The recently launched LinkedIn Salary product has been designed with the goal of providing compensation insights to the world's professionals and thereby helping them optimize their earning potential. We describe the overall design and architecture of the statistical modeling system underlying this product. We focus on the unique data mining challenges while designing and implementing the system, and describe the modeling components such as Bayesian hierarchical smoothing that help to compute and present robust compensation insights to users. We report on extensive evaluation with nearly one year of de-identified compensation data collected from over one million LinkedIn users, thereby demonstrating the efficacy of the statistical models. We also highlight the lessons learned through the deployment of our system at LinkedIn.
Statistical Smoothing : The idea of Bayesian hierarchical statistical smoothing originates from the smoothing of sparse events (e.g., CTR) in the context of computational advertising @cite_8 @cite_4 , where a natural hierarchy for the combination of ads category and publisher category is used for an (ad, publisher) pair with very little data to borrow strength from its ancestor nodes. However, that is an entirely different context and the models used are hence different.
@cite_4 @cite_8
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Filtering and smoothing methods are used to produce an accurate estimate of the state of a time-varying system based on multiple observational inputs (data). Interest in these methods has exploded in recent years, with numerous applications emerging in fields such as navigation, aerospace engineering, telecommunications and medicine. This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework. Readers learn what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages. They also discover how state-of-the-art Bayesian parameter estimation methods can be combined with state-of-the-art filtering and smoothing algorithms. The book's practical and algorithmic approach assumes only modest mathematical prerequisites. Examples include MATLAB computations, and the numerous end-of-chapter exercises include computational assignments. MATLAB GNU Octave source code is available for download at www.cambridge.org sarkka, promoting hands-on work with the methods. A hierarchical Bayesian model is considered for decomposing a matrix into low-rank and sparse components, assuming the observed matrix is a superposition of the two. The matrix is assumed noisy, with unknown and possibly non-stationary noise statistics. The Bayesian framework infers an approximate representation for the noise statistics while simultaneously inferring the low-rank and sparse-outlier contributions; the model is robust to a broad range of noise levels, without having to change model hyperparameter settings. In addition, the Bayesian framework allows exploitation of additional structure in the matrix. For example, in video applications each row (or column) corresponds to a video frame, and we introduce a Markov dependency between consecutive rows in the matrix (corresponding to consecutive frames in the video). The properties of this Markov process are also inferred based on the observed matrix, while simultaneously denoising and recovering the low-rank and sparse components. We compare the Bayesian model to a state-of-the-art optimization-based implementation of robust PCA; considering several examples, we demonstrate competitive performance of the proposed model. We consider the problem of estimating occurrence rates of rare eventsfor extremely sparse data, using pre-existing hierarchies to perform inference at multiple resolutions. In particular, we focus on the problem of estimating click rates for (webpage, advertisement) pairs (called impressions) where both the pages and the ads are classified into hierarchies that capture broad contextual information at different levels of granularity. Typically the click rates are low and the coverage of the hierarchies is sparse. To overcome these difficulties we devise a sampling method whereby we analyze aspecially chosen sample of pages in the training set, and then estimate click rates using a two-stage model. The first stage imputes the number of (webpage, ad) pairs at all resolutions of the hierarchy to adjust for the sampling bias. The second stage estimates clickrates at all resolutions after incorporating correlations among sibling nodes through a tree-structured Markov model. Both models are scalable and suited to large scale data mining applications. On a real-world dataset consisting of 1 2 billion impressions, we demonstrate that even with 95 negative (non-clicked) events in the training set, our method can effectively discriminate extremely rare events in terms of their click propensity. We introduce a hierarchical Bayesian approach to tackle the challenging problem of size recommendation in e-commerce fashion. Our approach jointly models a size purchased by a customer, and its possible return event: 1. no return, 2. returned too small 3. returned too big. Those events are drawn following a multinomial distribution parameterized on the joint probability of each event, built following a hierarchy combining priors. Such a model allows us to incorporate extended domain expertise and article characteristics as prior knowledge, which in turn makes it possible for the underlying parameters to emerge thanks to sufficient data. Experiments are presented on real (anonymized) data from millions of customers along with a detailed discussion on the efficiency of such an approach within a large scale production system.