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This paper re-examines the Shapley value methods for attribution analysis in the area of online advertising. As a credit allocation solution in cooperative game theory, Shapley value method directly quantifies the contribution of online advertising inputs to the advertising key performance indicator (KPI) across multiple channels. We simplify its calculation by developing an alternative mathematical formulation. The new formula significantly improves the computational efficiency and therefore extends the scope of applicability. Based on the simplified formula, we further develop the ordered Shapley value method. The proposed method is able to take into account the order of channels visited by users. We claim that it provides a more comprehensive insight by evaluating the attribution of channels at different stages of user conversion journeys. The proposed approaches are illustrated using a real-world online advertising campaign dataset.

Audience interest, demography, purchase behavior and other possible classifications are ex- tremely important factors to be carefully studied in a targeting campaign. This information can help advertisers and publishers deliver advertisements to the right audience group. How- ever, it is not easy to collect such information, especially for the online audience with whom we have limited interaction and minimum deterministic knowledge. In this paper, we pro- pose a predictive framework that can estimate online audience demographic attributes based on their browsing histories. Under the proposed framework, first, we retrieve the content of the websites visited by audience, and represent the content as website feature vectors; second, we aggregate the vectors of websites that audience have visited and arrive at feature vectors representing the users; finally, the support vector machine is exploited to predict the audience demographic attributes. The key to achieving good prediction performance is preparing representative features of the audience. Word Embedding, a widely used tech- nique in natural language processing tasks, together with term frequency-inverse document frequency weighting scheme is used in the proposed method. This new representation ap- proach is unsupervised and very easy to implement. The experimental results demonstrate that the new audience feature representation method is more powerful than existing baseline methods, leading to a great improvement in prediction accuracy.

This paper examines and proposes several attribution modeling methods that quantify how revenue should be attributed to online advertising inputs. We adopt and further develop relative importance method, which is based on regression models that have been extensively studied and utilized to investigate the relationship between advertising efforts and market reaction (revenue). Relative importance method aims at decomposing and allocating marginal contributions to the coefficient of determination (R^2) of regression models as attribution values. In particular, we adopt two alternative submethods to perform this decomposition: dominance analysis and relative weight analysis. Moreover, we demonstrate an extension of the decomposition methods from standard linear model to additive model. We claim that our new approaches are more flexible and accurate in modeling the underlying relationship and calculating the attribution values. We use simulation examples to demonstrate the superior performance of our new approaches over traditional methods. We further illustrate the value of our proposed approaches using a real advertising campaign dataset.

In the Cognitive Compressive Sensing (CCS) problem, a Cognitive Receiver (CR) seeks to optimize the reward obtained by sensing an underlying $N$ dimensional random vector, by collecting at most $K$ arbitrary projections of it. The $N$ components of the latent vector represent sub-channels states, that change dynamically from "busy" to "idle" and vice versa, as a Markov chain that is biased towards producing sparse vectors. To identify the optimal strategy we formulate the Multi-Armed Bandit Compressive Sensing (MAB-CS) problem, generalizing the popular Cognitive Spectrum Sensing model, in which the CR can sense $K$ out of the $N$ sub-channels, as well as the typical static setting of Compressive Sensing, in which the CR observes $K$ linear combinations of the $N$ dimensional sparse vector. The CR opportunistic choice of the sensing matrix should balance the desire of revealing the state of as many dimensions of the latent vector as possible, while not exceeding the limits beyond which the vector support is no longer uniquely identifiable., Comment: 8 pages, 2 figures

Spectrum sensing (SS) in cognitive radio (CR) systems is of paramount importance to approach the capacity limits for the Secondary Users (SU), while ensuring the undisturbed transmission of Primary Users (PU). In this paper, we formulate a cognitive radio (CR)systems spectrum sensing (SS) problem in which Secondary Users (SU), with multiple receive antennae, sense a channel shared among multiple asynchronous Primary Users (PU) transmitting Multiple Input Multiple Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) signals. The method we propose to estimate the opportunities available to the SUs combines advances in array processing and compressed channel sensing, and leverages on both the so called "shrinkage method" as well as on an over-complete basis expansion of the PUs interference covariance matrix to detect the occupied and idle angles of arrivals and subcarriers. The covariance "shrinkage" step and the sparse modeling step that follows, allow to resolve ambiguities that arise when the observations are scarce, reducing the sensing cost for the SU, thereby increasing its spectrum exploitation capabilities compared to competing sensing methods. Simulations corroborate that exploiting the sparse representation of the covariance matrix in CR sensing resolves the spatial and frequency spectrum of the sources., Comment: Submitted to Globecom 2013; 11 pages, 4 figures