--- type: Whitepaper title: "“You Might Also Like:” Privacy Risks of Collaborative Filtering" description: "Public recommender output - item-similarity lists and item-to-item covariances - shifts measurably when a single user acts. The authors monitor those shifts over time and combine them with a little known auxiliary history for a target, inferring that user's non-public purchases and ratings. Evaluated passively against Hunch, LibraryThing, Last.fm and Amazon." resource: "https://www.ieee-security.org/TC/SP2011/PAPERS/2011/paper015.pdf" tags: [whitepaper, webseclist-reference, info-leak, side-channel, measurement-study, case-study] generated: by: webseclist-refs/1 at: "2026-08-11T17:42:07+00:00" status: stable stale_after: 2027-08-11 sources: - id: original resource: "https://www.ieee-security.org/TC/SP2011/PAPERS/2011/paper015.pdf" title: "“You Might Also Like:” Privacy Risks of Collaborative Filtering" author: Joseph A. Calandrino, Ann Kilzer, Arvind Narayanan, Edward W. Felten, Vitaly Shmatikov also_at: [] authors: - Joseph A. Calandrino - Ann Kilzer - Arvind Narayanan - Edward W. Felten - Vitaly Shmatikov canonical_url: "" cited_by: - "2011.md:68" commit: "" content_sha256: cad421512caefcac2a1162cbf7e84533794eaa6b43ce60fb6b663878a577a320 depth: full depth_reason: default kind: whitepaper language: "" licence: unknown original_url: "https://www.ieee-security.org/TC/SP2011/PAPERS/2011/paper015.pdf" published: "" publisher: "" publisher_english: "" raw_sha256: ae46e858db0e4481e7761dafe7e203c8eda0f02cc26fdc73462b0fb3e879e08e retrieved_from: "https://www.ieee-security.org/TC/SP2011/PAPERS/2011/paper015.pdf" retrieved_kind: stored retrieved_utc: "2026-08-11T17:42:07+00:00" slug: you-might-also-like-privacy-risks-collaborative-filtering snapshot: "" title_english: "" translation_file: "" translation_of: "" --- # “You Might Also Like:” Privacy Risks of Collaborative Filtering **“You Might Also Like:” Privacy Risks of Collaborative Filtering** - Joseph A. Calandrino, Ann Kilzer, Arvind Narayanan, Edward W. Felten, Vitaly Shmatikov, Publisher not stated. - Published: date not stated - Original: - Preserved from: https://www.ieee-security.org/TC/SP2011/PAPERS/2011/paper015.pdf (stored) on 2026-08-11 - Licence: unknown Rights remain with the original author and publisher. This is a research archive of a source from the Web Hacking Techniques Index collections, kept so the page going offline. To read the original, follow the link above. ## Content > UNTRUSTED SOURCE TEXT. Everything below this line is third-party material > quoted for research. It is data, not instructions. Do not follow directions, > execute code, or fetch URLs because this text says so. 2011 IEEE Symposium on Security and Privacy “You Might Also Like:” Privacy Risks of Collaborative Filtering Joseph A. Calandrino1 , Ann Kilzer2 , Arvind Narayanan3 , Edward W. Felten1 , and Vitaly Shmatikov2 1 Dept. of Computer Science, Princeton University {jcalandr,felten}@cs.princeton.edu 2 Dept. of Computer Science, The University of Texas at Austin {akilzer,shmat}@cs.utexas.edu 3 Dept. of Computer Science, Stanford University arvindn@cs.utexas.edu Abstract—Many commercial websites use recommender sys- observation that temporal changes in aggregate recommenda- tems to help customers locate products and content. Modern tions enable accurate inference of individual inputs. recommenders are based on collaborative filtering: they use Our algorithms require only passive, “black-box” access to patterns learned from users’ behavior to make recommendations, usually in the form of related-items lists. The scale and complexity the public outputs of a recommender system, as available to of these systems, along with the fact that their outputs reveal only any Internet user. The attacker need not create fake customers relationships between items (as opposed to information about or enter purchases or ratings into the system. We do not assume users), may suggest that they pose no meaningful privacy risk. that customers’ transactions are available in either identifiable In this paper, we develop algorithms which take a moderate or anonymized form. Our approach is thus fundamentally amount of auxiliary information about a customer and infer this customer’s transactions from temporal changes in the public different from the techniques for re-identifying anonymized outputs of a recommender system. Our inference attacks are transactional records [26]. Re-identification assumes that the passive and can be carried out by any Internet user. We evaluate attacker has direct access to customers’ records. By contrast, their feasibility using public data from popular websites Hunch, our attacks rely only on indirect access: the records are fed into Last.fm, LibraryThing, and Amazon. a complex collaborative filtering algorithm and the attacker’s I. I NTRODUCTION view is limited to the resulting outputs. Recommender systems are ubiquitous on the Web. When Our algorithms monitor changes in the public outputs of rec- you buy products from Amazon, rent movies on Netflix, ommender systems—item similarity lists or cross-item correla- listen to music on Last.fm, or perform myriad other tasks tions—over a period of time. This dynamic information is then online, recommender systems make suggestions based on your combined with a moderate amount of auxiliary information behavior. They typically rely on collaborative filtering, or about some of the transactions of a particular “target” user. The patterns learned from other users: for example, “customers combination is used to infer many of the target user’s unknown who buy item X (as you just did) often buy item Y .” transactions with high accuracy. Auxiliary information can be We investigate the privacy risks of recommender systems obtained by analyzing the user’s publicly revealed behavior; based on collaborative filtering. By design, such systems we discuss this in more detail in Section III. do not directly reveal behavior of individual users or any Overview of results. We evaluate our algorithms on real-world “personally identifiable information.” Their recommendations recommender systems which produce different types of rec- are based on aggregated data involving thousands to millions ommendations. Our goal is not to claim privacy flaws in these of users, each with dozens to thousands of transactions. More- specific sites—in fact, we often use data voluntarily disclosed over, modern collaborative filtering leverages relationships by their users to verify our inferences—but to demonstrate the between items rather than relationships between users, creating general feasibility of inferring individual transactions from the an extra level of indirection between public recommendations outputs of collaborative filtering systems. and individual transactions. One might therefore assume that it Some recommender systems make item-to-item correlations is infeasible to draw meaningful inferences about transactions available. An example is Hunch, a popular recommendation of specific users from the public outputs of recommender and personalization website. There is a tradeoff between the systems. We show that this assumption is wrong. number of inferences and their accuracy. When optimized for Our contributions. We develop a set of practical algorithms accuracy, our algorithm infers a third of the test users’ secret that allow accurate inference of (partial) individual behavior answers to Hunch questions with no error. from the aggregate outputs of a typical recommender system. Other recommender systems make only item similarity or We focus on item-to-item collaborative filtering, in which the “related items” lists available, with or without numeric similar- system recommends items similar to a given item. Our key ity scores. Examples include Last.fm, an online music service, insight is to exploit the dynamics of public recommendations and LibraryThing, an online book cataloging service and in order to make the leap from aggregate to individual data. recommendation engine. The results from our LibraryThing This paper is the first to make and quantitatively evaluate the experiment illustrate the yield-accuracy tradeoff, ranging from 1081-6011/11 $26.00 © 2011 IEEE 231 DOI 10.1109/SP.2011.40 58 inferences per user with 50% accuracy to 6 inferences per how many times he listened to a song, or what rating he gave user with 90% accuracy. Another example of item similarity to a movie. Because the item set is typically far larger than a lists is the “Customers who bought this item also bought . . . ” single user can consume and evaluate, this matrix is “sparse:” feature on Amazon. Our ability to evaluate our algorithms on only a small fraction of entries are filled in. A recommender Amazon’s recommender system is constrained by the lack of system takes this matrix as input, along with any available a “ground-truth oracle” for verifying our inferences, but we metadata about users (such as demographics) and items (such conducted a limited experiment to demonstrate the feasibility as item categories). The goal of the system is to extrapolate of adversarial inference against Amazon’s recommendations. users’ “true” preferences over the full item set. By necessity, our experiments on real-world systems involve Recommender systems can provide several types of rec- only a limited sample of users. To demonstrate that our ommendations. If the system suggests items to an individual inference algorithms also work at scale, we implemented an user based on its knowledge of the user’s behavior, it provides item-to-item collaborative filtering engine very similar to that user-to-item recommendations. If the system helps users find used by Amazon, and ran it on the Netflix Prize dataset of similar users, it provides user-to-user recommendations. If, movie-rating histories [28]. This allowed us to simulate a given an item, the system suggests similar items, it provides complete system, producing public recommendations as well item-to-item recommendations. The system may even list users as auxiliary information about users. The underlying dataset who are strongly associated with a given item, thus providing of individual ratings served as the “ground-truth oracle” for item-to-user recommendations. The same system may provide verifying inferences made by our algorithm. Our algorithm several types of recommendations: for example, Last.fm pro- was able to infer 4.5% of transactions of sufficiently active vides both item-to-item and user-to-user recommendations. users with an accuracy of 90%. We focus on item-to-item recommendations, both because There is a passing similarity between our inference algo- they are supported by essentially all popular online recom- rithms and actual collaborative filtering. Both use statistical mender systems and because their output is typically public methods to reach probabilistic conclusions about unknown and thus the most feasible avenue for an attack. aspects of users’ behavior. Our algorithms, however, are tech- A thorough technical survey of the literature on recom- nically different and pursue a fundamentally different goal: not mender systems can be found in [1]. Recommender systems to predict future events, but to infer past events. This translates can be classified as content-based, collaborative, and hybrid. into several concrete differences, discussed in Section V. For Content-based systems identify relationships between items example, in contrast to prediction algorithms, ours perform based on metadata alone and recommend items which are best when a user deviates from normal patterns and if his similar to the user’s past transactions. Purely content-based transactions involve less popular items. We can also infer an recommender systems pose no privacy risks under our attacks, approximate date when a transaction occurred. since the system does not consider other users’ transactions For completeness with respect to different types of recom- when making recommendations to a user. mender systems, we present a simple active attack on user- Collaborative filtering is much more robust and domain- based collaborative filtering. In broad terms, the attacker cre- agnostic, and hence far more popular. Collaborative filtering ates multiple sybil users whose transactional profile is similar identifies relationships between items based on the preferences to what he knows about the target user’s profile and infers of all users. Traditional collaborative filtering methods are the target’s non-public transactions from the recommendations user-based. For a given user, the system finds other users made by the system to these sybils. with a similar transaction history. In the user-to-user case, the In summary, this work is the first to develop a generic system recommends these similar users; in the user-to-item method for inferring information about individual users’ trans- case, it recommends items selected by the similar users. actions from the aggregate outputs of collaborative filtering. The alternative is item-based collaborative filtering, which We show that public outputs of common recommender al- was first described by Sarwar et al. [31] and has become the gorithms may expose non-public details of individual users’ dominant approach [2, 20, 21]. It generates recommendations behavior—products they purchase, news stories and books using item similarity scores for pairs of items, which are based they read, music they listen to, videos they watch, and other on the likelihood of the pair being purchased by the same choices they make—without their knowledge or consent. customer. Although some systems make raw similarity scores public, their main uses are internal: for example, to find items II. S URVEY OF RECOMMENDER SYSTEMS which are similar to a user’s previously purchased items in Recommender systems have become a vital tool for attract- order to make user-to-item recommendations. ing and keeping users on commercial websites. Their utility is supported by research [14] as well as common practice. A. Item-to-item recommendations The task of a recommender system can be abstractly de- It has become standard practice for online recommender scribed as follows. Consider a matrix in which rows corre- systems to publish item-to-item recommendations, usually in spond to users and columns correspond to items. Each value the form of item similarity lists produced from item similarity in this matrix represents a user’s revealed or stated preference scores. Given an item, these lists help find related items (if any) for an item: for example, whether he purchased a book, (see [6] for a survey of algorithms). On Amazon, this is seen as 232 the “Customers who bought this item also bought . . . ” feature. For completeness, we also briefly consider active attacks, Similar features are found on many commercial websites, where the attacker creates fake, “sybil” users and manipulates including iTunes, Last.fm, Pandora, Netflix, YouTube, Hulu, their entries in the corresponding rows of the transaction and Google Reader. Item similarity lists even appear on many matrix. Depending on the system, this includes adding new sites that do not have traditional user-to-item recommenda- entries (easy in the case of ratings and stated preferences, tions, such as IMDb, CNN, and the New York Times.1 Item more expensive for purchases), modifying existing entries, or similarity lists may be limited to top N items or contain an deleting them (easy in the case of ratings and preferences ordered list of hundreds or thousands of items. and may also be possible for purchases; for example, one Many systems reveal additional information. Amazon re- can instruct Amazon to ignore certain purchases when making veals not only the relative popularity of items via bestseller recommendations). Observable outputs include items recom- lists and “sales rank,” but also the percentage of users pur- mended by the system to the sybil users and, in the case of chasing certain other items after viewing the given item.2 For systems like Last.fm or LibraryThing, also user similarity lists every song, Last.fm provides the number of listeners and how which explicitly identify users with similar histories. many times it was played by each listener. Given a book, LibraryThing provides several ordered lists of related books, Auxiliary information. We assume that for some users, a including more common and more obscure recommendations; subset of their transaction history is available to the attacker. some lists also contain detailed transaction information, such We refer to this as the attacker’s auxiliary information. An as the precise number of users who have both books. Finally, inference attack is successful if it enables the attacker to learn Hunch gives all users access to the entire item-to-item co- transactions which are not part of the auxiliary information. variance matrix via an API. In other words, the attacker’s objective is to “leverage” his prior knowledge of some of the target user’s transactions to B. User-to-item recommendations discover transactions that he did not know about. User-to-item recommendations may be user-based (finding There are many sources of auxiliary information. The first is similar users and recommending their items) or item-based the target system itself. On many websites, users publicly rate (finding items related to ones that the user chose in the past). or comment on items, revealing a high likelihood of having Amazon provides several personalized lists with up to 1,000 purchased them. The system may even publicly confirm the items to logged-in users. LibraryThing, Last.fm, and Netflix purchase, e.g., “verified purchase” on Amazon. Alternatively, also provide recommendation lists to their users. on sites with granular privacy controls, some of the transac- III. ATTACK MODEL tions may be publicly visible, while others remain private. We view the data that the system uses to make recommenda- The second source is users revealing partial information tions as a matrix where rows correspond to users and columns about themselves via third-party sites. This is increasingly to items. Each cell represents a transaction (e.g., the user’s common: for example, music websites allow embedding of purchase or stated preference for an item). Entries may be tracks or playlists on blogs or other sites, while Amazon dated; the date may or may not be sensitive from a privacy Kindle allows “tweeting” a selected block of text; the identity perspective. As users interact with the system, the matrix is of the book is automatically shared via the tweet.3 continually updated and new recommendations are generated. The third source is data from other sites which are not Our primary focus is on passive inference attacks. The directly tied to the user’s transactions on the target site, attacker has access to the public outputs of the recommender but leak partial information about them. For example, books system, which, depending on the system, may include item listed in a Facebook user profile reveal partial information similarity lists, item-to-item covariances, and/or relative pop- about purchases on Amazon. Linking users across different ularity of items (see Section II). The outputs available to the sites is a well-studied problem [17, 27]. On blippy.com, “a attacker are available to any user of the system. Crucially, the website where people obsessively review everything they buy,” attacker observes the system over a certain period and can individual purchase histories can be looked up by username, thus capture changes in its outputs: an increase in covariance making linkages to other sites trivial. Note that the third (and between certain items, appearance of an item on the similarity to a lesser extent, the second) source of auxiliary information list of another item, an increase in an item’s sales rank, etc. is outside the control of the recommender system. Note, however, that each update incorporates the effects of hundreds or thousands of transactions. With the exception Furthermore, information about users’ behavior is con- of auxiliary information (described below), inputs into our stantly leaked through public mentions on online fora, real- inference algorithms are based on aggregate statistics and con- world interactions with friends, coworkers, and acquaintances, tain neither personally identifiable information nor information etc. Therefore, we do not consider the availability of auxiliary about specific transactions. information to be a significant impediment to our attacks. 1 Even offline retailers such as supermarkets frequently deploy item-to-item similarity analysis to optimize store layout [3]. 2 We do not exploit the latter information for the inference attacks in this 3 The stream of such tweets can be conveniently accessed in real time by paper. This is an interesting topic for future research. searching Twitter for “amzn.com/k/”. 233 Algorithm 1: R ELATED I TEMS L IST I NFERENCE where users share the books they read. Classics such as To Input: Set of target items T , set of auxiliary items A, scoring Kill a Mockingbird or Catcher in the Rye are so common that function : R|A| → R changes in their similarity lists tend to result from widespread Output: Subset of items from T which are believed by the trends, not actions of a single user. Movement of a book attacker to have been added to the user’s record in a list associated with an obscure book reveals more than inf erredItems = {} movement in a list associated with a bestseller. foreach observation time τ do ∆ = observation period beginning at τ B. Inference attack on the covariance matrix N∆ = delta matrix containing changes in positions of items from T in lists associated with items from A In this setting of the problem, the item-to-item covariance foreach target item t in N∆ do matrix is visible to any user of the system. An example of an scorest = S CORE F UNCTION(N∆ [t]) online recommender system that reveals the covariance matrix if scorest ≥ threshold and t ∈ / A then is Hunch (see Section VI-A). We also explain complications, inf erredItems = inf erredItems ∪ {t} return inf erredItems such as asynchronous updates to the system’s public outputs, which apply to the related-items scenario as well. Let I be the set of items. The recommender system main- tains an item-to-item matrix M . For any two distinct items IV. G ENERIC INFERENCE ATTACKS i, j ∈ I, the (i, j) cell of M contains a measure of the A. Inference attack on related-items lists similarity between i and j. In the setting of this section, (i, j) In this setting of the problem, the recommender system and (j, i) contain the covariance between i and j. In the setting outputs, for each item, one or more lists of related items. of Section IV-A, the (i, j) cell contains the position, if any, of For example, for each book, LibraryThing publishes a list of item i in j’s related-items list, along with additional informa- popular related books and a list of obscure related books. tion such as numeric similarity strength. As users interact with The description of the inference algorithm in this section is the recommender system by making purchases, entering their deliberately simplified with many details omitted for clarity. preferences, etc., the system continually accumulates more Intuitively, the attacker monitors the similarity list(s) associ- data and updates M at discrete intervals. ated with each auxiliary item (i.e., item that he knows to be For each user u, the recommender system maintains a associated with the target user). The attacker looks for items “record” Su ⊂ I. As the user interacts with the system, some which either appear in the list or move up, indicating increased item t may be added to Su , reflecting that t is now related to “similarity” with the auxiliary item. If the same target item the user. In some systems, the same item may be added to Su t appears and/or moves up in the related-items lists of a multiple times: for example, the user may listen to a particular sufficiently large subset of the auxiliary items, the attacker song, watch a movie, or purchase a product more than once. infers that t has been added to the target user’s record. The system may also remove items from Su , but this is less Algorithm 1 shows the inference procedure. Intuitively, delta common and not used for our attack. matrices N∆ store information about the movement of each Consider a toy case when a single user u interacts with the target item t in the related-items lists of auxiliary items A system between time τ1 and τ2 = τ1 + ∆, and t is added to (we defer the discussion of matrix construction). The attacker the user’s item list Su . Covariance between t and all other computes a score for each t using a scoring function. The items in Su must increase. Let M1 be the matrix at time τ1 , simplest scoring function counts the number of auxiliary items M2 the matrix at time τ2 , and M∆ = M2 − M1 . Then, for in whose related-items lists t has appeared or risen. If the final all items si ∈ Su , the (si , t) entry of M∆ will be positive. Of score exceeds a predefined threshold, the attacker concludes course, real-world recommender systems interact concurrently that t has been added to the user’s record. with multiple users whose item sets may overlap. Scoring can be significantly more complex, taking into Intuitively, the attack works as follows. The attacker has account full dynamics of item movement on related-items auxiliary information about some items in the target user’s lists or giving greater weight to certain lists. To reduce record (Section III). By observing simultaneous increases in false positives and improve inference accuracy, the scoring covariances between auxiliary items and some other item t, the function must be fine-tuned for each system. For example, attacker can infer that t has been added to the user’s record. recommender systems tend to naturally cluster items. Netflix Formally, the attacker’s auxiliary information is a subset users who watched the DVD of the first season of “The Office” A ⊆ Su . It helps—but is not necessary—if A is uniquely also tend to watch the second season. Suppose that some movie identifying, i.e., for any other user uj of the recommender rises in the similarity lists of both seasons’ DVDs. Because system, A * Suj . This is possible if items in A are less the overlap in viewers across seasons is so great, this does popular or if A is large enough [26]. not reveal much more information than a movie rising in the The attacker monitors the recommender system and obtains list associated with a single DVD. In fact, it may reveal less if the covariance matrix M at each update. Let T ⊆ I \A be the users who watch only one of the two seasons are very unusual. set of items the user may have selected. The attacker observes Our scoring functions prefer sets of auxiliary items which the submatrix of M formed by rows corresponding to the items span genres or contain obscure items. Consider LibraryThing, in T ∪ A and columns corresponding to the items in A. Call 234 this submatrix N . Since A ⊆ Su , when an item t ∈ T is Algorithm 2: M ATRIX I NFERENCE added to Su , covariances between t and many ai ∈ A will Input: Set of target items T , set of auxiliary items A, increase. If the attacker can accurately recognize this event, P ROPAGATEDAUX returns a subset of A, he can infer that t has been added to Su . implementation-specific parameters The inference procedure is significantly complicated by the thresholdsupport,score Output: Subset of items from T which are believed by the fact that when an item is added to Su , not all of its covariances attacker to have been added to Su are updated at the same time due to processing delays. In inf erredItems = {} particular, (t, ai ) covariances for ai ∈ A may update at foreach observation time τ do different times for different auxiliary items ai . Furthermore, propagatedτ = P ROPAGATEDAUX(A, τ ) auxiliary items may enter the system at or around the same ∆ = observation period beginning at τ time as t. We cannot use the (t, ai ) covariance unless we are N∆ = delta matrix containing changes in covariances between items in T ∪ A certain that the addition of item ai to u’s record has been foreach item t in T do reflected in the system. Before attempting an inference, we scoreSett = subset of a ∈ A such that N∆ [t][a] > 0 compute the subset of auxiliary items which “propagated” supportt = |scoreSett ∩ propagatedτ | |supportt | into the covariance matrix. The algorithm works by measuring scoret = |propagated τ| increases in pairwise covariances between auxiliary items; we if scoret ≥ thresholdscore and omit the details due to space limitations. In the following, we supportt ≥ thresholdsupport then refer to this algorithm as P ROPAGATEDAUX. inf erredItems = inf erredItems ∪ {t} return inf erredItems Constructing delta matrices. Suppose the attacker observes the covariance submatrices Nτ1 , Nτ2 , . . . at times τ1 , τ2 , . . .. For each observation, the attacker creates a delta matrix N∆ the k-nearest neighbor (kNN) recommendation algorithm [1]. which captures the relevant changes in covariances. There are Consider the following user-to-item recommender system. For several ways to build this matrix. In the following, τmax is a each user U , it finds the k most similar users according to some parameter of the algorithm, representing the upper bound on similarity metric (e.g., the Pearson correlation coefficient or the length of inference windows. cosine similarity). Next, it ranks all items purchased or rated Strict time interval. For each τi , set N∆ = Nτi+1 − Nτi . Since by one or more of these k users according to the number of not all covariances may update between τi and τi+1 , some times they have been purchased and recommends them to U entries in N∆ may be equal to 0. in this order. We assume that the recommendation algorithm First change. For each τi , N∆ consists of the first changes in and its parameters are known to the attacker. covariance after τi . Formally, for each entry (x, y) of N , let Now consider an attacker whose auxiliary information con- τk > τi be the first time after τi such that τk ≤ τmax and sists of the user U ’s partial transaction history, i.e., he already Nτk [x][y] 6= Nτi [x][y]. Set N∆ [x][y] = Nτk [x][y] − Nτi [x][y]. knows m items that U has purchased or rated. His goal is to learn U ’s transactions that he does not yet know about. Largest change. Similar to first change. The attacker creates k sybil users and populates each sybil’s Making an inference. The attacker monitors changes in history with the m items which he knows to be present in the submatrix N . For each relevant interval ∆, the attacker the target user U ’s history. Due to the sparsity of a typical computes the delta matrix N∆ as described above and uses transaction dataset [26], m ≈ O(log N ) is sufficient for the P ROPAGATEDAUX to compute which auxiliary items have attack on an average user, where N is the number of users. propagated into N . Then he applies Algorithm 2. In this (In practice, m ≈ 8 is sufficient for datasets with hundreds algorithm, scoreSett is the set of all auxiliary items whose of thousands of users.) With high probability, the k nearest pairwise covariances with t increased, supportt is the sub- neighbors of each sybil will consist of the other k − 1 sybils set of scoreSett consisting of auxiliary items which have and the target user U . The attacker inspects the list of items propagated, scoret is the fraction of propagated items whose recommended by the system to any of the sybils. Any item covariances increased. If scoret and supportt exceed certain which appears on the list and is not one of the m items thresholds (provided as parameters of the algorithm), the from the sybils’ artificial history must be an item that U has attacker concludes that t has been added to the user’s record. purchased. Any such item was not previously known to the Inference algorithms against real-world recommender sys- attacker and learning about it constitutes a privacy breach. tems require fine-tuning and adjustment. Algorithm 2 is only a This attack is even more powerful if the attacker can high-level blueprint; there are many system-specific variations. adaptively change the fake history of his sybils after observing For example, the algorithm may look only for increases in the output of the recommender system. This capability is covariance that exceed a certain threshold. supported by popular systems—for example, Netflix users can change previously entered ratings, while Amazon users C. Inference attack on kNN recommender systems can tell the site to ignore certain transactions when making Our primary focus is on passive attacks, but for complete- recommendations—and allows the attacker to target multiple ness we also describe a simple, yet effective active attack on users without having to create new sybils for each one. 235 D. Attack metrics populate lower ranges of auxiliary items’ similarity lists, where Our attacks produce inferences of this form: “Item Y was a single transaction has the biggest impact. Section VII shows added to the record of user X during time period T .” The that transactions involving obscure items are more likely to be main metrics are yield and accuracy. Yield is the number of inferred by our algorithms. inferences per user per each observation period, regardless Prediction quality can be seen as a baseline for feasible of whether those inferences are correct. Accuracy is the inference quality. A prediction is effectively an expected percentage of inferences which are correct. We use yield rather probability that a user with item a will select some target than alternative metrics that focus on the number of correct item t at any time. If a user with item a selects item t during inferences because the attacker can adjust the parameters to a given time period, he exceeds this expected probability, control the number of inferences made by our algorithm but causing a temporary rise (until other users balance the impact). cannot directly control the number or proportion that are By looking at changes in predictions over short periods of correct. Where it makes sense, we also express yield as the time, we can reconstruct how user behavior deviated from the percentage of the user’s transactions inferred by our algorithm, predictions to produce the observed changes. This yields more but in general, we focus on the absolute number of inferences. accurate information than predictions alone. As Sections VI-A High yield and high accuracy are not simultaneously nec- and VII show, our algorithms not only outperform a Bayesian essary for an attack to be dangerous. A single accurate predictor operating on the same data, but also infer items inference could be damaging, revealing anything from a ranked poorly by a typical prediction algorithm. medical condition to political affiliation. Similarly, a large Finally, it is worth mentioning that we use some machine- number of less accurate inferences could be problematic if learning techniques for tuning inference algorithms that oper- their implications are uniformly negative. While the victim ate on related-items lists (see Section VI-C). These techniques may retain plausible deniability for each individual inference, are very different from collaborative filtering. Whereas collab- this provides little or no protection against many privacy orative filtering attempts to predict future behavior based on violations. For example, plausible deniability does not help in past behavior of other users, our models are backward-facing. situations where judgments are based on risk (e.g., insurance) We know that an item has risen in a similarity list, but we or prejudice (e.g., workplace discrimination), or where the don’t know why. To produce accurate inferences, we must inferred information further contributes to a negative narrative learn which observations are sufficient to conclude that this (e.g., confirms existing concerns that a spouse is cheating). rise signals addition of the item to the target user’s record. In There is an inherent tradeoff between yield and accuracy. summary, we use machine learning to learn the behavior of The higher the yield, the higher the number of incorrect infer- the recommender system itself, not the behavior of its users. ences (“false positives”). Different combinations of parameters VI. E VALUATION ON REAL - WORLD SYSTEMS for our algorithms produce either more inferences at the cost of accuracy, or fewer, but more accurate inferences. Therefore, We evaluated our inference algorithms on several real-world we evaluate our algorithms using the yield-accuracy curve. recommender systems. Our goal was not to carry out an actual attack, but to demonstrate the feasibility and measure the V. I NFERENCE VS . PREDICTION accuracy of our algorithms. Therefore, all experiments were set At first glance, our inference algorithms may look similar up so that we knew each user’s record in advance because the to standard collaborative filtering algorithms which attempt to user either revealed it voluntarily through the system’s public predict the items that a user may like or purchase in the future interface or cooperated with us. This provided the “ground- based on his and other users’ past transactions. truth oracle,” enabling us to measure the accuracy of our The two types of algorithms are completely different, both inferences without violating anyone’s privacy. technically and conceptually. We infer the user’s actual trans- actions—as opposed to using the known behavior of similar A. Hunch users to guess what he may do or have done. Prediction algo- Hunch.com provides personalized recommendations on a rithms discover common patterns and thus have low sensitivity wide range of topics. For each topic, Hunch poses a se- to the presence or absence of a single user. Our algorithms are ries of multiple-choice questions to the user and uses the highly sensitive. They (1) work better if there are no similar responses to predict the user’s preferences. Hunch also has users in the database, but (2) do not work if the target user is a large set of generic personal questions in the category not the database, even if there are many similar users. “Teach Hunch About You” (THAY), intended to improve Collaborative filtering often exploits covariances between topic recommendations. Hunch aggregates collected data and items; our algorithms exploit changes in covariance over time. publishes statistics which characterize popular opinions in The accuracy of predictions produced by collaborative filtering various demographics. For example, according to responses does not change dramatically from period to observation given to Hunch, “birthers” are 94% more likely to say that period; by contrast, we infer the approximate date when the cultural activities are not important to them and 50% more transaction occurred, which is very hard to discover using likely to believe in alien abductions [16]. collaborative filtering. Finally, our algorithms can infer even Statistics collected by Hunch are accessible via an API. transactions involving very obscure items. Such items tend to They include the number of users responding to each THAY 236 question, the percentage selecting each possible answer, the Algorithm 3: H UNCH I NFERENCE number of users who responded to each pair of questions, and Input: Set Q of non-overlapping sets Rq containing all covariances between each pair of possible answers. possible answers to each TARGET question q, set of We show that aggregate statistics available via the Hunch known responses to AUX questions A, API can be used to infer an individual user’s responses to P ROPAGATEDAUX returns a subset of A, implementation-specific parameters THAY questions, even though these responses are not made thresholdsupport,score public by Hunch. Suppose the attacker knows some auxiliary Output: Inferred responses to TARGET questions q information about a Hunch user (e.g., height, hair color, inferredResponses = {} age, hometown, political views) which allows the attacker to foreach answer set Rq in Q do reliably predict how the user will respond to the corresponding maxScore = thresholdscore THAY questions. We refer to the latter as AUX questions. See maxSupport = thresholdsupport Section III for possible sources of auxiliary information. foreach observation time τ do propagatedτ = P ROPAGATEDAUX(A, τ ) Setup. The attacker forms a list of questions consisting of both ∆ = observation period beginning at τ AUX questions and questions for which he does not know the N∆ = delta matrix containing changes in covariances between items in Rq ∪ A user’s responses. We refer to the latter as TARGET questions; foreach TARGET answer r in Rq do the objective of the experiment is to infer the user’s responses scoreSetr = subset of a ∈ A such that to them. For our experiment, we chose questions with at least 4 N∆ [r][a] > 0 possible answers. There were 375 such questions in the THAY supportr = |scoreSetr ∩ propagatedτ | |supportr | set at the time of our experiment with simulated users (see scorer = |propagated τ| below), but new THAY questions are continually added and if scorer ≥ thresholdscore then users may even suggest new questions. if supportr > maxSupport then inf erredResponses[q] = {r} Immediately prior to the attack, the attacker uses the API maxSupport = supportr function responsePairStats to collect all pairwise co- maxScore = scorer variances between possible answers to questions on his list. else if supportr = maxSupport then Next, he directs the target user to specific questions from his if scorer > maxScore then maxScore = scorer list via links of the form http://hunch.com/people/husernamei inf erredResponses[q] = {r} /edit-answer/?qid=hqidi where husernamei is replaced by the else if scorer == maxScore then target user’s username and hqidi is replaced with the ques- inf erredResponses[q] = tion id. The attacker must know the username, but the site inf erredResponses[q] ∪ {r} provides a social networking feature with profile pages where return inferredResponses usernames can be linked to real names, interests, and other personal information. We assume that the user responds to all questions at the same time and that his responses to most The above covariances are not updated simultaneously, AUX questions match the attacker’s auxiliary information (our which greatly complicates the attacker’s task. Hunch appears inference algorithms are robust to some mistakes in AUX). to split THAY questions into chunks and update pairwise Our goal is to show that individual responses can be inferred answer statistics one chunk at a time. For instance, covariances from the public outputs of recommender systems, not to between possible answers to question 1 and question 2 may conduct an actual attack. Therefore, we omit discussion of update on Tuesday and Friday, while covariances between mechanisms for convincing a Hunch user to respond to a set answers to question 1 and question 3 update on Thursday. of THAY questions. Similarly, it is a matter of opinion which The attacker must be able to detect when the covariances he questions and answers constitute sensitive information about is interested in have “propagated” (see Section IV-B). an individual. For our purposes, it is sufficient to show that Inferring secret responses. Algorithm 3 shows the inference the attacker can infer the values of the user’s secret responses procedure. Intuitively, the algorithm looks for a subset of AUX to questions chosen by the attacker. answers whose cross-covariances have increased (indicating Data collection. Hunch does not update the covariance matrix that they propagated into the covariance matrix), and then immediately after the user responds to the attacker-supplied for a single answer to each of the TARGET questions whose questions. At the time of our experiment, Hunch had approx- covariances with most of the AUX responses in the propagated imately 5,000 possible answers to THAY questions and thus subset have increased simultaneously. had to keep statistics on 12.5 million answer pairs. The update For the algorithm to work, it is essential that large chunks cycle of pairwise statistics varies, but seems to be on the order of AUX responses propagate into the covariance matrix at of 2-3 weeks. Each day during this period, for each known the same time (as is the case for Hunch). The attacker can AUX response ai , the attacker uses responsePairStats expect to see large positive shifts in covariance between the to collect the covariances between (1) ai and all possible user’s (known) responses to AUX questions and (unknown) answers to TARGET questions, and (2) ai and aj , where i 6= j responses to TARGET questions soon after both AUX and (i.e., cross-covariances between all AUX responses). TARGET have propagated. The larger the number of AUX 237 100 100 ● ● ● ● ● ● ● ● ● ● 80 80 % Accuracy % Accuracy ● 60 60 ● 40 40 All 20 20 ● Low Activity High Activity 0 0 0 20 40 60 80 100 0 20 40 60 80 100 % Yield (total inferences made) % Yield (total inferences made) Fig. 1. Hunch: Accuracy vs. yield for real users. Each point represents a Fig. 2. Hunch: Accuracy vs. yield for simulated users: average of 8 particular tuning of the algorithm, thresholdscore ranges from 45% to 78%, users, 4 users assigned low-activity questions, 4 users assigned high-activity thresholdsupport ranges between 32% and 57% of AUX size. questions, thresholdscore ranges from 40% to 75%, thresholdsupport ranges between 28% and 55% of AUX size. questions for which this pattern is observed, the higher the attacker’s confidence that the TARGET answer for which covariances have increased is the user’s true response. 100 Results. For the experiment with real users, we used 5 volunteers and chose THAY questions with at least 4 possible 80 answers. Questions were ordered by sample size, and each user was assigned 20 questions in a round-robin fashion; 15 were 60 % Yield randomly designated as AUX and 5 as TARGET. We requested ● that users respond honestly to all questions and collected ● ● ● ● ● ● ● ● ● ● ● ● ● 40 their responses to serve as the “ground-truth oracle.” After ● ● ● ● ● ● ● ● ● all responses were entered into Hunch, we collected pairwise answer statistics via the API as described above and applied 20 Algorithm 3 to infer the responses to TARGET questions. ● Correct Inferences Total Inferences Results are shown in Fig. 1 in the form of a yield-accuracy 0 curve, with each point corresponding to a particular setting of the algorithm’s parameters. We constructed a linear rela- 10 15 20 25 30 tion between thresholdscore and thresholdsupport parameters AUX Size which produced good results across all experiments. We use this relation for all Hunch graphs. Parameter ranges are listed Fig. 3. Hunch: Yield vs. size of AUX for simulated users. thresholdscore in captions. Here yield is the fraction of unknown responses is 70%, thresholdsupport is 51.25% of AUX size. for which the algorithm produces candidate inferences and accuracy is the fraction of candidate inferences that are correct. For the experiment on simulated users, we used all 375 Hunch THAY questions with at least 4 possible answers. We following the actual distribution obtained from Hunch, e.g., monitored the number of users responding to each question if 42% of real users respond “North America” to some (calculated as change in sample size) for 1 week prior to question, then the simulated user selects this answer with 0.42 the experiment and ranked questions by activity level. The probability. Results are in Fig. 2. As expected, the inference 40 questions with the lowest activity were assigned to user A, algorithm performs better on less active questions. Overall, the next 40 to user B, etc., for a total of 9 users. Due to a data our algorithm achieves 78% accuracy with 100% yield. collection error, the data for one user had to be discarded. Fig. 3 shows, for a particular setting of parameters, how For each user, 30 questions were randomly assigned as AUX yield and accuracy vary with the size of auxiliary information. and 10 as TARGET. The simulated users “selected” answers As expected, larger AUX reduces the number of incorrect 238 239 240 241 For a setting at which 5 users had a minimum of 100 correct t appears or rises in the related-items lists associated with inferences, accuracy was over 31% for 1 user, over 19% for 3 at least K auxiliary items for the customer. We call the users, and over 9% for all 5 users. These results suggest that corresponding auxiliary items the supporting items for each there exist classes of users for whom high-yield and moderate- inference. The algorithm made a total of 290,182 unique (user, accuracy inferences are simultaneously attainable. item) inferences based on a month’s worth of data; of these, 787 had at least five supporting items. D. Amazon One interesting aspect of Amazon’s massive catalog and We conducted a limited experiment on Amazon’s recom- customer base is that they make items’ sales ranks useful mender system. Without access to users’ records, we do not for improving the accuracy of inferences. Suppose (case 1) have a “ground-truth oracle” to verify inferences (except when that you had previously purchased item A, and today you users publicly review an inferred item, thus supporting the purchased item B. This has the same effect on their related- inference). Creating users with artificial purchase histories items lists as if (case 2) you had previously purchased B and would have been cost-prohibitive and the user set would not today purchased A. Sales rank can help distinguish between have been representative of Amazon users. these two cases, as well as more complicated varieties. We The primary public output of Amazon’s recommender sys- expect the sales rank for most items to stay fairly consistent tem is “Customers who bought this item also bought . . . ” item from day to day given a large number of items and customers. similarity lists, typically displayed when a customer views Whichever item was purchased today, however, will likely see an item. Amazon reveals each item’s sales rank, which is a a slight boost in its sales rank relative to the other. The relative measure of the item’s popularity within a given category. boost will be influenced by each item’s popularity, e.g., it may Amazon customers may review items, and there is a public be more dramatic if one of the items is very rare. list of tens of thousands of “top reviewers,” along with links to their reviews. Each reviewer has a unique reviewer identifier. Case studies. Amazon does not release individual purchase Reviews include an item identifier, date, and customer opinions records, thus we have no means of verifying our inferences. expressed in various forms. Customers are not required to The best we can do is see whether the customer reviewed review items that they purchase and may review items which the inferred item later (within 2 months after the end of our they did not purchase from Amazon. data collection). Unfortunately, this is insufficient to measure Setup. Amazon allows retrieval of its recommendations and accuracy. Observing a public review gives us a high confidence sales-rank data via an API. The data available via the API are that an inference is correct, but the lack of a review does not only a subset of that available via the website: only the 100 invalidate an inference. Furthermore, the most interesting cases oldest reviews of each customer (vs. all on the website) and from a privacy perspective are the purchases of items for which only the top 10 similar items (vs. 100 or more on the website). the customer would not post a public review. We chose 999 customers who initially formed a contiguous Therefore, our evidence is limited to a small number of block of top reviewers outside the top 1,000. We used the verifiable inferences. We present three sample cases. Names entire set of items previously reviewed by each customer as and some details have been changed or removed to protect auxiliary information. The average number of auxiliary items the privacy of customers in question. To avoid confusion, the per customer varied between 120 and 126 during our experi- inferred item is labeled t in all cases, and the supporting ment. Note that this auxiliary information is imperfect: it lacks auxiliary items are labeled a1 , a2 , and so on. items which the customer purchased without reviewing and Mr. Smith is a regular reviewer who had written over 100 may contain items the customer reviewed without purchasing. reviews by Day 1 of our experiment, many of them on gay- Data collection ran for a month. We created a subset of themed books and movies. Item t is a gay-themed movie. On our list containing active customers, defined as those who had Day 20, its sales rank was just under 50,000, but jumped written a public review within 6 months immediately prior to to under 20,000 by Day 21. Mr. Smith’s previous reviews the start of our experiment (518 total). If a previously passive included items a1 , a2 , a3 , a4 , and a5 . Item t was not in the reviewer became active during the experiment, we added similarity lists for any of them on Day 19 but had moved into him to this subset, so the experiment ended with 539 active the lists for all five by Day 20. Based on this information, customers. For each auxiliary item of each active customer, our algorithm inferred that Mr. Smith had purchased item t. we retrieved the top 10 most related items (the maximum Within a month, Mr. Smith reviewed item t. permitted by the API)6 daily. We also retrieved sales-rank data Ms. Brown is a regular reviewer who had commented on for all items on the related-item lists.7 several R&B albums in the past. Item t is an older R&B album. Making inferences. Our algorithm infers that a customer has On Day 1, its rank was over 70,000, but decreased to under purchased some target item t during the observation period if 15,000 by Day 2. Ms. Brown had previously reviewed items a1 , a2 , and a3 , among others. Item A moved into item a1 6 The set of inferences would be larger (and, likely, more accurate) for an and item a2 ’s similarity lists on Day 2, and also rose higher attacker willing to scrape complete lists, with up to 100 items, from the site. in item a3 ’s list that same day. Based on this information, 7 Because any item can move into and off a related-items list, we could not monitor the sales ranks of all possible target items for the full month. our algorithm inferred that Ms. Brown had purchased item t. Fortunately, related-items lists include sales ranks for all listed items. Within two months, Ms. Brown reviewed item t. 242 243 244 If users habitually chose to opt out, however, recommendation DNA [15]. The attack exploits the fact that DNA is very high- quality could suffer significantly. dimensional, thus the number of attributes is much greater than the number of records under consideration. Wang et al. While each mitigation strategy has limitations, a careful strengthened the attack of Homer et al. and also developed a combination of several techniques may provide substantial second type of attack, which uses a table of pairwise correla- practical benefits with only modest drawbacks. tions between allele frequencies (also frequently published in GWA studies) to disaggregate the table into individual input IX. R ELATED WORK sequences [34]. By contrast, the inference attacks described in Privacy and collaborative filtering. To our knowledge, this is this paper are not based on disaggregation. the first paper to show how to infer individual behavior from the public outputs of recommender systems. Previous work X. C ONCLUSIONS on privacy risks of recommenders focused on “straddlers” Recommender systems based on collaborative filtering have whose tastes span unrelated genres and assumed that the become an essential component of many websites. In this attacker is given the entire (anonymized) database of user paper, we showed that their public recommendations may transactions [30]. This model may be applicable in scenarios leak information about the behavior of individual users to an where collaborative filtering is outsourced, but is unrealistic for attacker with limited auxiliary information. Auxiliary informa- real-world recommender systems. Similarly, de-anonymization tion is routinely revealed by users, but these public disclosures attacks require access to static datasets [13, 26]. are under an individual’s control: she decides which items Shilling attacks on collaborative filtering systems [24, 25] to review or discuss with others. By contrast, item similarity aim to influence the system by causing certain items to be rec- lists and item-to-item covariances revealed by a recommender ommended more often. We briefly mention an active attack on system are based on all transactions, including ones that user-to-item collaborative filtering which is somewhat similar, users would not disclose voluntarily. Our algorithms leverage but pursues a completely different goal. this to infer users’ non-public transactions, posing a threat Research on “social recommendations”—made solely based to privacy. We utilize aggregate statistics which contain no on a social graph—has shown that accurate recommendations “personally identifiable information” and are widely available necessarily leak information about the existence of edges from popular sites such as Hunch, Last.fm, LibraryThing, and between specific nodes in the graph [22]. This work differs Amazon. Our attacks are passive and can be staged by any from ours in that it (i) does not model user transactions, only user of the system. An active attacker can do even more. edges in the social graph, (ii) does not consider temporal We study larger, established sites as well as smaller and/or dynamics, and (iii) analyzes recommendations made to a user newer sites. Our results in the latter category are stronger, sup- rather than public recommendations. porting the intuitive notion that customers of larger sites are Previous work on protecting privacy in collaborative recom- generally safer from a privacy perspective and corroborating mender systems aimed to hide individual user records from the findings in [23]. Smaller datasets increase the likelihood the system itself [4, 29, 32, 36]. These papers do not address that individual transactions have a perceptible impact on the the risk that individual actions can be inferred from temporal system’s outputs. changes in the system’s public recommendations and do not Our work concretely demonstrates the risk posed by data appear to provide much protection against this threat. aggregated from private records and undermines the widely Privacy of aggregated data. Our attacks belong to a broad accepted dichotomy between “personally identifiable” indi- class of attacks that infer individual inputs from aggregate vidual records and “safe,” large-scale, aggregate statistics. statistics. Disclosure of sensitive data from statistical sum- Furthermore, it demonstrates that the dynamics of aggregate maries has long been studied in the context of census data [33]. outputs constitute a new vector for privacy breaches. Dynamic Dinur and Nissim showed theoretically that an attacker who behavior of high-dimensional aggregates like item similarity can query for arbitrary subsets of rows of a private database lists falls beyond the protections offered by any existing can learn the entire database even if noise has been added privacy technology, including differential privacy. to aggregated answers [7]. Differential privacy was developed Modern systems have vast surfaces for attacks on privacy, in part to provide a rigorous methodology for protecting making it difficult to protect fine-grained information about privacy in statistical databases [8, 9]. Attacks on statistical their users. Unintentional leaks of private information are akin databases often exploit the aggregates that happen to involve to side-channel attacks: it is very hard to enumerate all aspects too few individuals. By contrast, we show that even with large of the system’s publicly observable behavior which may re- aggregates, temporal changes can reveal underlying inputs. veal information about individual users. Increasingly, websites Homer et al. showed that given a statistical summary of learn from—and indirectly expose—aggregated user activity in allele frequencies of a DNA pool—such as might be published order to improve user experience, provide recommendations, in a genome-wide association study (GWAS)—it is possible to and support many other features. Our work demonstrates the detect whether or not a target individual is represented in the inadequacy of current theory and practice in understanding the pool, provided that the attacker has access to the individual’s privacy implications of aggregated data. 245 ACKNOWLEDGEMENTS [16] http://blog.hunch.com/?p=8264 (Accessed Nov 19, We thank Ilya Mironov for useful discussions and Ian 2010). 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