Browsing by Subject "Aggregated data"
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Item Learning from aggregated data(2019-02-11) Bhowmik, Avradeep; Ghosh, Joydeep; Vikalo, Haris; Sanghavi, Sujay; Dimakis, Georgios-Alexandros; Koyejo, OluwasanmiData aggregation is ubiquitous in modern life. Due to various reasons like privacy, scalability, robustness, etc., ground truth data is often subjected to aggregation before being released to the public, or utilised by researchers and analysts. Learning from aggregated data is a challenging problem that requires significant algorithmic innovation, since naive application of standard techniques to aggregated data is vulnerable to the ecological fallacy. In this work, we explore three different versions of this setting. First, we tackle the problem of using generalised linear models when features/covariates are fully observed but the targets are only available as histograms- a common scenario in the healthcare domain where many datasets contain both non-sensitive attributes like age, sex, zip-code, etc., as well as privacy sensitive attributes like healthcare records. We introduce an efficient algorithm that uses alternating data imputation and GLM estimation steps to learn predictive models in this setting. Next, we look at the problem of learning sparse linear models when both features and targets are in aggregated form, specified as empirical estimates of group-wise means computed over different sub-groups of the population. We show that if the true sub-populations are heterogeneous enough, the optimal sparse parameter can be recovered within an arbitrarily small tolerance even in the presence of noise, provided the empirical estimates are obtained from a sufficiently large number of observations. Third, we tackle the scenario of predictive modelling with data that is subjected to spatio-temporal aggregation. We show that by formulating the problem in the frequency domain, we can bypass the mathematical and representational challenges that arise due to non-uniform aggregation, misaligned sampling periods and aliasing. We introduce a novel algorithm that uses restricted Fourier transforms to estimate a linear model which, when applied to spatio-temporally aggregated data, has a generalisation error that is provably close to the optimal performance by the best possible linear model that can be learned from the non-aggregated data set. We then focus our attention on the complementary problem that involves designing aggregation strategies that can allow learning, as well as developing algorithmic techniques that can use only the aggregates to train a model that works on individual samples. We motivate our methods by using the example of Gaussian regression, and subsequently extend our techniques to subsume binary classifiers and generalised linear models. We deonstrate the effectiveness of our techniques with empirical evaluation on data from healthcare and telecommunication. Finally, we present a concrete example of our methods applied to a real life practical problem. Specifically, we consider an application in the domain of online advertising where the complexity of bidding strategies require accurate estimates of most probable cost-per-click or CPC incurred by advertisers, but the data used for training these CPC prediction models are only available as aggregated invoices supplied by an ad publisher on a daily or hourly basis. We introduce a novel learning framework that can use aggregates computed at varying levels of granularity for building individual-level predictive models. We generalise our modelling and algorithmic framework to handle data from diverse domains, and extend our techniques to cover arbitrary aggregation paradigms like sliding windows and overlapping/non-uniform aggregation. We show empirical evidence for the efficacy of our techniques with experiments on both synthetic data and real data from the online advertising domain as well as healthcare to demonstrate the wider applicability of our framework.