Aggregation is a common technique in data-driven applications for handling issues like privacy, scalability and reliability in a vast range of domains including healthcare, sensor networks and web applications. However, despite the ubiquitousness, extending machine learning methods to the aggregation context is unfortunately not well-studied. In this work, we consider the problem of learning individual level predictive models when the target variables used for training are only available as aggregates. In particular, this problem is a critical bottleneck in designing effective bidding strategies in the context of online advertising where ground-truth cost-per-click (CPC) data is aggregated before being released to advertisers. 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.

Existing work in spatio-temporal data analysis invariably assumes data available as individual measurements with localised estimates. However, for many applications like econometrics, financial forecasting and climate science, data is often obtained as aggregates. Data aggregation presents severe mathematical challenges to learning and inference, and application of standard techniques is susceptible to ecological fallacy. In this manuscript we investigate the problem of predictive linear modelling in the scenario where data is aggregated in a non-uniform manner across targets and features. We introduce a novel formulation of the problem in the frequency domain, and develop algorithmic techniques that exploit the duality properties of Fourier analysis to bypass the inherent structural challenges of this setting. We provide theoretical guarantees for generalisation error for our estimation procedure and extend our analysis to capture approximation effects arising from aliasing. Finally, we perform empirical evaluation to demonstrate the efficacy of our algorithmic aproach in predictive modelling on synthetic data, and on three real datasets from agricultural studies, ecological surveys and climate science. approximation effects arising from aliasing. Finally, we perform empirical evaluation to demonstrate the efficacy of our algorithmic aproach in predictive modelling on synthetic data, and on three real datasets from agricultural studies, ecological surveys and climate science.

Learning the true rank ordering among objects by aggregating a set of expert opinion rank order lists is an important and ubiquitous problem in many applications ranging from social choice theory to recommendation systems and search aggregation. We study the problem of unsupervised rank aggregation where no ground truth ordering information in available, neither about the true preference ordering among any set of objects nor about the quality of individual rank lists. Aggregating the often inconsistent and poor quality rank lists in such an unsupervised manner is a highly challenging problem, and standard consensus-based methods fall short in terms of both quality and scalability. In this manuscript we propose a novel framework to bypass these issues by using object attributes to augment the standard rank aggregation framework. We design algorithms that learn joint models on both rank lists and object features to obtain an aggregated rank ordering that is more accurate and robust, and also helps weed out rank lists of dubious validity. We validate our techniques on synthetic datasets where our algorithm is able to estimate the true rank ordering even when the rank lists are corrupted. Experiments on three real datasets, MQ2008, MQ2007 and OHSUMED, show that using object features can result in significant improvement in performance over existing rank aggregation methods that do not use object information. Furthermore, when at least some of the rank lists are of high quality, our methods are able to effectively exploit such information to output an aggregated rank ordering of high accuracy.

While matrix factorisation models are ubiquitous in large scale recommendation and search, real time application of such models requires inner product computations over an intractably large set of item factors. In this manuscript we present a novel framework that exploits structural properties of sparse vectors, using the inverted index representation, to significantly reduce the run time computational cost of factorisation models. We develop techniques that use geometry aware permutation maps on a tessellated unit sphere to obtain high dimensional sparse embeddings for latent factors with sparsity patterns related to angular closeness of the original latent factors. We also design several efficient and deterministic realisations within this framework and demonstrate with experiments that our techniques lead to faster run time operation with minimal loss of accuracy.

Data aggregation is becoming an increasingly common technique for sharing sensitive information, and for reducing data size when storage and/or communication costs are high. Aggregate quantities such as group-average are a form of semi-supervision as they do not directly provide information of individual values, but despite their wide-spread use, prior literature on learning individual-level models from aggregated data is extremely limited. This paper investigates the effect of data aggregation on parameter recovery for a sparse linear model, when known results are no longer applicable. In particular, we consider a scenario where the data are collected into groups e.g. aggregated patient records, and first-order empirical moments are available only at the group level. Despite this obfuscation of individual data values, we can show that the true parameter is recoverable with high probability using these aggregates when the collection of true group moments is an incoherent matrix, and the empirical moment estimates have been computed from a sufficiently large number of samples. To the best of our knowledge, ours are the first results on structured parameter recovery using only aggregated data. Experimental results on synthetic data are provided in support of these theoretical claims. We also show that parameter estimation from aggregated data approaches the accuracy of parameter estimation obtainable from non-aggregated or “individual" samples, when applied to two real world healthcare applications- predictive modeling of CMS Medicare reimbursement claims, and modeling of Texas State healthcare charges.

Databases in domains such as healthcare are routinely released to the public in aggregated form. Unfortunately, naive modeling with aggregated data may significantly diminish the accuracy of inferences at the individual level. This paper addresses the scenario where features are provided at the individual level, but the target variables are only available as histogram aggregates or order statistics. We consider a limiting case of generalized linear modeling when the target variables are only known up to permutation, and explore how this relates to permutation testing; a standard technique for assessing statistical dependency. Based on this relationship, we propose a simple algorithm to estimate the model parameters and individual level inferences via alternating imputation and standard generalized linear model fitting. Our results suggest the effectiveness of the proposed approach when, in the original data, permutation testing accurately ascertains the veracity of the linear relationship. The framework is extended to general histogram data with larger bins - with order statistics such as the median as a limiting case. Our experimental results on simulated data and aggregated healthcare data suggest a diminishing returns property with respect to the granularity of the histogram - when a linear relationship holds in the original data, the targets can be predicted accurately given relatively coarse histograms.

We consider the team formation problem where the goal is to find a team of experts for a specific project. In the past, several attempts have been made to formulate this problem and each formulation focuses only on a subset of design criteria such as skill coverage, social compatibility, economy, skill redundancy, etc. In this paper, for the first time, we show that most of the important design criteria for this problem can be fully modeled within one single formulation as an unconstrained submodular function maximization problem. In our formulation, the submodular function turns out to be non-negative and non-monotone. The maximization of this class of submodular function is much less explored than its monotone constrained counterpart. A few recent works [7] [4] have come up with a simulated annealing based randomized approximation scheme for this problem with an approximation ratio of 0.41. In this paper, we customize this algorithm to our formulation and conduct an extensive set of experiments to show its efficacy. Our proposed formulation offers several advantageous features over the existing formulations including skill cover softening, better team communication, and connectivity relaxation. Unlike previous formulations, the skill cover softening feature allows a designer to specify Must Have and Should Have skills. Similarly, through better team communication, we avoid the restriction that all the communication among team members should pass through only the team members and not the outsiders. Finally, connectivity relaxation feature alleviates the constraint of whole team being connected and thereby, lowering the cost.