Repairing Provenance Policy Violations by Inventing Non-Functional Nodes

Abstract

In scientific collaborations, provenance is increasingly used to explain, debug, reproduce, and determine the validity and quality of data products. In such environments, it can be infeasible or undesirable to publish the complete provenance of all the final output data products. We have developed PROPUB, a system that allows users to publish a customized version of their data provenance, based on a set of publication and customization requests, while observing certain provenance publication policies, expressed as logic integrity constraints. The user's customization requests may violate one or more integrity constraints. In previous work, we removed additional parts of the provenance graph (i.e., not directly requested by the user) to repair policy violations. In this paper, we present an alternative approach which ensures that all relevant nodes are retained in the provenance graph. The key idea is to introduce new (non-functional) nodes that are used to represent lineage dependencies, without revealing information that the user wants to protect. With this new approach, a user may now explore different provenance publication strategies, and choose the most appropriate one before publishing sensitive provenance data.

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In the emerging paradigm of collaborative, data-intensive science, sharing data products even prior to publication is desirable [ 1,2 ]. Yet, without a proper scientific publication associated with openly published data, its validity and accuracy might be questionable. This is problematic in an open environment, where published data by one scientist is used by another scientist as input for further data analyses. In such an environment, data provenance (the lineage and processing history of data) can help to ensure data quality [ 3,4,5,6,7 ]. It is thus desirable to publish data products together with their provenance.

In many cases, however, provenance data can be sensitive and may contain private information or intellectual property that should not be revealed [ 7,8,5 ]. Consequently, a balancing act (Figure 1) is necessary between (i) the desire to publish provenance data so that collaborators can understand and rely on the shared data products, and (ii) the need to protect sensitive information, e.g., due to privacy concerns or intellectual property issues.

We view provenance as a bipartite, directed, acyclic graph, capturing which data nodes were consumed and produced, respectively, by invocation (i.e., computation) nodes. Our model thus corresponds to the Open Provenance Model (OPM) which captures the dependencies between data artifacts and invocations [ 9,10 ].

The Balancing Act

Privacy &

Relevancy

Concerns

Provenance

Publishing

To sanitize provenance graphs, a scientist can remove sensitive data nodes or invocations nodes from the provenance graph. Alternatively, she can abstract a set of sensitive nodes by grouping them into a single, abstract node. This update may violate some of the integrity constraints of the provenance graph [ 11 ]. For example, grouping multiple nodes into one abstraction node may introduce new dependencies which were absent in the initial provenance graph. Hiding nodes may also make some nodes in the final graph appear independent of each other even though they are dependent in the initial graph. Thus, one can no longer trust that the published provenance data is “correct” (e.g., there are no false dependencies) or “complete” (e.g., there are no false independencies). Therefore, we propose a system that allows a publisher to provide a high-level specification what parts of the provenance graph are to be published and which parts are to be sanitized, while guaranteeing that at the same time certain provenance publication constraints are observed. 2

Motivating Example

Figure 2(a) shows the provenance graph (PG) taken from the First Provenance Challenge [ 12 ]. Data nodes are depicted as circles and invocation nodes (representing computations) as boxes; dependencies among them are shown as directed edges. These edges capture the lineage of data and thus are typically drawn from right (newer nodes) to left (older nodes). For example, d16 was generated by an invocation s2, and was in turn used by invocation c2, denoted by, respectively s2 g←en−by d16 and d16 u←se−d c2.

Let us assume, the user wants to publish data products d18 and d19 along with their lineage data. Then, she will issue the publication requests as shown in Figure 2(a). A recursive query is used to retrieve all data and invocation nodes upstream from d18 and d19 and we get a modified provenance graph (PG!) as shown in Figure 2(b). Note that the lineage of d20 up to s3 is not relevant for d18 and d19 and hence not included in PG!. Further assume that before publishing PG!, the user also requests a set of customizations as shown in Figure 2(b).

Figure 3 shows the provenance graph we get after applying all the customization requests. We see that this provenance graph violates three provenance policies: There !"# !$%# !$$# !$&# '$! !$(# !$)#

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"#$%&'(!%&)*+,*! *$! *&! !$+# !$-# ,$! ,&! !$/# !$"# %&)*+,*-./01! %&)*+,*-./21! !"# !$%# !$$# !$&# "#$#%&'()! '$! !$(# !$)# "*+,-".,! *$! !$+# *&! !$-# ,$! ,&! /'0)! /'0)! "*+,-".,10234!526! "*+,-".,1+24!526! !$.# "*+,-".,1&24!526!

"#$#%&'()10226! !$"# "#$#%&'()10276! is a cycle between d13 and g1, a type error for the edge from s2 to g1 (the graph should be bipartite), and there is no dependency between d19 and d16, violating, respectively, the No-Cyclic Dependency (NCD), No-Type Error (NTE) and No-False Independence (NFI) policies. On the other hand, the provenance policies No-Write Conflict (NWC) and No-False Dependence (NFD) are not violated by these customization requests. Outline and Contributions. In Section 3, we first describe the provenance model, user requests, provenance policies, and logical architecture of PROPUB. This overall framework was proposed recently in [ 11 ]. In Section 4 we present our main contribution, i.e., a new way to repair policy violations, not by removing additional nodes (as in our prior work), but by introducing new (non-functional) nodes that represent the original lineage dependencies, without revealing information that the user wants to protect. We describe in detail how policy violations will be repaired such that all relevant nodes are retained in the final provenance graph. Related work is discussed in Section 5 and Section 6 presents some concluding remarks and suggestions for future work. 3

Provenance Publisher (PROPUB)

In our recent work, we developed the system PROPUB [ 11 ], which uses a declarative approach to publish customized policy-aware provenance. PROPUB accepts the initial provenance graph and two types of input specifications. (i) User Requests: the publication and customization requests, and (ii) Provenance Policies: the integrity constraints Relation Name Description used(I, D) An edge specifying that the invocation I used the data artifact D. gen by(D, I) An edge to indicate that the data artifact D was generated by invocation I. actor(I, A) An invocation node I, which was executed by actor A. data(D, R) A data artifact node, whose value can be retrieved using the reference R. dep(X, Y) An auxiliary relation and defined as dep = used ∪ gen by and to specify that node X depends on node Y , irrespective of the node types. to be observed. PROPUB then applies all user requests on the initial provenance graph and checks for policy violations. In case there is a violation, it applies repairs and generates the customized provenance graph.

Provenance Model. The provenance model used in PROPUB is based on OPM, the Open Provenance Model [ 13 ] and our earlier work [ 14 ]: A provenance (or lineage) graph is an acyclic graph P G = (V, E), where the nodes V = D ∪ I represent either data items D or actor invocations I. The graph G is bipartite, i.e., the edges E = Euse ∪ Egby are either used edges Euse ⊆ I × D or generated-by edges Egby ⊆ D × I. Here, a used edge (i, d) ∈ E means that invocation i has read d as part of its input, while a generated-by edge (d, i) ∈ E means that d was output data, written by invocation i. We use the schema shown in Table 1.

User Requests. The user requests supported by the PROPUB framework are summarized in Table 2. The PROPUB system expects user requests to be asserted as relational facts that can then be used by a Datalog rule engine. An user request can be a publication request or a customization request. A customization user request can request to remove a node or an edge or to keep that in the final graph.

Provenance Policies. The provenance graph supported by PROPUB is a bipartite directed acyclic graph. Also, an invocation can read many data artifacts, but a data artifact is written by exactly one invocation. We developed three provenance policies to verify if these structural properties are satisfied in the provenance graph PG!Δu, which we get after applying all the customization requests on PG!. PROPUB has two more provenance policies to ensure the correctness and completeness of information. These provenance policies are briefly defined in Table 3.

Provenance Policy Description

No-Write Conflict (NWC) A data artifact can be written by only one invocation. No-Cyclic Dependency (NCD) There is no cycle between any two nodes X and Y.

No-Type Error (NTE) Two nodes with a direct dependency are of different types. No-False Dependence (NFD) Two nodes are dependent in PG!Δu only if they are dependent in PG!.

No-False Independence (NFI) Two nodes are independent in PG!Δu only if they are independent in PG!. Constraint Description ic:wc(X, Y) Write conflict: invocations X and Y are creating the same data node. ic:cd(X, Y) Cyclic dependency between nodes X and Y. ic:te(X, Y) Type error: nodes X and Y are connected via used or gen by edges, but don’t have the corresponding node types. ic:fd(X, Y) False dependency: node Y depends on X in PG!Δu, but not in PG!. ic:fi(X, Y) False independence: node Y depends on X in PG!, but not in PG!Δu.

We use a set of integrity constraints (ICs) to check whether the provenance policies defined in Table 3 are satisfied. Table 4 lists the “witness relations” that are defined by rules (not shown) and which are used to detect particular IC violations.3 3.1

Logical Architecture

The logical architecture of the PROPUB system is shown in Figure 4. The user submits a set of publication and customization requests U0. The module Direct-Conflict-Detection detects direct conflicts among the given user-requests. For example, a hide and a retain request on the same node is an obvious conflict. The user needs to update her original requests until all direct conflicts are resolved, resulting in a conflict-free user request U. The Lineage-Selection module computes the sub graph PG!, which contains all tobe-published data items (specified using the ‘lineage’ predicate) together with their complete provenance.

The Request-Policy-Evaluation module calculates the updates (Δu: inform of insert and delete) needed to apply all the user requests from U on PG!. It applies Δu on PG! and get a customized provenance graph PG!Δu. Then it checks if all the selected provenance policies (PP) are observed by evaluating respective integrity constraints. In case some of the policies are violated, this module calculates updates (Δp: inform of insert and delete) needed to repair the violations. In a final conflict resolution step using the module Implied-Conflict-Detection-Resolution, the system detects all such implied 3 For example., we can detect whether a data node is created by different invocations X and Y and record this as ic:wc(X, Y ).

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1$/23% conflicts by comparing Δu and Δp. In case an implicit conflict is detected, it selects another subset from the given U and PP following the user preferences. These steps are repeated until there is no more policy violations. It then applies Δp on PG!Δu to get the customized provenance graph (CG) ready to be published. 4

Repairing Policy Violations

If we apply the customization user requests on PG!, we get an intermediate provenance graph PG!Δu as we shown in Figure 2(a), 2(b) and 3. But, PG!Δu may violate one or more provenance policies. In case the PG!Δu violates a structural policy (NWC, NCD, and NTE), it will no more be a proper provenance graph. Also, in case it violates a non-structural policy (NFI and NFD), PG!Δu may contain incorrect information or may become incomplete. Thus, user will not be able to publish PG!Δu. To resolve this issue, we apply the customization requests U on PG! in a strategic way such that it confirms to all the provenance policies.

Our strategy is primarily based on two ideas (i) inventing non-functional nodes, and (ii) converting user requests using other forms of user requests.

Inventing Non-functional Nodes. In case PG!Δu has a structural violation, PROPUB resolves the violation by adding a new non-functional node. A non-functional node is added to maintain the structure of provenance graph. Presence of a non-functional node in the final customized graph may represent one data or invocation node or a set of data and invocation nodes. No mapping is maintained between the non-functional node and the nodes it replaced. Also, it will not carry any URL. Thus, no one will be able to reach to the value of a data artifact or the source code of an actor from a non-functional node. PROPUB invents minimum numbers of non-functional nodes to resolve a policy violation.

PROPUB uses the same strategy to resolve NFD policy violations. The fix to the violation of this policy is complex and may need more than one non-functional node to be added. In spite of this complexity, PROPUB resolves the violation using the minimum numbers of non-functional nodes.

Converting User Requests. A publisher can use ur:hide requests to hide individual nodes or the partial structure of the provenance graph. When we apply these user requests all the selected nodes and the associated edges are removed from the provenance graph PG! and a set of independence may be created which violates the NFI policy. We can use the inventing new non-functional node strategy as discussed above and replace the selected node by a non-functional node to resolve this policy violation. But, this approach keeps the structure of the original provenance graph in the final provenance graph. Instead, PROPUB converts these ur:hide user requests into an equivalent set of ur:abstract user requests so that all the selected nodes are removed and no unintended dependencies are removed. 4.1

Repairing Structural Policy Violations

No-Type Error. This policy is violated in case there is a direct dependency between two nodes of same type (i.e. a dependency between two data artifacts or a dependency between two invocations). PROPUB invents a non-functional invocation node in case the policy violation is between two data artifacts as shown in Fig. 5. In the similar way, PROPUB invents a non-functional data node in case the policy violation is between two invocation nodes. We used the rules as shown below to create the non-functional nodes and fix the violations of this policy. del_dep(X,Y) :- ic:te(X,Y). add_data(f(X,Y),T) :- ic:te(X,Y), d_actor(X,_), T=‘ic:te’. add_actor(f(X,Y),T) :- ic:te(X,Y), d_data(X,_), T=‘ic:te’. add_dep(X,f(X,Y)) :- ic:te(N1,N2), X is N1. add_dep(f(X,Y),Y) :- ic:te(N1,N2), Y is N2.

No-Write Conflict. This policy is violated in case there are N (N ≥ 2) gen by edges for a data node. To resolve this violation PROPUB removes incorrect gen by edges for the violated data node and keeps only one gen by edge, which is there in PG. But, this may violate the NFI policy as it removes dependencies for N − 1 invocation nodes. To get around this side effect PROPUB invents N − 1 non-functional data nodes and creates N − 1 gen by edges as shown in Fig. 6. Lastly, it copies all the used edges for the violated data node over to all N − 1 non-functional data nodes. Following rules are used to create the non-functional nodes and fix the violations of this policy: del_data(D) :- ic:wc(D). del_dep(D,I) :- ic:wc(D), d_gen_by(D,I). add_data(f(D,I),T) :- ic:wc(D), d_gen_by(D,I), T=‘ic:wc’. add_dep(f(D,I),I) :- ic:wc(D), d_gen_by(D,I). add_dep(I,f(D,I1)) :- ic:wc(D), d_gen_by(D,I1), d_used(I,D). No-Cyclic Dependency. This policy is violated in case a node is reachable from itself. In Fig. 7, there is a cycle between a invocation node and a data node. To fix this violation PROPUB invents a non-functional invocation node and creates a used edge between the data node and the non-functional invocation node. Then it removes all the gen by edges from the invocation node (except the one with the data node with which it has the cycle) and copies them over to the non-functional invocation node. In the similar way, PROPUB resolves this violation between two invocation nodes.

4.2 Repairing No-False Independence (NFI) Policy Violations

This policy is violated in case two nodes are not dependent in PG!Δu even though they are in PG!. This may occur in case the ur:hide user requests are applied on PG! as shown in Fig. 8. One way to resolve this violation is to insert direct dependencies, which (a) User Requests: ur:hide nodes (b) Policy Violation (c) Fix are there in PG! but missing in PG!Δu, between any two nodes in PG!Δu. But, this process may add too many edges and the graph may become unreadable. One optimization to this process is to develop transitive dependencies to reduce the total number of new edges needed. This may be computation intensive. PROPUB uses a different strategy to fix this violation. Following rules are used to transform the ur:hide requests into an equivalent set of ur:abstract requests: hide_connected(X,Y) :- ur:hide(X), ur:hide(Y), dep(X,Y). hide_connected(X,X) :- ur:hide(X). hide_connected(X,Y) :- hide_connected(Y,X). hide_connected(X,Y) :- hide_connected(X,Z), hide_connected(Z,Y). smaller(X) :- hide_connected(X,Y), X < Y. minimum(X) :- ur:hide(X), not(smaller(X)). abstract_hide(X,G) :- hide_connected(X,G), minimum(G).

The customization user requests ur:abstract removes nodes from PG!, but does not violate the NFI policy. To avoid the NFI polic violations PROPUB transforms the ur:hide user requests into an equivalent set of ur:abstract user requests. These will be applied to PG! in the same way the User issued ur:abstract requests are applied.

4.3 Repairing No-False Dependence (NFD) Policy Violations

This policy is violated in case two nodes are dependent in PG!Δu even though they are not in PG!. This may occur in case the ur:abstract user requests are applied on PG! as shown in Fig. 9. In Fig. 9(a) we have a partial provenance graph showing the ur:abstract requests and the nodes with direct dependencies with one or more nodes selected to be abstracted. This figure shows that in PG! the data artifact ‘1’ depends on data artifact ‘a’ and ‘b’. In the similar way, the data node ‘2’ depends on invocation nodes ‘b’ and ‘c’ and so on. Now, if we apply these ur:abstract requests by collapsing all the selected nodes into a abstracted node then in PG!Δu the data artifact ‘1’ become depended on nodes ‘a’, ‘b’, ‘c’, ‘d’, and ‘e’ and thus making PG!Δu incorrect, as shown in Fig. 9. !" !" &" $" )"

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To avoid this policy violations PROPUB takes a systematic three stages approach to apply the ur:abstract user requests. Instead of collapsing into one abstracted node, it invents a number of non-functional data and invocation nodes to maintain the dependencies between any two nodes in PG!Δu as they are in PG!. This systematic approach ensures that the minimum number of non-functional nodes are invented. In the first stage, PROPUB develops two sets in and out. The in is a set of data nodes which is used by some of the invocation nodes selected to be abstracted and invocation nodes which generated some of the data nodes selected to be abstracted. The out is a set of data nodes which is generated by one of the invocation node selected to abstracted and invocation nodes which used some of the data nodes selected to abstracted. It also calculates the dependencies for each of the node in set out on the nodes of the set in.

Now, PROPUB creates non-functional data nodes for each of the invocation nodes from the sets in and out. One non-functional data node is created for exactly one invocation node from the set in through a gen by edge. One non-functional data node is created for more then one invocation node from the set out through used edges in case these invocations have the same dependencies on the set in. At this stage, a nonfunctional data node is connected either to a node from the set in or to one or many nodes from the set out. For example, invocation node ‘4’ ‘5’ and depends on invocation nodes ‘b’ and ‘c’ and PROPUB will create only one non-functional data node and two used edges. This is shown in Fig. 10(a).

In the second stage, it calculates the list of dependencies of all nodes from the set out to the nodes from in. PROPUB creates one non-functional invocation node for each of these unique dependency lists and it creates gen by edges for nodes from the set out which has the same dependency list. Then it creates used edges to connect to the nodes in in set from any of these non-functional invocation nodes. It will connect with respective non-functional data node created in the last stage in case an edge needs to be created with an invocation either from in or out. This outcome is shown in Fig. 10(b). !" !" &" $" )" #" %" '" (" +" *" !" !" &" $" )" #" %" '" (" +" *" !" !" &" $" )" #" %" '" (" +" *" (a) Stage 1 (b) Stage 2 (c) Fix Stage 3 In the final stage, PROPUB combines nodes if possible. For example, in Fig. 10(b) the path from node ‘6’ to node ‘e’ has three consecutive non-functional nodes with no other dependencies. These three nodes can be replaced by only one non-functional data node. The result is shown in Fig. 10(c). Now, PROPUB removes all the nodes selected to be abstracted and associated edges from PG!. 4.4

Algorithm

The algorithm mentioned in Fig. 11 finds the customized provenance graph, if available. In this approach, we add non-functional nodes to repair policy violations. In Figure 3 we show that PG!Δu has a structural policy violation between nodes g1 and s2. Using this approach, we introduce a non-functional data node d such that d is dependent on g1; and s2 is dependent on d. Now, to fix the cycle between d13 and g1 we introduce the non-functional invocation node g2 and create a dependency (gen by) edge from d15 to g2. Then, we get the final CG as shown in Figure 12. Note that we are now able to keep all the relevant nodes in CG.

!&$ !"'$ !""$ !"($ !"# !$ !")$ /:# !:#

-./+0-'+1)"23#!"4# !#%&'# !#%')# -./+0-'+1/"3#!"4# !#%()# !#%*# !#%+,# -./+0-'+15"3#!"4# !"#$ !$# !"&$ --%%66%%77558899,,11))""":44## !"%$ ;8),1)"<4# ;8),1'"4# ;8),1':4# In [ 3,4,5,6,7 ], it has been observed that provenance can be used, e.g., to interpret results, diagnose errors, fix bugs, improve reproducibility, and generally to build trust on the final data products and the underlying processes. In addition, provenance can be used to enhance exploratory processes [ 15,16,17 ], and techniques have been developed to deal with provenance efficiently [18,19].

In many cases, provenance carries sensitive information, which can cause privacy concerns related to a data, actor, or workflow specification. Studying provenance, one can capture the functionality (being able to guess the output of the actor given a set of inputs) of an actor (module), or the execution flow of a workflow [ 8 ].

The security view approach [ 5 ] limits the available provenance to a user by providing a partial view of the workflow through a role-based access control mechanism, and by defining a set of access permissions on actors, channels, and input/output ports as specified by the workflow owner at design time. The ZOOM∗UserViews approach [20] allows to define a partial, zoomed-out view of a workflow, based on a user-defined distinction between relevant and irrelevant actors. Provenance information is restricted by the definition of that partial view of the workflow.

In our recent work [ 11 ], we developed PROPUB, which uses a declarative approach to publish customized policy-aware provenance. In this paper, we developed a new way to repair policy violations, not by removing additional nodes (as in [ 11 ]), but by introducing new (non-functional) nodes that represent the original lineage dependencies, without revealing information that the user wants to protect. We described in detail how policy violations will be repaired such that all relevant nodes are retained in the final provenance graph. 6

Conclusions

We discussed the need for provenance in scientific collaboration. Provenance data helps to build trust in the published results and data. However, provenance can also contain sensitive data and/or too much irrelevant detail. Thus, scientists should be able to “customize” provenance data before sharing it.

Our current PROPUB system is based on the open provenance model (OPM). We plan to extend PROPUB to include model extensions, e.g., to support structured data structures, in particular nested collections [19]. Furthermore, PROPUB currently suggests only one specific modified graph based on a given U and PP. In future work, we plan to investigate how to extend this approach to rank alternative solutions, thus supporting scientists even more in finding the desirable balance between revealing provenance information and preserving privacy when sharing data with collaborators. 16. Freire, J., Silva, C., Callahan, S., Santos, E., Scheidegger, C., Vo, H.: Managing rapidlyevolving scientific workflows. Provenance and Annotation of Data (2006) 10–18 17. Silva, C., Freire, J., Callahan, S.: Provenance for visualizations: Reproducibility and beyond.

Computing in Science & Engineering (2007) 82–89 18. Heinis, T., Alonso, G.: Efficient Lineage Tracking For Scientific Workflows. In: Proceedings of the 2008 ACM SIGMOD conference. (2008) 1007–1018 19. Anand, M., Bowers, S., Luda¨scher, B.: Techniques for efficiently querying scientific workflow provenance graphs. In: Proceedings of the 13th International Conference on Extending Database Technology, ACM (2010) 287–298 20. Biton, O., Cohen-Boulakia, S., Davidson, S.: Zoom* userviews: Querying relevant provenance in workflow systems. In: Proceedings of the 33rd international conference on Very large data bases, VLDB Endowment (2007) 1366–1369

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