Mining Advertiser-specific User Behavior Using Adfactors
Nikolay Archak
New York University, Leonard
N. Stern School of Business
44 West 4th Street, Suite
8-185
New York, NY, 10012
narchak@stern.nyu.edu
Vahab S. Mirrokni
Google Research
76 9th Ave
New York, NY 10011
mirrokni@google.com
S. Muthukrishnan
Google Research
76 9th Ave
New York, NY 10011
muthu@google.com
ABSTRACT
Consider an online ad campaign run by an advertiser. The
ad serving companies that handle such campaigns record
users' behavior that leads to impressions of campaign ads,
as well as users' responses to such impressions. This is sum-
marized and reported to the advertisers to help them eval-
uate the performance of their campaigns and make better
budget allocation decisions.
The most popular reporting statistics are the click-through
rate and the conversion rate. While these are indicative of
the eectiveness of an ad campaign, the advertisers often
seek to understand more sophisticated long-term eects of
their ads on the brand awareness and the user behavior that
leads to the conversion, thus creating a need for the report-
ing measures that can capture both the duration and the
frequency of the pathways to user conversions.
In this paper, we propose an alternative data mining frame-
work for analyzing user-level advertising data. In the ag-
gregation step, we compress individual user histories into a
graph structure, called the adgraph, representing local cor-
relations between ad events. For the reporting step, we in-
troduce several scoring rules, called the adfactors (AF), that
can capture global role of ads and ad paths in the adgraph,
in particular, the structural correlation between an ad im-
pression and the user conversion. We present scalable local
algorithms for computing the adfactors; all algorithms were
implemented using the MapReduce programming model and
the Pregel framework.
Using an anonymous user-level dataset of sponsored search
campaigns for eight dierent advertisers, we evaluate our
framework with dierent adgraphs and adfactors in terms
of their statistical t to the data, and show its value for
mining the long-term behavioral patterns in the advertising
data.
Categories and Subject Descriptors
H.4.m [Information Systems]: Miscellaneous; J.4 [Social
and Behavioral Sciences]: Economics
General Terms
Performance, Measurement, Economics
Copyright is held by the International World Wide Web Conference Com-
mittee (IW3C2). Distribution of these papers is limited to classroom use,
and personal use by others.
WWW 2010, April 26–30, 2010, Raleigh, North Carolina, USA.
ACM 978-1-60558-799-8/10/04.
Keywords
sponsored search, ad auctions, online advertising, PageR-
ank, user behavior models, clickthrough rate, conversion
rate
1. INTRODUCTION
The Internet has become a major advertising medium.
Although a number of dierent factors contributed to this,
what distinguishes the Internet advertising from the oine
advertising competitors is its inherently interactive nature.
Measuring eectiveness of a particular advertising campaign
and allocating the advertising budget optimally was and still
remains a very challenging task, yet the Internet made the
task easier by connecting ad impressions 1 to tangible user
actions and artifacts such as posing a search query, click-
ing on an ad or converting 2. The simplicity of measuring
and attributing user clicks has established the clickthrough
rate (CTR) 3 as the current de-facto standard of ad qual-
ity for sponsored search. It is now customary to dene the
advertiser's optimization problem as maximization of the
expected number of ad clicks given a certain budget con-
straint [13, 23, 10]. The conversion rate (CR), dened sim-
ilarly as the probability of the user conversion, is another
popular ad eectiveness measure; together with the CTR
it is frequently used by the advertisers to measure the re-
turn on investment of specic keywords in the advertising
campaign.
Recent empirical studies show that the eects of online ads
cannot be fully captured by the CTR or the CR. In particu-
lar, the sponsored search advertising, as well as the display
advertising, can have a signicant number of indirect eects
such as building the brand awareness [18]. For instance,
Lewis and Reiley [20], in cooperation between Yahoo! and
a major retailer, performed a randomized controlled experi-
ment to measure the eect of the online advertising on sales.
They found that the online advertising campaign had sub-
stantial impact not only on the users who clicked on the
ads but also on those who merely viewed them. In another
study, comScore [8] reported an incremental \lift" of 27% in
1Impression is simply an act of showing an ad in a page
viewed by the user.
2Conversions are dened by the advertisers and may rep-
resent a wide range of user activities from buying an item
to simply spending a suitable amount of time on the adver-
tiser's website.
3The clickthrough rate (CTR) is dened as the fraction of
times an ad was clicked by users when shown.

the online sales after the initial exposure to an online ad, as
well as lift in other important online behaviors, such as the
brand site visitation and the trademark searches.
The advertisers seek to understand the impact of their
ad not just on the immediate click or conversion, but the
likelihood of the eventual conversion in the long term and
other long term eects. Users take specic trajectories in
terms of the search queries they pose and the websites they
browse, and this aects the sequence of ads they see; con-
versely, the sequence of ads they see aects their search and
browsing behavior. This interdependence results in struc-
tural patterns in users' behavior; advertisers need new tools
and concepts beyond simple aggregates (like the CTR and
the CR) to understand them.
What are the systematic ways to help the advertisers rea-
son about structural correlations in the data? In this paper,
we take an advertiser-centric data mining approach. We
start with data that is directly pertinent to the advertiser's
campaign, that is, user trajectories that involved ads from
the campaign of that advertiser, including ad impressions,
clicks and conversions. Such data can usually be reported
to the advertiser, provided it is aggregated and anonymized
appropriately. Next, we build a data mining framework that
can help advertisers identify structural patterns in this data.
Our contributions are as follows.
 We propose a graphical model based approach. We
formulate graphs from the data called adgraphs to cap-
ture co-occurrences of events adjacent to each other in
users' trajectories. Then, we introduce a variety of ad-
factors, where every adfactor is a scoring rule for nodes
in the adgraph: these are designed to capture impact
of ad nodes on eventual conversion. For example, we
introduce adfactors based on random walks, that, for
every event, calculate the long term probability that a
certain random walk involving that event would even-
tually lead to conversion. Our paper presents highly ef-
cient algorithms for constructing adgraphs and com-
puting all adfactors we introduce. All algorithms were
implemented using MapReduce [11] parallel program-
ming model.
 Using data from the sponsored search campaigns of
eight dierent advertisers, we study various adgraphs
and adfactors. We validate the adgraph models by
showing their statistical t to the data. Also, we show
interesting empirical properties of the adfactors that
provide insights into user behavior with respect to brand
vs non-brand ads. Moreover, we show various natural
data mining queries on adgraphs and adfactors that
maybe of independent interest to advertisers. Finally,
using adfactors, we show how to eciently prune the
adgraph to localize and depict the in
uence of any par-
ticular ad by its small neighborhood in the ad graph.
Our approach works by transforming the dataset of users'
trajectories into graphs. This is achieved by pooling data
from dierent users. As a result, adgraphs lose information
about specic users or their trajectories, and only encode
aggregate information. Also, because of the way adgraphs
pool data only based on adjacent events, they encode certain
independence assumption about user behavior over paths of
multiple edges. We carefully study statistical t of adgraph
models to the data to ensure that this assumption is reason-
able. Pooling this way also results in signicant compression.
For large advertisers in sponsored search, the number of dif-
ferent queries the advertiser can be matched with is often
in tens of thousands, and the number of viewing users can
be in millions. In contrast, adgraphs have more manageable
sizes.
Our approach generalizes to dierent settings. While in
this paper we apply it to study user conversions in the spon-
sored search data, it can equally be used to study trajectories
in sponsored search that lead to clicks only, or conversions
when both sponsored search and content-based display ad
data is available, etc.
2. RELATED WORK
There are empirical studies showing that the sponsored
search advertising, as well as the display advertising, can
have a signicant number of the indirect eects such as
building the brand awareness and lift in the cross-channel
conversions [18, 20]. The prior research attempted to mea-
sure impact of an ad on the user conversion by the number of
independent paths from the ad to the conversion event [5].
Our work here is a substantial generalization of the prior
research, as we apply more advanced PageRank-based mea-
sures for analyzing pathways to the user conversion and,
more importantly, introduce a generic adgraph/adfactor based
framework for reasoning about the structural properties of
the users' behaviors.
Mining patterns in the user behavior is not a novel idea.
Market basket analysis using association rule mining [2] is a
popular tool used by retailers to discover actionable business
intelligence from user level transaction data. User behavior
data has numerous applications, including, but not limited
to, improving the web search ranking [1], fraud detection [12]
and personalization of the user search experience [25]. In
this paper, we mine the user behavior from the perspective
of an advertiser running a sponsored search campaign.
There are several standard mining techniques that can
be applied to the user-level advertising data such as mining
for the frequent itemsets [2] or the frequent episodes in se-
quences of user actions [22]. However, these do not capture
the structural correlations in the data such as the impact of
multiple paths between events that our work captures. A dif-
ferent approach that attempts to capture structural correla-
tions is mining the frequent substructures in graph data [16].
Due to data pooling in our graph construction, patterns that
we identify may or may not have high support, because some
patterns may combine behavior of multiple users. Also, we
are not interested simply in frequent patterns but in patterns
that indicate a high likelihood of the designated action: user
conversion. Further, our approach of using the steady state
probabilities of dierent random walks to capture structural
correlations diers from the prior graph mining techniques.
This approach is widely used in other areas including web
search [24, 4], personalized video recommendations [6] and
user signatures in communication graphs [9].
Our research is closely related to the problem of modeling
user search sessions, for which a wide number of solutions
have been proposed in the literature, including advanced la-
tent state models such as vl-HMM [7] and Markov models
that take into account transition time between user's ac-
tions [14]. We intentionally refrained from using complex
generative models for the underlying data due to several
reasons. At rst, generative models often require individ-
ual user sessions for training, while, due to privacy reasons,

advertisers usually have access only to aggregate level data.
At second, advertisers generally do not have access to infor-
mation on user actions for which the advertiser's ad was not
shown (even at the aggregate level). Finally, the patterns of
user behavior extracted from the data must be easy to com-
municate and represent, ideally in a graphical form. This is
often not true for generative statistical models.
3. DATASET
Our sample covers 8 dierent anonymous advertisers, who
were running a sponsored search campaign with Google.
The dataset was collected at user level and includes infor-
mation on a random sample of users who \converted" with
the advertiser within a certain time period of several weeks.
The activity of every user was tracked by a cookie, thus any
user who deleted the cookie was later identied as a dif-
ferent user. For every (anonymous) user, the data has the
information on all actions of this user before the conversion,
where we dene an action as either a search query issued on
Google and for which the advertiser's ad was shown in the
paid search results or a click on the advertiser's ad.
In the rest of the paper, we will refer to the rst action
type as an \impression" event (as it resulted in the adver-
tiser's ad impression) and to the second action type as a
\click" event. We emphasize that search queries for which
the advertiser's ad was not shown, such as irrelevant search
queries, queries on which the advertiser bid too low, or
queries for which the advertiser was excluded from the auc-
tion due to a daily budget constraint, are not included in our
dataset. While such data might be available in some form
to the search engine, it is not reported to the advertisers,
e.g. due to several privacy issues, and therefore we inten-
tionally refrain from including it as an input into our data
mining process. Same applies to the ad position and the
competitors' information in the sponsored search auction:
advertisers do not observe their ad placement and competi-
tors' ads on an individual query basis. The information that
we assume to be available for every event includes only the
event timestamp, the search query issued by the user and
the match type (exact or broad 4).
The number of data points for the converted users varied
from approximately 30,000 impressions and 10,000 clicks for
the smallest advertiser to about 5.8 million impressions and
2.6 million clicks for the largest advertiser. 5 The number of
dierent user queries in the data varied from approximately
500 for the smallest advertiser to about 27,000 for the largest
advertiser.
A special event in our dataset is a user conversion. User
conversions were reported by the advertisers, therefore the
exact denition of what constitutes the conversion event is
advertiser-specic. In practice, it can vary from visiting a
particular web site page or registering on the website to
making an expensive purchase online. We will use the term
\conversion path" to represent an ordered sequence of events
for a single user that ends in a conversion.
Finally, our dataset also includes data on users who were
exposed to at least one ad impression of the advertiser but
4Most search engines support broad match functionality,
which allows for an imprecise match between a query issued
by the user and the keyword the advertiser bids on [10].
5Note that the high clickthrough rate implied by these num-
bers is due to the fact that we describe the sample of users
who eventually converted with the advertiser.
Figure 1: Distance to conversion
did not convert within the monitored time period. As the
number of non-converted (yet) users is much larger than the
number of converted users, we sampled from the pool of such
users randomly with a sampling probability of 1%.
3.1 Descriptive Statistics
To ensure anonymity of the advertisers in our dataset, we
do not report the descriptive statistics table, instead pre-
senting two plots illustrating some of the most interesting
properties of the data. We rst ask how long (how many
searches) does is take for a user to convert with the ad-
vertiser (assuming that the user eventually converts)? The
exact value of the statistics depends on how we average data
across dierent users. Figure 1 shows the histogram of the
distance to conversion for a randomly selected event in the
sample of converted users. The distance is dened as the
number of future ad impressions for the same advertiser (in-
cluding the current impression) that this user will get before
the conversion. The data on the plot is slightly distorted (by
a small multiplicative random factor for every advertiser) to
preserve advertiser anonymity; the distortion does not aect
the main message of the plot. In about one third of the cases,
the user who converts will convert immediately after the ob-
served impression, however a larger fraction (2/3) will be
matched to the same advertiser at least one more time before
they convert. Moreover, the distribution has a heavy tail:
in about 10% of the observations, the user will be matched
to the same advertiser in at least 10 more searches before
eventually converting. The plot also shows that there is a lot
of variation across advertisers, therefore our estimates of the
distance to conversion have limited generalizability outside
of our sample. What we would expect to generalize is the
observation that the interaction between the advertiser and
the user is far more complex than a simple \search; click;
convert" scenario and many users will be exposed to the ad-
vertiser's ad multiple times before they eventually convert.
Finally, Figure 2 presents a plot showing the number of
dierent path types of certain length in our conversion data.
The path type is dened as the equivalence class of all con-
version paths that are identical once the timestamps are
omitted. Furthermore, we normalize all values by the num-
ber of dierent path types of the length 1, which is essentially
the number of dierent user queries that we observed in the
conversion data. In order to understand the plot better, one
can think of the two extreme cases of the data generating
process. In the rst scenario, the data generating process
samples new events i.i.d., i.e., the queries that the user is-
sued before do not aect the queries that the user will use
later. In such setting, the number of dierent path types of
the length k (assuming a very large sample size) will grow

Figure 2: Number of dierent paths of length kNumber of dierent paths of length 1
exponentially with respect to the number of possible user
queries (which is often in the order of thousands or even
tens of thousands for a large advertiser). This is clearly not
the behavior we see in Figure 2, even taking into account
nite size of our sample (we formally test the i.i.d. model in
the next Section). On the other hand, a perfect correlation
between user searches would imply a
at plot, which is also
not the case in our sample. While there is again signicant
variation across advertisers, we would expect the following
observation to generalize: there are strong \structural corre-
lations" between user searches in a single conversion path.
4. GENERATIVE MODELS
In this section, we formally dene and evaluate a set of
generative statistical models for the conversion path data.
The rst baseline model we evaluate is a simple i.i.d. model:
every new event in a conversion path is sampled indepen-
dently from everything that has happened before that. The
number of parameters in the model is equal to the number
of dierent user queries in the dataset (minus one).
All others models we evaluate represent user behavior as
a random (Markov) walk in some directed graph (adgraph),
what makes the models dier is the way the adgraph is con-
structed. The adgraph construction involves dening the
set of graph nodes V , dening the set of graph edges E,
and dening the edge weights wij which represent transi-
tion probabilities between nodes i and j. While denition of
the nodes in the adgraph is model-specic, all adgraphs that
we construct will have three special nodes: the \begin" node
representing the start of the conversion (or non-conversion)
path for any user, the \conversion" node representing the
conversion event and the \null" node representing the state
of the users who have not converted within the observation
period. The \null" node is always an absorbing node and
the \conversion" node always leads to the \null" node. The
\begin" node has no incoming edges.
Simple Markov. In a \Simple Markov" adgraph, every
graph node is an event (impression or click) and the edge
weights are just probabilities of observing the two events
consecutively in a conversion path. We also consider \For-
ward Markov" and \Backward Markov" adgraphs, in which
we incorporate the distance from the rst user observation
(the distance to the last user observation) as a part of the
node id, thus allowing the next event to be sampled depend-
ing on how many events for the same user we have observed
so far (\Forward Markov") or how many more events we
are going to observe before the user converts (\Backward
Markov").
Regime Switching Markov. We also consider three ad-
ditional \Regime Switching Markov" adgraphs. In all three
Model Stab. (RMSE) Stab. (MAE)
i.i.d. 0:0000 0:0000
Simple Markov 0:1164 0:0414
Forward Markov 0:2128 0:1080
Backward Markov 0:2130 0:1068
RS Markov 1 0:1317 0:0489
RS Markov 2 0:1291 0:0475
RS Markov 3 0:1326 0:0494
Table 1: Model stability, out of sample
Model 2 LogL (Out) BIC (In) AIC (In)
i.i.d. 8:9860 9:0042 8:9714
Simple Markov 5:1155 5:2718 5:0762
Forward Markov 4:3607 4:7591 4:3229
Backward Markov 3:6291 4:0926 3:5964
RS Markov 1 4:9965 5:1797 4:9545
RS Markov 2 5:0360 5:2146 4:9949
RS Markov 3 5:0169 5:1969 4:9759
Table 2: Model tness, in and out of sample
models, the user is assumed to have two dierent possible
regimes: the\search"regime representing a regular browsing
behavior and the\interested"regime representing the behav-
ior of a user interested in a particular advertiser. Thus, for
every user query we will have two dierent nodes: one for
the \search" regime and one for the \interested" regime. The
user always starts in the \search" regime and, once switched
to the \interested" regime, always stays there. We consider
three possible signals of the user switching the \regime":
clicking on the advertiser's ad (\RS Markov 1"), using the
advertiser's brand name in a search query (\RS Markov 2")
or a combination of both (\RS Markov 3").
We have evaluated all seven models in terms of several
criteria: average stability (sampling variance) of the edge
weights in the constructed graph (parameter estimates for
the i.i.d. model) and tness both in and out of sample.
Stability scores were calculated in two forms: the average
(across all edges) root mean squared error (RMSE) and the
mean absolute error (MAE) of the edge weight estimates in
a ve sample split of the data. Table 1 shows that, with
exception of the i.i.d. model, the edge weight estimates are
quite volatile in our dataset, due to the fact that we have
limited number of observations for many node pairs. 6 As
the next Section shows, this in fact is not a problem for
stability of the corresponding adfactors.
Next, we present the tness results for all models in Ta-
ble 2. We report the statistical model t to the data in-
sample as measured by the Akaike Information Criterion
(AIC) and the Bayesian Information Criterion (BIC) [3].
We also report the out of sample t from ve-fold cross-
validation [19] using the log-likelihood as the tness crite-
ria. As expected, the i.i.d. model shows the worst t by far.
The best tting model according to all three criteria is the
\Backward Markov" model, indicating that the distribution
of queries issued by the user varies signicantly with the dis-
tance from the conversion event. Regime switching models
t slightly better than the \Simple Markov" model.
5. AD FACTORS
In this section, we dene and evaluate a number of ad-
factors that capture structural correlations in the conver-
sion path data. All adfactors are calculated directly on the
graph structures we dened in the previous section, for in-
stance, the same adfactor can be calculated both for a \Sim-
6While the i.i.d. model is stable, it provides bad t to the
data as shown in Table 2. This is just another example of
the classic bias-variance tradeo.

ple Markov" adgraph as well as for a regime switching ad-
graph. We present several alternative versions of the adfac-
tors and evaluate their properties on the actual data. The
adfactor is calculated for every node in the adgraph and,
informally, can be thought of as a measure of structural cor-
relation between this node and the target node (the conver-
sion node). The simplest adfactor would be a simple edge
weight between the pair of nodes in the adgraph. Such ad-
factor would capture a simple correlation between a pair of
consecutive events: how often do users who get an ad im-
pression for a particular query click on it? (clickthrough
rate) how often do users who click on the ad convert with
the advertiser? (conversion rate) The more sophisticated
adfactors we dene are expected to capture the structural
properties of the adgraph such as: ceteris paribus, the larger
the number of the disjoint paths from an event to the con-
version is, the higher the adfactor should be, and also, the
closer these events are, the higher the adfactor should be.
Three important points should be made about the adfac-
tors. First, while we expect the adfactors to have useful
applications (and we show some of the applications in this
paper) and be useful for ranking and reporting purposes,
we do not and cannot attach any causal meaning to the val-
ues. What adfactors capture are correlations not causations.
This is even true for the simplest of the currently used mod-
els of ad performance such as the conversion rate; what the
conversion rate says is what fraction of the users converted
with the advertiser after clicking on an ad, not what frac-
tion of the users converted with the advertiser because of the
ad (some users would have converted anyway even if the ad
was not shown; other users who did not convert immediately
may have converted later because of the ad). Establishing
causation would require running an actual experiment or, at
least, having a good exogenous source of randomness in the
data; this is beyond the scope of the paper.
Second, there is no ex-ante measure of quality of an adfac-
tor and we are not going to say that one adfactor is always
better than another. What we will say in the rest of the
paper is what structural properties of the data the dier-
ent adfactors are able to capture. Third, in order for the
adfactors to be practically useful, they should be eciently
computable on large-scale data sets. To address this issue,
we design ecient algorithms for all adfactors we introduce
in this paper, using distributed computation paradigm. In
fact, for one of the adfactors (the PPR adfactor), we can
directly use a local pushback algorithm developed by Ander-
sen et. al [4]. For the rest of adfactors, we present suitable
adaptations of the pushback algorithm.
5.1 LastAd
LastAd adfactor represents the conversion rate of the cor-
responding ad: it measures the weight of the direct edge
from the corresponding node to the conversion node. For-
mally, for any event e (either simple ad impression or ad
click), the LastAd adfactor is
lastad(e) =
number of occurrences of f e, conversion g
number of occurrences of e
5.2 PageRank contribution (PPR, CPR)
PageRank contribution adfactor is dened as the Person-
alized PageRank contribution of the evaluated node v to
the conversion node c (ppr(v; c)). Below, we give a formal
denition.
Assume some restart probability  > 0 and a graph given
by the n  n random walk matrix M (M(i; j) =
wijP
k wik
).
Let I be the identity matrix and ev is the row unit vector
whose v-th entry is equal to one.
The Personalized PageRank matrix is dened as a n by n
matrix solution of the following equation
ppr = I + (1 ) pprM:
Fix a node v. The v-th row of the matrix satises
ppr(v;
) = ev + (1 ) ppr(v;
)M:
This is known as the Personalized PageRank (PPR) vector
of a node v with restart probability  and it was introduced
by Haveliwala [15] as the stationary distribution of a random
walk on the graph with  probability restart at node v after
each step.
The dual construct to the PPR vector is obtained by tak-
ing a single column of the matrix. The column correspond-
ing to the conversion node c, consists of all PPR contribu-
tions for dierent nodes v and the xed conversion node c
and, when written in a row form, solves the following equa-
tion
ppr(
; c) = ec + (1 ) ppr(
; c)M
T :
This is PageRank contribution (CPR) vector and it is de-
noted as cpr  ppr(
; c) [4]. The CPR vector naturally
captures important structural properties of the graph such
as the number of dierent paths from every node v to the
conversion node c as well as the lengths of these paths. A
nice property of cpr is that the sum of all cpr's for the node c
is equal to the PageRank of the node c, so it can be thought
of as a way to divide the PageRank score (which captures the
total credit of the conversion node in the graph) into con-
tributions from other nodes. Moreover, varying the restart
probability of the random walk () can be used to ne-tune
the trade-o between the short-term and the long-term ef-
fects of the ads. The higher the restart probability is, the
more the score captures the short-term contribution of the
ad as compared to the long-term one.
5.3 Eventual Conversion
The eventual conversion adfactor is a limiting case of cpr
when the restart probability  converges to zero. The follow-
ing proposition says that, after normalization, this adfactor
is equivalent to the probability of hitting the conversion node
as opposed to hitting the null node in a random walk with
no restart. This adfactor is denoted hit(
; c).
Proposition 1. Let M^ be the random walk matrix with
the \null" node excluded and assume that the matrix IM^ is
invertible, where I is the identity matrix. 7 Dene the \hit"
vector hit(
; c) as a row vector solving the following equation:
hit(
; c) = hit(
; c)M^T + ec:
Then,
lim
!0
@ ppr(
; c)
@
= lim
!0
ppr(
; c)

= hit(
; c):
7A sucient but not necessary condition for this is that
every node except for the \null" node has a small probability
of transition to \null". This is a reasonable assumption for
our application as the user can always \drop out" with some
positive probability.

5.4 Visit
For comparison purposes, we dene the visit adfactor which
represents the random walk (no restart) visit probability of
a node from the \begin" node. This adfactor is not related
to the conversion node but simply captures the likelihood
of the event happening in a user conversion path. Formally,
the adfactor is dened as a row vector hit(b;
) solving
hit(b;
) = hit(b;
)M^ + eb:
Similar to Propositon 1, one can show that
lim
!0
@ ppr(b;
)
@
= hit(b;
):
5.5 Marginal Increase (Passthrough)
We introduce the MI(j) adfactor, which represents the
marginal increase in the probability of hitting conversion
from the \begin" node b if we increase the weight of all edges
outgoing from the node j by ", allocated in proportion to the
current edge weights. We rst compute MI(j) in the con-
text of Personalized PageRank with a restart probability .
Let @ ppr(b;c)@wji be the marginal in
uence of an edge weight
wji on the PPR of the \begin" node for the conversion node.
The adfactor MI(j) can be proxied by the following sum-
mation (note that sensitivity with respect to each outgoing
edge is weighted proportionally to the current edge weight).
MI(j) =
X
i
wji
@ ppr(b; c)
@wji
;
We rst observe that, in the setting of random walks with
restart , @ ppr(b;c)@wij can be computed by using the following
Proposition:
Proposition 2. The marginal in
uence of an edge weight
on the PPR of the sink c with restart at the source node b is
given by a product of the PPR of the start node of the edge
(i) with restart at the source node b and the PPR of the sink
node c with restart at the end node of the edge (j):
@ ppr(b; c)
@wij
=
1 

ppr(b; i) ppr(j; c):
Using this proposition, we derive a simple closed-form for-
mula for MI(j).
Proposition 3. The marginal eect of increasing the weight
of the outgoing edges of a node j, MI(j), is equal to:
MI(j) =
ppr(b; j) ppr(j; c)

: (1)
The proofs are left to the appendix. An advantage of this
closed-form formula is that it lets us apply fast algorithms
for computing the MI adfactor. The above proposition
also implies that, as  tends to zero, the MI adfactor can be
computed as follows:
Proposition 4. The marginal eect of increasing the weight
of the outgoing edges from a node j on the hitting probability
of conversion, MI(j), is equal to:
MI(j) = lim
!0
MI(j)

= hit(b; j) hit(j; c): (2)
Table 3: Correlation matrix for adfactors.  = 0:05
PPR Ev.Conv. LastAd Visit Pass
PPR 1.0000 0.9733 0.7285 -0.0657 0.1321
Ev.Conv. 0.9733 1.0000 0.7064 -0.0614 0.1370
LastAd 0.7285 0.7064 1.0000 -0.0542 0.0991
Visit -0.0657 -0.0614 -0.0542 1.0000 0.8006
Pass 0.1321 0.1370 0.0991 0.8006 1.0000
The above observation implies that the MI adfactor is
the same as the passthrough adfactor which is the change in
hit(b; c) if we remove the node j from the graph and redirect
all incoming edges to this node to the \null" node, or formally,
Pass(i) = hit(b; i) hit(i; c):
We call the corresponding adfactor the \passthrough" or
Pass adfactor, since it captures the value of random walks
passing through the evaluated node.
5.6 The Removal Effect
In this part, we introduce the adfactor RE(i) for each
node i which is dened as the change in the probability of
hitting conversion starting from the \begin" node b if we re-
move node i from the graph. Intuitively, this adfactor cap-
tures the change in the probability of reaching conversion if
we remove a node i, or the incoming edges of node i. Simi-
lar to the MI adfactor, we dene the RE adfactor in the
context of a random walk with restart probability  as
RE(i) =
X
j
wji
@ ppr(b; c)
@wji
;
Using Proposition 2, we can derive a similar closed-form
formula for RE(i) which is shown to be equal to Pass(i).
Proposition 5. The RE and RE adfactors can be com-
puted as follows:
RE(i) =
ppr(b; i) ppr(i; c)

: (3)
RE(i) = lim
!0
RE(i)

= hit(b; i) hit(i; c): (4)
The proofs are left to the appendix. The Pass adfactor is
a proxy for both MI and RE adfactors, i.e., MI(i) = RE(i) =
Pass(i). As a result, we only report empirical results for the
passthrough (Pass) adfactor, and this will imply the same
results for the MI and RE adfactors.
5.7 Efficient Algorithms
Computational eciency is crucial for successful applica-
tion of any data mining algorithm to the real world advertis-
ing data. Fortunately, all adfactors introduced in the previ-
ous Section can be eciently computed on large scale graphs
using parallel machines. The key is the observation that the
PageRank contribution vectors (cpr  ppr(
; c)) can be e-
ciently computed using a local algorithm which adaptively
examines only a small portion of the input graph near a spec-
ied vertex [4]. We have implemented the algorithm of [4] in
the distributed computing environment of MapReduce [11]
using the Pregel framework [21]. In the Pregel framework,
every node in the graph can perform its local computation
and the nodes interact with each other by a periodic ex-
change of messages. The cpr computation can be achieved
by a simple local algorithm (Algorithm 1), in which every
node has state consisting of two variables: the currently ac-
cumulated cpr and the residual value obtained from other

nodes but not yet distributed(resid). The nodes run a simple
pushback operation (pushing fraction of the residual to its
neighbors over incoming edges) until the value of the resid-
ual in each node does not exceed ". Andersen et al [4] proves
the following:
Theorem 1. [4] The following algorithm calculates an "-
approximation of the PageRank contribution vector for the
conversion node, i.e. cpr  ppr(
; c), using only 1" + 1
pushback operations. Moreover, using this algorithm, one
can identify the top k nodes with the maximum PageRank
contribution using only O( k ) pushback operations.
Algorithm 1 Local algorithm to calculate cpr  ppr(
; c)
adfactor of the conversion node c.
Initialization:
cpr(u)( 0, resid(u)( 1 if conversion node otherwise 0
Main Loop:
while 9u such that j resid(u)j  " do
Pushback(u; )
end while
Pushback (u; ):
cpr(u)( cpr(u)+ resid(u) faccumulate  fraction of the current
residualg
for every incoming edge w ! u do
resid(w)( resid(w) + (1) resid(u)dout(w) fdistribute 1 fraction
of the current residual to neighborsg
end for
resid(u)( 0
Using Propositions 3 and 5, one can see that calcula-
tion of the MI and RE, and passthrough (Pass) adfactors
requires estimating both the Pagerank contribution vector
for conversion (i.e, the ppr(
; c) value for every node in the
graph) and the Personalized PageRank vector of the begin
node (the ppr(b;
) value for every node in the graph). The
"-approximation of the Pagerank contribution vector can
be calculated eciently using pushback operations in Algo-
rithm 1. Moreover, a similar pushforward algorithm devel-
oped in [17] can be used for calculation of the "-approximation
of the PPR vector for the begin node. Using Propositions 3, 4,
and 5, by multiplying these two vectors, we get the following
theorem:
Theorem 2. There exists a local "-approximation algo-
rithm for computing the MI and RE using O

1
"


push
operations. Moreover, an "-approximation for Pass, MI, and
RE can be computed using O

1
0"


where 0 = mini wi;null.
6. EMPIRICAL PROPERTIES OF ADFAC-
TORS
In this section, we present some interesting empirical prop-
erties of the adfactors in our dataset. All experiments were
done with the \Simple Markov" graph, except where explic-
itly specied otherwise. The primary reason we chose \Sim-
ple Markov" over other adgraph models is that it simplies
interpretation of the results. While similar experiments can
be performed with other adgraphs, the results and their in-
terpretation would be dierent for every particular adgraph
model used.
Table 3 presents correlations between dierent adfactors
in our data. As expected, for a suciently small value of the
restart probability ( = 0:05), the PageRank contribution
adfactor is highly ( = 0:9773) correlated to the Eventual
Conversion (hit(
; c)) adfactor. There is also a signicant
Table 4: Stability of the adfactors for the top 1000
nodes.
Std.Dev. Mean Std.Dev. Mean
PPR 0.0014 0.0123 Visit 0.00005 0.0046
Ev.Conv. 0.0301 0.2796 Pass 0.000007 0.0015
LastAd 0.0272 0.1577
but much lower correlation between the PPR factor and the
Last Ad adfactor ( = 0:7285). The visit adfactor is almost
uncorrelated to the PPR, eventual conversion and the Last
Ad adfactors, indicating that the user queries that occur fre-
quently are not necessarily well connected to the conversion
event. Since the passthrough adfactor incorporates the visit
adfactor, it is also weakly correlated to the rest of the ad-
factors. All correlations are statistically signicant at 1%
level.
Table 4 shows stability results (the sample standard de-
viation) for the adfactors of the top 1,000 graph nodes in a
ve-fold sample split. One can see that the standard devia-
tions of all adfactors are relatively low compared to the mean
values suggesting that the adfactors of the most important
nodes in the graph are relatively stable in the presence of
sampling variance even though the edge weights in the graph
can be volatile (Table 1).
In the rest of this Section, we evaluate how adfactors corre-
late with other node attributes such as brand/non-brand 8,
click/impression and broad/exact match. Note that in all
three cases the evaluated attribute is a binary variable, thus,
instead of presenting simple correlations, one can deliver
better intuition by using ROC curves for the correspond-
ing classier. Consider, for instance, Figure 3. For every
adfactor, one can construct a classier of node \brand-iness"
by using the adfactor < T decision rule: if the adfactor is
larger than the threshold T , classify it as brand (or non-
brand depending on which one is better), otherwise classify
it as nonbrand (brand). Varying values of T , one can achieve
dierent (precision, recall) points; all such points constitute
the ROC curve.
Figure 3 shows that the PPR adfactor is an excellent pre-
dictor of \brand-iness" for impressions (AUC = 0.95509),
even stronger than the last ad score (AUC = 0.89930). At
the same time, for clicks the conversion Pass adfactor gives
the best predictor of the brand (AUC = 0.87707), although
it is an extremely weak predictor for impressions (AUC =
0.57120). We suggest that users who search with brand
queries are (naturally) much more likely to convert with
the advertiser, than users that search with generic queries,
thus the PPR adfactor measuring structural correlation to
the conversion event is a good signal of the brand nature
of the user query. Yet, once the user clicks on the adver-
tiser's ad, the signal loses its value, because, once the ad
attracted enough user attention, the query that triggered
the ad in the rst place becomes much less important. The
good predictive power of the Pass adfactor on click but not
impression \brand-iness" suggests that users are more likely
to convert with the advertiser through click on a brand query
ad rather than through click on a non-brand query ad, how-
ever converting users get equal exposure to both brand and
non-brand impressions before they convert.
8Queries were marked as brand if they included a phrase with
the edit distance of at most three to the advertiser's name or
the brand name, and marked as non-brand otherwise. The
results were manually inspected to ensure that the mapping
is reasonable.

Figure 3: ROC curve for brand prediction for clicks
(top) and impressions (bottom)
Figure 4: ROC curve for click prediction for brand
queries (top) and nonbrand queries (bottom)
Figure 4 shows that for brand queries the Last Ad adfac-
tor and the PPR adfactor are excellent signals of the click
attribute; for non-brand queries they predict well for recall
of up to approximately 0.6, after which the precision-recall
curve becomes
at (until the eventual jump to (1.0,1.0)).
This weird behavior can be attributed to the fact that, in
our dataset, we observe a number of rare generic (non-brand
specic) queries, for which click on the ad does not lead to
any conversion. We emphasize that such queries are rare,
therefore using the Pass adfactor lters them out and the
Pass adfactor shows excellent predictive power for the non-
brand queries in Figure 4.
Next, we compare the PPR and the Last Ad adfactors
by using a dierence between the ad rank in both models
as a predictor for brand/non-brand, click/impression and
Figure 5: ROC curve for (PPR rank - last ad rank)
predictor
Figure 6: PPR behavior as a function of distance to
conversion
Figure 7: ROC curve for brand prediction by dier-
ent models
broad/exact attributes. Results in Figure 5 suggest that
the dierence is a good predictor of the brand attribute;
manual inspection shows that this is because the PPR ad-
factor ranks brand nodes even higher than the Last Ad ad-
factor. On the other hand, the ROC curves for click and
phrase(broad)/exact match prediction are close to diagonal
suggesting that there is no systematic dierence in rankings
of clicks/impressions and broad/exact match nodes by both
methods.
Next, we plot the PPR behavior as a function of the dis-
tance to conversion in Figure 6. The gure was constructed
using the data from the\Backward Markov"model, in which
every user query is represented by multiple nodes in the
graph, depending on its distance from the conversion node.
Thus, for every query q, one can calculate
log (ppr(q at distance d; c)) log (ppr(q at distance 1; c)) 9:
Figure 6 shows average of these results for dierent groups.
Note that for clicks the PPR values at distance two and more
from conversion are signicantly smaller than the PPR val-
ues at distance one, suggesting that if the user clicks on the
ad and does not convert immediately, the likelihood to con-
vert in the future goes down. Consistent with our prior ob-
servations, the PPR behavior for brand and non-brand clicks
is similar. On the other hand, for non-brand impressions the
PPR grows (or at least doesn't decrease) with distance to
conversion, indicating that exposure to the advertiser ad on
non-brand queries can have a long-term positive correlation
with the likelihood of the user to convert. For brand im-
pressions, the PPR decreases with distance to conversion,
although not as strongly as for clicks, again suggesting that,
if the user searches for a brand and does not convert soon
enough, the likelihood of converting in the future goes down.
Finally, Figure 7 investigates how dierent graph struc-
tures aect the relationship between the PPR adfactor and
the brand attribute of the node. We consider three models:
\Simple Markov", \Backward Markov" and \RS Markov 1".
9The log representation was primarily chosen to reduce sen-
sitivity to outliers.

For \Simple Markov" model we simply plot the ROC curve
using the PPR adfactor as a predictor for brand. For \Back-
ward Markov" model we use the observation (from Figure 6)
that the PPR of brand nodes decays with distance from con-
version while the PPR of nonbrand nodes grows with dis-
tance from conversion, thus we use
10X
d=2
(log (ppr(q at distance d; c)) log (ppr(q at distance 1; c)))
as the predictor. For the \RS Markov 1" model, we would
expect similar behavior to hold and the PPR of the brand
nodes in the \search" state (before the user clicked on any
ads) to be lower than that in the \interested" state (after the
user clicked on some ad), while the PPR of the nonbrand
nodes in the \interested" state to be higher than that is the
\search" state; thus, we construct the predictor as
log (ppr(q in search state; c))log (ppr(q in interested state; c)) :
Figure 7 shows that the \RS Markov 1" model has the best
predictive power for the brand attribute, conrming the in-
tuition that user clicks have dierent value in brand and
non-brand contexts.
7. DATA MINING TOOLS
Producing intuitive and concise reports from huge amounts
of data is the desired goal for advertisers. In this section,
we discuss various data mining tools that can be developed
using our ad factors dened on the graph models introduced
in the paper.
Identifying the top k ads with the largest adfactor.
The simplest type of report one can think of is identifying
the top k ads with the largest adfactors in a particular graph
model. The value of such report depends on the particular
adfactor and the underlying graph model used. For instance,
in Section 6, we show that the PPR adfactor (in the \Simple
Markov"graph) has high but not perfect correlation with the
brand attribute of the ad impression. Identifying the top k
impressions with the PPR adfactor can thus be interpreted
as identifying the top k impressions (user queries) with the
highest\branding"impact: many of these user queries will in
fact have the advertiser name or the brand name in them,
but some will not and thus can be thought of as \shadow
brands". Due to privacy issues, we cannot show an actual
example of such output. Another interesting example of the
top k output is the top k impressions for the Pass adfactor;
they can be thought of as the top k user queries associated
with the largest revenue to the advertiser if one takes into
account the long-term correlations in the graph. Interest-
ingly, from Figure 3, we know that these are uncorrelated
with the brand attribute.
Identifying ads with signicant long-term eects not
taken into account by the Last Ad model.
Advertisers traditionally rely on the Last Ad reports (click-
through and conversion rates) to evaluate ad eectiveness.
An alternative report we suggest would be to look for ads
that are ranked higher with adfactors taking into account
the long-term correlations (like PPR) than with the Last Ad
adfactor. One such criteria for ranking is the dierence be-
tween the PPR adfactor node rank and the Last Ad adfactor
node rank (properties of this criteria are shown in Figure 5).
Another criteria is to look for impressions that either have
the PPR growing with the distance from conversion (\Back-
ward Markov" model) or have the PPR in the \search" state
higher than in the \interested" state (\RS Markov 1"model).
As Figure 7 shows, the second approach is more biased to-
wards the brand impressions than the rst one.
Identifying the top k ads with the maximum marginal
increase (MI) adfactor.
A popular advertising objective is to maximize the expected
number of user conversions given a certain budget constraint.
In a random walk model, we can restate it as maximizing
the probability of hitting the conversion node starting from
the \begin" node. A heuristic way to identify the valuable
nodes to invest on is to examine a small increase on the bid
of a query (or keyword) which will have the maximum ef-
fect on the probability of hitting the conversion node. This
small increase on the bid results in a small increase in the
weight of incoming edges for this query. Thus, in order to
identify queries for which the increase in their bid results in
the maximum marginal increase in the probability of hitting
conversion, we can look for the top k ads with the maximum
MI adfactor, and the advertiser may consider increasing the
bid for queries with large MI. 10
Explaining the adfactor value
The adfactor assigned to any particular node in the graph,
must be easily explained by a local structure around this
node. For instance, for the PPR (PageRank contribution)
adfactor of a node u, one can always consider the top-m
neighbor nodes through which the explained node u con-
tributes the largest fraction of the PageRank to the con-
version node. Formally, let u be the permutation of all
neighbors of the node u that arranges them in the decreas-
ing order of wuv ppr(v; c). We dene u(m) as the set of
the rst m nodes in the permutation. These nodes can be
thought of as the most likely next actions of the user after the
explained action, assuming that the user is going to convert.
It is straightforward to extend the pushback Algorithm 1 to
keep track of the top m contributors for every node, thus one
can eciently generate corresponding reports. The reports
are best represented as graph plots, constructed starting at
a seed node s and going up to a distance d in a graph of the
top-m neighbors of every node. Due to privacy reasons as
well as the space limit, we omit an example of such plot.
8. CONCLUSIONS
Online advertisers have access to aggregate statistics such
as the clickthrough rate, the conversion rate or the lift of
their ad campaigns, but seek to understand more sophisti-
cated correlations in users' trajectories of ads seen and users'
actions. Here we introduce an alternative data mining tech-
nique for aggregating user-level advertising data. We dene
various adgraphs to model the data pertinent to the ad-
vertiser and propose several adfactors based on stationary
probabilities of suitable random walks to quantify the im-
pact of ad events. We show anecdotal evidence for adfactors
and describe their potential data mining applications.
Our research introduces novel primitives for mining advertiser-
specic data for ad eects. Adfactors we dene are succinct,
easy to compute and capture many structural properties of
10We emphasize that this is only a heuristic. Any practical
bidding strategy should also take into account the current
bidding landscape (how much do the advertiser and the com-
petitors bid) for a particular keyword.

users' trajectories. In the future, richer data mining prim-
itives can be developed using adfactors, which may poten-
tially reveal more sophisticated correlations in user behav-
ior, including negative correlations. Other valuable direc-
tions for future research include developing richer graphical
models of user behavior, beyond the Markov models in this
paper, and adapting adfactors to them.
Acknowledgements. We would like to thank Chao Cai,
Zhimin He, and Sissie Hsiao for helping us with the data sets,
and Sheng Ma, Fernando Pereira, R. Srikant for interesting
discussions.
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10. APPENDIX
Proof of Proposition 1
Proof. From [4]
ppr(
; v) = ev
1X
t=0
(1 )t(MT )t:
After taking the derivative
@ ppr(
; c)
@
=
ppr(
; c)

+ ec
1X
t=1
t(1 )t1(MT )t:
It immediately follows that





@ ppr(
; c)
@

ppr(
; c)






1
! 0:
Next, we have h = ec + hM
T and
ppr(
; c) = ec + (1 ) ppr(
; c)M
T ;
which is equivalent to
ppr(
; c)

= ec +
1 

ppr(
; c)M
T :
After substraction
h
ppr(
; c)

=

h
1 

ppr(
; c)
!
MT ;
or

h
ppr(
; c)

!
= ppr(
; c)M
T

I MT
1
! 0;
as ppr(
; c) ! 0.
Proof of Proposition 2
Proof. We know that the ppr vector p with restart at node b solves the equa-
tion p = eb + (1 )pM, where M is the transition matrix. Fix nodes i and j
and take a derivative with respect to wij :
@p
@wij
= (1 )p
@M
@wij
+ (1 )
@p
@wij
M:
Now, @M@wij
is a zero matrix with a single 1 at row i and column j. It follows
that
@p
@wij
= (1 )p[i]ej + (1 )
@p
@wij
M;
where p[i] is the i-th component of the vector p. This can be written as
@p
@wij
=

1 

p[i]
!
ej + (1 )
@p
@wij
M;
and by linearity of the PPR we can see that this is just

1
 p[i]

times the
PPR vector with restart at node j, i.e.,
@ ppr(b; c)
@wij
=
1 

ppr(b; i) ppr(j; c):
Proofs of Propositions 3 and 5
Proof. For outgoing edges, we can use the equality ppr(i; c) = I(i ==
c) + (1 ) ppr(j; c)wij [4], as shown below:
X
j
wij
@ ppr(b; c)
@wij
=
(1 ) ppr(b; i)

0
@
X
j
wij ppr(j; c)
1
A
=
1 

ppr(b; i)
1
1 
ppr(i; c)
=
ppr(b; i) ppr(i; c)

:
For incoming edges, we can use similar trick with ppr(b; i) = I(i == b)+(1
) ppr(b; j)wji.
Proof of Theorem 2
Proof. MI and RE can be approximated by Theorem 1 of [4]. For MI,
RE and Pass simply note that M^ can be written as (1 0)M, where M is
a valid random walk matrix (every row sums to at most 1.0, the rest goes to
\null"). One can therefore calculate hit and all derivative adfactors (MI, RE and
Pass) via a pushback algorithm for the PPR of a random walk with the restart
probability 0 so Theorem 1 of [4] works again.