A multichannel attribution model based on gradient boosting over trees is proposed, which was compared with the state of the art models: bagged logistic regression, Markov chains approach, shapely value. Experiments on digital advertising datasets showed that the proposed model is better than the solutions considered by ROC AUC metric. In addition, the problem of probability prediction of conversion by the consumer using the ensemble of the analyzed algorithms was solved, the meta-features obtained were enriched with consumers and o ine activities of the advertising campaign data.
In recent years, the volume of advertising on the Internet has begun to reach the
volume of advertising on television [
The paper is organised as follows. Section 2 introduces mathematical formalisation of the problem. Section 3 shortly describes how to address multichannel attribution problem with such ensemble learning techniques as Gradient Boosting over Decision Trees and Staking. Related work on both heuristic-based and data-driven approaches is summarised in 4. Section 5 is devoted to machine experiments with the data of three real Internet advertising campaigns. Finally, Section 6 concludes the paper. 2
Let us consider a set of users or clients U = fu1; : : : ; ung and a set of advertisement channels C = fc1; : : : ; cpg. Our data are represented by a matrix-vector pair (A; y), where A 2 Rn p is a matrix of user-to-channel interactions, and its element aij shows the number of interactions of the user ui 2 U with the advertising channel cj 2 C, while y is a binary vector of size n with yi = 1 for happened conversion action and yi = 0 otherwise.
Let the function f (Ai; ) describes a certain classi er that receives the vector of interactions Ii of the consumer ui with advertising channels C as an input; the function determines a certain value of r, which re ects the chance of a conversion action by this consumer. Under certain conditions, the value r can be transformed into a probability that a consumer will take a conversion action; one of these conditions is monotonicity meaning the higher the value of r, the higher the probability of a conversion. It is necessary to nd such parameters under which the classi er will give the best probability estimates in terms of the selected metrics. The weight of the in uence of the advertising channel on the decision to perform the conversion action should be considered as follows: we choose k consumers U 0 U , for them we get the matrix I0 2 Rk p. We introduce an indicator function 1(ui; cj ) = then we express the in uence of the advertising channel as impact(cj ) =
ui2U0 1 X f (I0; ) 1(ui; cj ): k Ensemble Learning for Multi-Channel Attribution
Boosting over decision trees is considered one of the most e cient machine
learning algorithms. The idea of boosting approach is as follows: it iteratively trains
new basic classi ers that improve the composition of previously chosen ones, i.e.
each new classi er compensates the errors of the composition of all the previously
ones. In turn, gradient boosting optimises the di erentiable loss function. The
initial idea of boosting arose from the question [
Today, there are several methods for solving the multichannel attribution
problem. They can be divided into two types: heuristic-based approaches and
databased approaches [
Let us consider heuristic-based multichannel attribution techniques.
1. Last-touch attribution is the most common method of attribution, which is
based on intuition to a greater extent. This method assigns all the \weight" to the
last channel, after which the consumer completed conversion action. However,
in essence, the approach is erroneous [
3. In case of linear-touch attribution, all \weights" are equally distributed between all channels leading to the conversion.
4. Time decay attribution is a model in which the largest \weights" are given to the most recent consumer interactions with advertising channels. 4.2
In order to evaluate the impact of advertising channels on consumers'
decision to perform a conversion action, it is proposed to use logistic regression [
In [
The proportions of observations and attributes as well as the number of
iterations M are hyper parameters of bagged-logistic regression. The authors
conclude that for fractions that are very di erent from 0 and 1, the results of
the meta-algorithm are similar, and the number of iterations does not a ect the
results [
In this approach, the authors propose using a graph model based on Markov
chains [
Visits to all consumers are presented as chains in the Markov graph. Formally, this model can be formulated as follows:
Let us consider a Markov graph M = (S; W ), which is composed from the states S = fs1; : : : ; sng along with the associated transition matrix W with edge weights wij = P (Xt = sijXt 1 = sj ), such that 0 wij 1 and PiN=1 wij = 1 for all i.
Consumer chains contain one or more interactions with advertising channels. In this model, each state corresponds to one advertising channel. Three special states are also introduced: START is a state that represents the beginning of the consumer chain, CONVERSION is a state indicating the successful completion of the conversion action, and for chains that were not completed by the conversion action, the NULL state is introduced.
The element of the transition matrix wij corresponds to the probability that after interacting with advertising channel i, interaction with advertising channel j will follow. For the rst channel in the chain, an incoming connection with the START state is added. If the consumers sequence of actions ends with a conversion, then after the last interaction with the advertising channel, a connection with the CONVERSION state is added. Otherwise, it falls into the NULL state, and each CONVERSION state goes into the NULL state as well.
Since the number of parameters in such a model grows exponentially with the chain length, the authors limit themselves to a maximum chain order of four.
To assess the impact of each advertising channel on the conversion action, the authors propose using the e ect of removing the advertising channel si from the model and tracking the change of the probability of reaching CONVERSION from START state. Since this removal e ect re ects well the degree of change in conversion, it can serve as an estimate of the contribution of each channel. 4.4
This attribution methodology is equivalent to the Shapely Value solution to
value distribution in Cooperative Game Theory [
To compute SHAP values the authors de ne fx(S) = E[f (x) j xS ] where E[f (x) j xS ] is the expected value of the function conditioned on a subset S of the input features.
SHAP values combine these conditional expectations with the classic Shapley values from game theory to attribute i values to each feature: i =
X S Nnfig jSj!(M
jSj M ! 1)! (fx(S [ fig) fx(S)) ; (1) where N is the set of all input features. In our advertising setting channels play the role of features. All experiments performed in this work were carried out on real data from advertising campaigns of advertisers from the food industry and the production of consumer goods. The experiments were carried out on three data sets.
Each data set contains data on the interaction of consumers with an advertising message with a time stamp. For each consumer and advertising message, it is known on which site the interaction took place, the category of the advertising message (online video, promo post on the social network, banner advertising, etc.), creative ID, consumer action category (ad display, click, conversion), time stamp, the identi er of the location of advertising on the site.
It is worth noting that two of the three data sets have a great advantage over the third. In fact, most data on advertising campaigns is collected only in special advertising servers, where each consumer is identi ed by cookie. This approach has several disadvantages: { A consumer may have multiple cookies, for example, when a consumer uses multiple devices; { One cookie may belong to multiple consumers, for example, when more than one person uses the same device { Advertising servers may \nullify" some cookies when trying to use thirdparty targeting services; { In such data, many cookies may be assigned to crawlers, not real persons; { Browsers update cookies every month.
To cope with the above problems, each cookie is matched with the account of a real person on the advertiser's website and only after that the consumer ID is used.
Below are the statistics for each advertising campaign.
For advertising campaign 2 additional data about consumers are known: city of residence, region of residence, platform used (web, iOS, Android, etc.), browser used, categories of purchased items, data on the advertiser's o ine activities (TV advertising, outdoor advertising, etc.). These additional data were used in conjunction with meta-attributes to train the meta-algorithm.
As follows from Table 5, in our case, the proposed method for solving the multichannel attribution problem provides better results than the state-of-theart solutions according to the ROC AUC metric. However, it can be seen from In this work, the problem of multichannel attribution was considered, which is devoted to assessing the impact of advertising channels on consumer conversion actions. In the scienti c literature, the problem of multichannel attribution is usually divided into two approaches: heuristic, attribution based on intuition, and a data-driven approach. Due to the growing interest and development of cloud technologies in the modern world, many advertisers are beginning to collect more data about their advertising campaigns, which makes data-driven approaches the most popular.
We considered di erent approaches to multi-channel attribution: the approach based on game theory, the approach based on Markov chains, and Bagging of logistic regressions among the others.
To solve the multichannel attribution problem, we used Gradient Boosting method and an ensemble of classical algorithms to increase the accuracy of predicting the probability of a conversion action by a consumer.
The quality of the proposed algorithms was compared with conventional solutions of the multichannel attribution problem for three real data sets. The proposed solution gave the best result among all in terms of ROC AUC. Thus, the used ensemble classi cation has improved the ability to estimate the likelihood of a consumer to perform a conversion action.
One of the direction for future work might be analyses of market segments
(represented by groups of users) with respect to channels where the positive
response was recorded by means of abject-attribute biclustering [