entire population of respondents, it is frequently the case that a patterned response to one set of questions leads to a predictable response to another question. Consider a hypothetical example where a vast majority of respondents who answer 'Yes' on the first two questions of a survey also answer 'Yes' on the third question. If this is the case, then the third question could be skipped for the respondents who answer 'Yes' to the first two questions. We refer to skipping the third question, based on a 'Yes' to the first two questions, as a branching rule. Using past survey data to learn branching rules is the subject of this paper. Incorporating branching rules into a survey optionally shortens the survey for a respondent based on their individual responses. This approach differs from shortening the survey by simply eliminating questions altogether. We are not attempting to shorten the survey by entirely removing one or more questions. Instead, branching rules offer respondents alternative paths through the survey. The paths vary in length and are dictated by the developing pattern of responses. One respondent might only be able to skip a few of the questions, while another might be able to skip many. Some respondents may not skip any questions. Our premise is that the individual questions on the survey have already been vetted for their potential to provide unique value. What is more difficult to do a-priori is judge if there are branching rules that could effectively shorten the survey. We propose to identify these situations by mining a repository of past survey data. Depending on the number of questions in a survey, it may be suitable to individually examine subsections of related questions when learning associations. We focus on the context where the questions on the survey have binary responses. We discuss how our approach can be adapted for more general situations. Key to our strategy for learning branching rules is an inputted accuracy level. The accuracy level specifies the maximum allowable discrepancy rate between the actual answers provided in the repository of surveys and the answers that would be implied by running those respondents through the new survey design that incorporates the branching rules. In this way, the inputted accuracy level controls the level of loss in the information that results from implementing branching rules. The rest of this paper is organized as follows. Section 2 places the work presented in this paper into context with related literature. In Section 3, we provide the motivation for our work. First, we describe a survey used for geriatric assessment that provides guidance on treatment therapy for breast cancer patients. Second, we discuss the challenges of administering the survey to these patients and highlight the value in shortening the time needed for the patients to complete the survey. In Section 4, we describe in detail our solution for learning branching rules from past survey data. Our description is aided by a sketch of an algorithm included in the appendix that implements the solution. Section 5 discusses some properties of our proposed solution. In Section 6, we use our proposed solution to learn branching rules for three different subsections of questions on the geriatric assessment survey.