Internet data has surfaced as a primary source for investigation of different aspects of human behavior. A crucial step in such studies is finding a suitable cohort (i.e., a set of users) that shares a common trait of interest to researchers. However, direct identification of users sharing this trait is often impossible, as the data available to researchers is usually anonymized to preserve user privacy. To facilitate research on specific topics of interest, especially in medicine, we introduce an algorithm for identifying a trait of interest in anonymous users. We illustrate how a small set of labeled examples, together with statistical information about the entire population, can be aggregated to obtain labels on unseen examples. We validate our approach using labeled data from the political domain. We provide two applications of the proposed algorithm to the medical domain. In the first, we demonstrate how to identify users whose search patterns indicate they might be suffering from certain types of cancer. This shows, for the first time, that search queries can be used as a screening device for diseases that are currently often discovered too late, because no early screening tests exists. In the second, we detail an algorithm to predict the distribution of diseases given their incidence in a subset of the population at study, making it possible to predict disease spread from partial epidemiological data.
The task of determining labels for individuals from population statistics relates to the ecological inference problem. Ecological inference aims at inferring characteristics about individuals from ecological data (i.e., of the entire population). As an example, it might be used to answer the following question: '' Ecological inference has a long history in the fields of statistics and social studies @cite_17 . Recently, Flaxman, et al @cite_16 used kernel embeddings of distributions to predict which demographics groups supported Barack Obama in the 2012 US Presidential Election. Park and Gosh @cite_25 introduced LUDIA, a low-level rank approximation algorithm designed that leverages ecological inference to predict hospital spending for individuals based on their length of stay. Culotta, et al @cite_7 used website traffic data to predict demographics of Twitter user. Ultimately, our problem differs from ecological inference in that we are interested in identifying individuals whose distribution is known rather than inferring behaviors at an individual level from population data.
@cite_16 @cite_25 @cite_7 @cite_17
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We present a new solution to the ecological inference'' problem, of learning individual-level associations from aggregate data. This problem has a long history and has attracted much attention, debate, claims that it is unsolvable, and purported solutions. Unlike other ecological inference techniques, our method makes use of unlabeled individual-level data by embedding the distribution over these predictors into a vector in Hilbert space. Our approach relies on recent learning theory results for distribution regression, using kernel embeddings of distributions. Our novel approach to distribution regression exploits the connection between Gaussian process regression and kernel ridge regression, giving us a coherent, Bayesian approach to learning and inference and a convenient way to include prior information in the form of a spatial covariance function. Our approach is highly scalable as it relies on FastFood, a randomized explicit feature representation for kernel embeddings. We apply our approach to the challenging political science problem of modeling the voting behavior of demographic groups based on aggregate voting data. We consider the 2012 US Presidential election, and ask: what was the probability that members of various demographic groups supported Barack Obama, and how did this vary spatially across the country? Our results match standard survey-based exit polling data for the small number of states for which it is available, and serve to fill in the large gaps in this data, at a much higher degree of granularity. In the past few years, the government and other agencies have publicly released a prodigious amount of data that can be potentially mined to benefit the society at large. However, data such as health records are typically only provided at aggregated levels (e.g. per State, per Hospital Referral Region, etc.) to protect privacy. Unfortunately aggregation can severely diminish the utility of such data when modeling or analysis is desired at a per-individual basis. So, not surprisingly, despite the increasing abundance of aggregate data, there have been very few successful attempts in exploiting them for individual-level analyses. This paper introduces LUDIA, a novel low-rank approximation algorithm that utilizes aggregation constraints in addition to auxiliary information in order to estimate or "reconstruct" the original individual-level values from aggregate data. If the reconstructed data are statistically similar to the original individual-level data, off-the-shelf individual-level models can be readily and reliably applied for subsequent predictive or descriptive analytics. LUDIA is more robust to nonlinear estimates and random effects than other reconstruction algorithms. It solves a Sylvester equation and leverages multi-level (also known as hierarchical or mixed-effect) modeling approaches efficiently. A novel graphical model is also introduced to provide a probabilistic viewpoint of LUDIA. Experimental results using a Texas inpatient dataset show that individual-level data can be reasonably reconstructed from county-, hospital-, and zip code-level aggregate data. Several factors affecting the reconstruction quality are discussed, along with the implications of this work for current aggregation guidelines. Understanding the demographics of users of online social networks has important applications for health, marketing, and public messaging. Whereas most prior approaches rely on a supervised learning approach, in which individual users are labeled with demographics for training, we instead create a distantly labeled dataset by collecting audience measurement data for 1,500 websites (e.g., 50 of visitors to gizmodo.com are estimated to have a bachelor's degree). We then fit a regression model to predict these demographics from information about the followers of each website on Twitter. Using patterns derived both from textual content and the social network of each user, our final model produces an average held-out correlation of .77 across seven different variables (age, gender, education, ethnicity, income, parental status, and political preference). We then apply this model to classify individual Twitter users by ethnicity, gender, and political preference, finding performance that is surprisingly competitive with a fully supervised approach.