Patent Description:
Digital resources can be accessed by large numbers of remotely located users. Determining the number of users that access digital resources can be used, e.g., to manage distribution and storage of digital resources.

The extent to which a process is privacy preserving can be measured in various ways. For example, differential privacy techniques can be used to quantify the extent to which processes are privacy preserving. A computational process operating on a dataset can be referred to as being privacy sensitive (or privacy preserving), e.g., if the process is adapted to prevent leakage of information from the dataset.

<CIT> describes a user access path prediction method, according to which, firstly, a user access sequence set is constructed from a log file, and then on the sequence set, a PLWAP algorithm is used for conducting frequent path mining to obtain frequent access paths.

<CIT> describes techniques relating to determining statistics associated with the storage of data on a medium; in an example, a computing system maintains a management statistic for a storage device, and uses the management statistic as a proxy for a workload statistic for a storage block within the storage device.

<NPL>) describes a hashing scheme to partition metadata namespace tree and serve large-scale distributed storage systems.

This specification describes a system implemented as computer programs on one or more computers in one or more locations that can perform efficient and privacy sensitive estimation of digital resource access frequency.

According to a first aspect there is provided a method performed by one or more computers, the method including: obtaining access data for a digital resource, where the access data comprises, for each time point in a sequence of time points, data identifying a set of users that accessed the digital resource at the time point, processing the access data to generate data defining a tree model, where the tree model includes a set of nodes, and each node in the set of nodes is associated with: (i) a key that specifies a plurality of time intervals in the time span, and (ii) a value that is based on a respective number of users that satisfy a node-specific selection criterion based on the plurality of time intervals specified by the key for the node, receiving a request to determine a number of users that accessed the digital resource at least a predefined number of times within a time window, and in response to the request: processing the tree model to generate an estimate for the number of users that accessed the digital resource at least the predefined number of times within the time window.

In some implementations, for one or more nodes in tree model, the key for the node specifies at least a first time interval, a second time interval, and a third time interval, where the first time interval, the second time interval, and the third time interval are each different.

In some implementations, for one or more nodes in the tree model, a user satisfies the node-specific selection criterion for the node only if: (i) the user accesses the digital resource at least once in the first time interval and at least once in the second time interval, and (ii) the user accesses the digital resource a target number of times in the third time interval.

In some implementations, for one or more nodes in the tree model, the target number of times is zero.

In some implementations, (i) the tree model is a two-dimensional tree model, (ii) for each node in the tree model, the key for the node is parameterized by a set of parameters that define a region of two-dimensional space, and (iii) for each parent node in the tree model, the region of the two-dimensional space defined by the key of the parent node is partitioned by regions of the two-dimensional space defined by keys of child nodes of the parent node.

In some implementations, for each node in the tree model: the key for the node is parameterized by respective parameters a, b, c, d, the parameters define the region of two-dimensional space given by: [a,b] × [c,d], the first time interval includes [a - <NUM>, b - <NUM>], the second time interval includes [T + <NUM> - d,T + <NUM> - c], where T is a last time point in the sequence of time points, and the third time interval includes [b,T + <NUM> - d].

In some implementations, for each node in the tree model, the value associated with the node is based on a difference between: (i) a number of users that satisfy a first node-specific selection criterion based on the plurality of time intervals specified by the key for the node, and (ii) a number of users that satisfy a second node-specific selection criterion based on the plurality of time intervals specified by the key for the node.

In some implementations, for one or more nodes in the tree model, the key for the node specifies at least a first time interval, a second time interval, a third time interval, and a fourth time interval, where the first time interval, the second time interval, the third time interval, and the fourth time interval are each different.

In some implementations, for one or more leaf nodes in the tree model: a user satisfies the first node-specific selection criterion for the node only if the user: (i) accesses the digital resource in the first time interval, and (ii) accesses the digital resource a target number of times in the second time interval, and a user satisfies the second node-specific selection criterion for the node only if: (i) the user accesses the digital resource in the third time interval, and (ii) accesses the digital resource the target number of times in the fourth time interval.

In some implementations, the target number of times is zero.

In some implementations, (i) the tree model is a one-dimensional tree model, (ii) for each node in the tree model, the key for the node is parametrized by a set of parameters that define a region of a one-dimensional space, and (iii) for each parent node in the tree model, the region of the one-dimensional space defined by the key of the parent node is partitioned by regions of the one-dimensional space defined by keys of child nodes of the parent node.

In some implementations, for one or more leaf nodes of the tree model: the key for the node is parameterized by parameter t, the parameters define the region of one-dimensional space given by t, the first time interval includes t - <NUM>, the second time interval includes [t, t + W - <NUM>], where W is a predefined hyper-parameter, the third time interval includes t + W - <NUM>, and the fourth time interval includes [t - <NUM>, t + W - <NUM>].

In some implementations, generating the tree model includes: adding respective noise to the value associated with each node in the tree model.

In some implementations, processing the tree model to generate the estimate for the number of users that accessed the digital resource at least the predefined number of times within the time window includes: identifying a plurality of nodes in the tree model that each have a respective key which satisfies an identification criterion based on the time window, determining a combination of the values associated with the identified nodes, and generating the estimate for the number of users based at least in part on the combination of the values associated with the identified nodes.

In some implementations, identifying the plurality of nodes in the tree model includes: identifying that one or more leaf nodes of the tree model and one or more internal nodes of the tree model each have a respective key which satisfies the identification criterion based on the time window, and where determining the combination of the values associated with the identified nodes includes: determining a sum of the values associated with the identified nodes.

In some implementations, a user accesses the digital resource by receiving a transmission of a digital component.

In some implementations, the tree model includes a set of edges, where each edge connects a respective pair of nodes in the tree model, and where the tree model is a binary tree model.

In some implementations, the method further includes: outputting the estimate for the number of users that accessed the digital resource at least the predefined number of times within the time window.

According to a second aspect, there is provided a system including: one or more computers, and one or more storage devices communicatively coupled to the one or more computers, where the one or more storage devices store instructions that, when executed by the one or more computers, cause the one or more computers to perform the operations of the method of any preceding aspect.

According to a third aspect, there are provided one or more non-transitory computer storage media storing instructions that when executed by one or more computers cause the one or more computers to perform the operations of the method of any preceding aspect.

The system described in this specification can generate accurate and privacy preserving access frequency estimates. An access frequency estimate can refer to an estimate for a number of users that accessed a digital resource at least a threshold number of times during a time window. Access frequency estimates generated by the system can be referred to as being privacy preserving (or privacy sensitive), e.g., because they are adapted to prevent leakage of information about users. For instance, access frequency estimates generated by the system can satisfy criteria for being differentially private, e.g., such that the access frequency estimates cannot be leveraged to determine when and if individual users have accessed the digital resource.

To enable generation of privacy preserving access frequency estimates, the system can process access data for a digital resource (e.g., that identifies a respective set of users that accessed the digital resource at each of multiple time points) to generate a tree model (data structure). A tree model can refer to a hierarchical structure that includes a set of nodes and a set of edges, where each edge connects a respective "parent" node to a respective "child" node, and where each node (except for a root node) has one parent node.

The system can construct the tree model to encode the access data in a manner that enables an access frequency estimate to be generated for any time window by combining values associated with nodes in the tree model. To preserve privacy, the system can combine respective noise with the value associated with each node in the tree model, which has the effect of noising access frequency estimates generated using the tree model and thus preserving privacy. In particular, noising the access frequency estimates can preserve privacy by obfuscating information regarding individual users that might otherwise be leaked from the access frequency estimates.

The tree model can encode the access data in a manner that is tailored toward enabling the system to generate an access frequency estimate by combining the values associated with a limited number of nodes in the tree model, e.g., at most log (T) or log<NUM>(T) nodes, where T is the number of time points covered by the access data. Generating an access frequency estimate using a limited number of nodes from the tree model has the effect of limiting the amount of noise injected into the access frequency estimate, and thus increasing the accuracy of the access frequency estimate while preserving privacy. In contrast, some conventional approaches to preserving privacy, e.g., that operate without the benefit of the tree model described in this specification, can only preserve privacy at the cost of injecting significantly more noise into access frequency estimates, thus resulting in significantly lower accuracy.

The system described in this specification enables reduced consumption of computational resources, e.g., memory and computing power, by enabling access frequency estimates to be generated for any time interval by combining values associated with a limited number of nodes in a tree model. In contrast, some conventional approaches for generating access frequency estimates require storing an entire set of access data (which requires more memory than storing the tree model) and processing the entire set of access data each time an access frequency estimate is generated (which consumes significantly more computing power than generating access frequency estimates by leveraging the tree model).

This specification describes an access frequency estimation system that can generate an accurate and privacy preserving access frequency estimate, e.g., an estimate for a number of users that accessed a digital resource at least a threshold number of times (e.g., at least once) during a time window.

A digital resource can refer to any appropriate digital data that is accessible to a set of users, e.g., by way of a computer. A user can access a digital resource in any of a variety of possible ways. A few examples of digital resources and of possible ways that users can access digital resources are described next.

In some implementations, a digital resource can be a data storage location, e.g., a database. A user can access a database, e.g., through an application programming interface (API) made available by the database, e.g., to query information from the database, or to store information in the database, or both.

In some implementations, a digital resource can be an application or a webpage, e.g., which a user can access by way of a user interface made available on a user device. Accessing an application or a webpage can refer to interacting with the application or webpage.

In some implementations, a digital resource can be a computational resource, e.g., one or more processors (e.g., central processing units (CPUs) or graphics processing units (GPUs)) made available to users in a cloud computing environment. A user can access a computational resource, e.g., by providing data defining one or more computational tasks to be performed using the computational resource.

In some implementations, a digital resource can be a digital component, and a user can access a digital resource by receiving a transmission of the digital resource at a user device, e.g., from a digital component transmission system. An example of a digital component transmission system is described with reference to <FIG>.

As used throughout this document, the phrase "digital components" refers to discrete units of digital content or digital information that can include one or more of, e.g., video clips, audio clips, multimedia clips, images, text segments, or uniform resource locators (URLs). A digital component can be electronically stored in a physical memory device as a single file or in a collection of files, and digital components can take the form of video files, audio files, multimedia files, image files, or text files and include streaming video, streaming audio, social network posts, blog posts, and/or advertising information, such that an advertisement is a type of digital component. Generally, a digital component is defined by (or provided by) a single source (e.g., a digital component provider), but a digital component provided from one source could be enhanced with data from another source (e.g., weather information, real time event information, or other information obtained from another source).

The access frequency estimation system can generate a privacy-preserving access frequency estimate. Throughout this specification, an "access frequency estimate" refers to an estimate for a number of users that accessed a digital resource at least a threshold number of times (e.g., at least once) during a time window. A "privacy-preserving" access frequency estimate refers to an access frequency estimate that is adapted to prevent leakage of information about users.

To enable generation of privacy preserving access frequency estimates, the access frequency system can process access data for a digital resource (e.g., that identifies a respective set of users that accessed the digital resource at each of multiple time points) to generate a tree model, e.g., a 1D or 2D tree model. Throughout this specification, a "tree model" refers to a hierarchical data structure that includes a set of nodes and a set of edges, where each edge connects a respective "parent" node to a respective "child" node, and where each node (except for a root node) has one parent node. A "one-dimensional," or "1D," tree model refers to a tree model where each node of the tree model is parametrized by a set of parameters that define a region of a one-dimensional space. An example 1D tree model is illustrated in <FIG>. A "two-dimensional," or "2D," tree model refers to a tree model where each node of the tree model is parametrized by a set of parameters that define a region of a two-dimensional space. An example 2D tree model is illustrated in <FIG>.

The access frequency estimation system can process the 1D tree model to generate a fixed-window access frequency estimate. In the fixed-window implementation of the access frequency estimation system, a user of the system can be restricted to querying access frequency estimates for time intervals of a fixed length, e.g., including a fixed number of time points. The access frequency estimation system can process the 2D tree model to generate a time-window access frequency estimate. In the time-window implementation of the access frequency estimation system, a user of the system can query access frequency estimates for time intervals of any appropriate length, e.g., a first interval having two time points, and a second interval having five time points.

To preserve privacy, the access frequency estimation system can combine respective noise with the value associated with each node in the tree model (e.g., 1D or 2D tree model), which has the effect of noising access frequency estimates generated using the tree model and thus preserving privacy. The access frequency estimation system can process the tree model to generate an estimate for the number of users that accessed the digital resource at least the predefined number of times within the time window in a privacy-sensitive manner. These and other features are described in more detail below.

<FIG> is a block diagram of an example access frequency estimation system <NUM>. The access frequency estimation system <NUM> is an example of a system implemented as computer programs on one or more computers in one or more locations in which the systems, components, and techniques described below are implemented.

The system <NUM> is configured to obtain access data <NUM> for a digital resource and process the access data <NUM> to generate an estimate for a number of users <NUM> that accessed the digital resource at least a threshold number of times during a time window. The access data <NUM> for a digital resource can specify a respective set of users that accessed the digital resource at each time point in a sequence of time points. (Each user can be associated, e.g., with a unique alphanumeric identifier). For each time point in the sequence of time points, the access data <NUM> can include data that identifies a set of users that accessed the digital resource at the time point. The access data <NUM> can include any appropriate number of time points, e.g., <NUM> time points, <NUM>,<NUM> time points, <NUM>,<NUM> time points, or any other appropriate number of time points. The set of users that accessed the digital resource at a time point can include any appropriate number of users, e.g., <NUM> users, <NUM>,<NUM> users, <NUM>,<NUM> users, or any other appropriate number of users. The system <NUM> can obtain the access data <NUM> in any appropriate manner. For example, the system <NUM> can receive the access data <NUM>, e.g., through an API made available by the system <NUM>.

As described above, the access frequency estimation system <NUM> can process the access data <NUM> to generate the estimate for the number of users <NUM> that accessed the digital resource at least the threshold number of times during the time window. The access frequency estimation system <NUM> can generate the estimate of the number of users <NUM> using: (i) a tree model engine <NUM>, and (ii) an estimator engine <NUM>, each of which is described in more detail next.

The tree model engine <NUM> can be configured to process the access data <NUM> to generate data defining a tree model <NUM>. As described above, the tree model <NUM> can be a hierarchical data structure that includes a set of nodes and a set of edges, where each edge connects a respective pair of nodes in the tree model. Each edge can connect a "parent" node to a respective "child" node in the tree model, and each node (except for a root node) in the tree model can have one parent node. The set of nodes of the tree model can further include a set of leaf nodes, e.g., nodes that are each connected by an edge to a parent node, but not connected to any child nodes. In some cases, the tree model can be a binary tree model, e.g., a tree model where each non-leaf node is connected by edges to two child nodes. In some cases, the tree model can be a quadtree model, e.g., a tree model where each non-leaf node is connected by edges to four child nodes. In some cases, the tree model <NUM> can be a 1D tree model or a 2D tree model. The access frequency estimation system <NUM> can process the 1D tree model to generate a fixed-window access frequency estimate. The access frequency estimation system <NUM> can process the 2D tree model to generate a time-window access frequency estimate. Example tree models are described in more detail below with reference to <FIG> and <FIG>.

As a particular example, referring to <FIG>, the tree model <NUM> can be a 1D tree model that includes, e.g., a pair of nodes 212a, 212b that are connected by an edge <NUM>, where the node 212b is a parent node, and the node 212a is a child node of the parent node 212b. The parent node 212b is also a root node, e.g., a node that is connected by edges to one or more child nodes, but not connected to any parent node. The set of nodes in the tree model <NUM> can further include a set of leaf nodes <NUM>, e.g., nodes that are each connected by an edge to a parent node, but not connected to any child nodes. The other nodes in the tree model <NUM> that are not included in the set of leaf nodes <NUM> can be referred to as internal nodes <NUM> in the tree model <NUM>. As a particular example, if the access data includes a sequence of time points that includes, e.g., eight time points, the tree model engine can generate the tree model <NUM> illustrated in <FIG> that includes eight leaf nodes <NUM>, one for each time point included in the access data.

Turning back to <FIG>, each node in the tree model <NUM> is associated with a "key" that specifies multiple time intervals in a time span. Generally, the key can specify any appropriate number of time intervals, e.g., three time intervals or four time intervals. Each node in the tree model <NUM> can be associated with a "value" that is based on a respective number of users that satisfy a node-specific selection criterion based on the time intervals specified by the key for the node. Generally, the node-specific selection criterion can be any appropriate criterion. In some cases, the node-specific selection criterion can characterize, e.g., a number of times that a user accesses the digital resource in each of the time intervals specified by the key. Examples of node-specific selection criteria are described in more detail below.

In some cases, as part of generating the tree model <NUM>, the tree model engine <NUM> can add respective noise to the value associated with each node in the tree model <NUM>. For example, the tree model engine <NUM> can sample a noise value from a probability distribution and add (or otherwise combine) the noise value to the value associated with a node in the tree model <NUM>. The distribution can be, e.g., a Gaussian distribution, a Laplace distribution, or any other appropriate distribution. In some cases, the tree model engine <NUM> can sample a new (e.g., different) noise value for each of the nodes included in the tree model <NUM>. Example tree models are described in more detail below with reference to <FIG> and <FIG>.

As described above, the tree model engine <NUM> is configured to receive the access data <NUM> and process the access data <NUM> to generate the tree model <NUM>. The access frequency estimation system <NUM> can receive a request <NUM> to estimate the number of users <NUM> that accessed the digital resource at least a predefined number of times within a time window, e.g., at least <NUM> time, <NUM> times, or any other appropriate number of times. The system <NUM> can receive the request <NUM> in any appropriate manner. For example, the system <NUM> can receive the request <NUM> from a user of the system <NUM>, e.g., through an API made available by the system <NUM>.

In response to the request, the system <NUM> can use the estimator engine <NUM> to process the tree model <NUM> to generate the estimate for the number of users <NUM> that accessed the digital resource at least the predefined number of times within the time window. For example, the estimator <NUM> can process the tree model <NUM> to identify multiple nodes in the tree model <NUM> (e.g., including one or more leaf nodes and/or one or more internal nodes) that each have a respective key which satisfies an identification criterion based on the time window. The identification criterion can be any appropriate identification criterion. In some cases, the estimator <NUM> can identify that one or more leaf nodes and one or more internal nodes in the tree model <NUM> each have a respective key that satisfies the identification criterion based on the time window. For example, with reference to <FIG>, the estimator can identify that the leaf node 212c and the internal node 212d each have a respective key that satisfies the identification criterion based on the time window.

Turning back to <FIG>, the estimator <NUM> can determine a combination of the values associated with the identified nodes, e.g., as a sum of the values associated with the identified nodes, or in any other appropriate manner. Then, the estimator <NUM> can generate the estimate for the number of users <NUM> based at least in part on the combination of the values associated with the identified nodes. In some cases, the access frequency estimation system <NUM> can output the estimate for the number of users <NUM> that accessed the digital resource at least the predefined number of times within the time window, e.g., to a user of the system <NUM> through the API made available by the system <NUM>.

In this manner, the access frequency estimation system <NUM> can generate the estimate for the number of users <NUM> (e.g., the access frequency estimate) by combining the values associated with a limited number of nodes in the tree model <NUM>, e.g., at most log (T) or log<NUM>(T) nodes, where T is the number of time points included in the access data <NUM>. Generating the access frequency estimate <NUM> using a limited number of nodes from the tree model <NUM> has the effect of limiting the amount of noise injected into the access frequency estimate <NUM>, and thus increasing the accuracy of the access frequency estimate <NUM> while preserving privacy.

The access frequency estimation system <NUM> can use the access frequency estimate <NUM> in a variety of possible ways, a few examples of which are described next.

In some implementations, the system <NUM> can generate a notification indicating an access frequency estimate, and provide the notification, e.g., for display by way of a user interface.

In some implementations, the system <NUM> can use an access frequency estimate to determine whether a cyberattack, e.g., a distributed denial-of-service (DDoS) attack, has occurred. For instance, the system can determine that a cyberattack has occurred if at least a threshold number of users have accessed the digital resource at least a threshold number of times within a time window.

In some implementations, the system <NUM> can modify conditions under which the digital resource is available to users based on an access frequency estimate. For instance, if users access the digital resource by receiving transmissions of a digital component, the system can modify distribution parameters controlling when the digital resource is transmitted to users based on an access frequency estimate, e.g., to cause the digital component to be transmitted to more or fewer users.

In some implementations, the system <NUM> can modify a digital resource based on an access frequency estimate. For instance, if the digital resource is a computational resource, then the system can increase or decrease the computing power available by way of the computational resource in response to determining that an access frequency estimate satisfies a threshold.

Example tree models <NUM> are described in more detail below with reference to <FIG> and <FIG>.

<FIG> illustrates an example one-dimensional (1D) tree model <NUM> generated by an access frequency estimation system, e.g., the system <NUM> in <FIG>. The tree model <NUM> illustrated in <FIG> is an example of a one-dimensional tree model. The access frequency estimation system can process the 1D tree model <NUM> to generate a fixed-window access frequency estimate.

As described above, the access frequency estimation system can generate the tree model <NUM> by processing access data for a digital resource. The access data can include, for each time point in a sequence of time points, data identifying a set of users that accessed the digital resource at the time point. <FIG> provides a simplified example of the tree model <NUM> that is generated based on access data that includes a sequence of eight time points. Generally, the access frequency estimation system can generate the tree model <NUM> by processing access data that includes any appropriate number of time points in the sequence of time points.

The tree model <NUM> includes a set of nodes, e.g., multiple leaf nodes <NUM> and multiple internal nodes <NUM>, and a set of edges, where each edge connects a pair of nodes. Each node in the tree model <NUM> is associated with a key that specifies multiple time intervals in a time span. In <FIG>, an example key for each node is illustrated as a pair of numbers in square brackets. For example, the node 212a includes the [<NUM>, <NUM>] key. Similarly, the root node 212b includes the [<NUM>,<NUM>] key.

For each node in the one-dimensional tree model <NUM>, the key for the node can be parametrized by a set of parameters that define a region of a one-dimensional space <NUM>. For example, the key for each leaf node <NUM> in the one-dimensional tree model <NUM> can be parametrized by parameter t, and the parameters for the leaf nodes <NUM> can define a region of one-dimensional space given by t. For each parent node in the tree model <NUM>, the region of the one-dimensional space defined by the key of the parent node can be partitioned by regions of the one-dimensional space defined by keys of child nodes of the parent node. For example, as illustrated in <FIG>, the region of the one-dimensional space defined by the key [<NUM>, <NUM>] of the parent node 212a is partitioned by the region of space defined by the key [<NUM>, <NUM>] of the child node 212e and the region of space defined by the key [<NUM>, <NUM>] of the child node 212d.

For one or more nodes in tree model <NUM>, the key for the node can specify at least a first time interval, a second time interval, a third time interval, and a fourth time interval. In some cases, the first time interval, the second time interval, the third time interval, and the fourth time interval can be each different. As a particular example, for leaf nodes, the first time interval specified by each key can include t - <NUM>. The second time interval specified by each key can include [t,t + W - <NUM>], where W is a predefined hyper-parameter of the access frequency estimation system. The third time interval specified by each key can include t + W - <NUM>. The fourth time interval specified by each key can include [t - <NUM>, t + W - <NUM>]. In this implementation (e.g., the fixed-window reach implementation) of the access frequency estimation system, a user of the system can be restricted to querying access frequency estimates for time intervals of length W. Throughout this specification, in some cases, a single number can define a time interval, e.g., t - <NUM> can define [t - <NUM>, t - <NUM>] time interval.

As described above, each node in the tree model <NUM> can be associated with a value that is based on a respective number of users that satisfy a node-specific selection criterion based on the time intervals specified by the key for the node. For each leaf node in the one-dimensional tree model <NUM> illustrated in <FIG>, the value associated with the node can be based on a difference between: (i) a number of users that satisfy a first node-specific selection criterion based on the time intervals specified by the key for the node, and (ii) a number of users that satisfy a second node-specific selection criterion based on the time intervals specified by the key for the node.

For one or more leaf nodes <NUM> in the tree model <NUM>, a user can satisfy the first node-specific selection criterion for the node only if the user: (i) accesses the digital resource in the first time interval, and (ii) accesses the digital resource a target number of times in the second time interval. A user can satisfy the second node-specific selection criterion for the node only if: (i) the user accesses the digital resource in the third time interval, and (ii) the user accesses the digital resource the target number of times in the fourth time interval. In some cases, the target number of times can be, e.g., zero. Each time the system generates the value based on the number of users for a leaf node in the tree model, e.g., as described above, the system can add this value to the parent node of the leaf node, and to any other ancestor nodes of the leaf node in the tree model. In this manner, the system can use the values determined for the leaf nodes in the tree model to determine the values for each other (e.g., non-leaf) node in the tree model.

An example two dimensional tree model is described in more detail below with reference to <FIG>.

<FIG> illustrates an example two-dimensional (2D) tree model <NUM> generated by an access frequency estimation system, e.g., the access frequency estimation system <NUM> in <FIG>. The access frequency estimation system can process the 2D tree model <NUM> to generate a time-window access frequency estimate.

As described above, the access frequency estimation system can generate the tree model <NUM> by processing access data for a digital resource. The access data can include, for each time point in a sequence of time points, data identifying a set of users that accessed the digital resource at the time point. Similarly to <FIG> above, <FIG> provides a simplified example of the tree model <NUM> that is generated based on access data that includes a sequence of eight time points. Generally, the access frequency estimation system can generate the tree model <NUM> by processing access data that includes any appropriate number of time points in the sequence of time points. In <FIG>, some nodes of the tree model <NUM> are omitted for clarity.

For each node in the two-dimensional tree model <NUM>, the key for the node is parameterized by a set of parameters that define a region of two-dimensional space <NUM>. For example, the key for the node can be parameterized by respective parameters a, b, c, d. The parameters can define the region of the two-dimensional space given by: [a,b] × [c,d]. For each parent node in the tree model <NUM>, the region of the two-dimensional space defined by the key of the parent node is partitioned by regions of the two-dimensional space defined by keys of child nodes of the parent node. For example, as illustrated in <FIG>, for the parent node <NUM>, the region of space <NUM> defined by the key of the parent node <NUM> is partitioned by the region of space <NUM>-A of the child node <NUM>-A, the region of space <NUM>-B of the child node <NUM>-B, the region of space <NUM>-C of the child node <NUM>-C, and the region of space <NUM>-D of the child node <NUM>-D. Similarly, for the parent node <NUM>-D, the region of space <NUM> defined by the key of the parent node <NUM>-D is partitioned by the region of space <NUM>-A of the child node <NUM>-A, the region of space <NUM>-B of the child node <NUM>-B, the region of space <NUM>-C of the child node <NUM>-C, and the region of space <NUM>-D of the child node <NUM>-D. For one or more nodes in the two-dimensional tree model <NUM>, the key for the node specifies at least a first time interval, a second time interval, and a third time interval. In some cases, the first time interval, the second time interval, and the third time interval are each different. As a particular example, the first time interval specified by each key can include [a - <NUM>, b - <NUM>]. The second time interval specified by each key can include [T + <NUM> - d,T + <NUM> - c], where T is a last time point in the sequence of time points. The third time interval specified by each key can include [b,T + <NUM> - d].

As described above, each node in the two-dimensional tree model <NUM> can be associated with a value that is based on a respective number of users that satisfy a node-specific selection criterion based on the time intervals specified by the key for the node. For each of one or more nodes in the two-dimensional tree model <NUM> illustrated in <FIG>, a user can satisfy the node-specific selection criterion for the node only if: (i) the user accesses the digital resource at least once in the first time interval and at least once in the second time interval, and (ii) the user accesses the digital resource a target number of times in the third time interval. In some cases, for one or more nodes in the two-dimensional tree model <NUM>, the target number of times can be, e.g., zero.

An example process for digital resource access frequency estimation performed by the access frequency estimation system is described in more detail below with reference to <FIG>.

<FIG> is a flow diagram of an example process for digital resource access frequency estimation. For convenience, the process <NUM> is described as being performed by a system of one or more computers located in one or more locations. For example, an access frequency estimation system, e.g., the access frequency estimation system <NUM> of <FIG>, appropriately programmed in accordance with this specification, can perform the process <NUM>.

The system obtains access data for a digital resource (<NUM>). The access data can include, for each time point in a sequence of time points, data identifying a set of users that accessed the digital resource at the time point. In some cases, a user can access the digital resource by receiving a transmission of a digital component.

The system processes the access data to generate data defining a tree model (<NUM>). The tree model can be a binary tree model. The tree model can include a set of nodes, and each node in the set of nodes can be associated with: (i) a key that specifies multiple time intervals in the time span, and (ii) a value that is based on a respective number of users that satisfy a node-specific selection criterion based on the time intervals specified by the key for the node. In some cases, the tree model can further include a set of edges, where each edge connects a respective pair of nodes in the tree model. In some cases, the system can generate the tree model by adding respective noise to the value associated with each node in the tree model.

In some cases, for one or more nodes in the tree model, the key for the node can specify at least a first time interval, a second time interval, and a third time interval that are each different. In some cases, for one or more nodes in the tree model, a user can satisfy the node-specific selection criterion for the node only if: (i) the user accesses the digital resource at least once in the first time interval and at least once in the second time interval, and (ii) the user accesses the digital resource a target number of times in the third time interval. In some cases, for one or more nodes in the tree model, the target number of times can be zero.

In some implementations, the tree model can be a two-dimensional tree model. For each node in the tree model, the key for the node can be parameterized by a set of parameters that define a region of two-dimensional space. For example, for each parent node in the tree model: the region of the two-dimensional space defined by the key of the parent node is partitioned by regions of the two-dimensional space defined by keys of child nodes of the parent node. As a particular example, the key for the node can be parameterized by respective parameters a, b, c, d. The parameters define the region of two-dimensional space given by: [a,b] × [c,d]. The first time interval can include [a - <NUM>, b - <NUM>]. The second time interval can include [T + <NUM> - d,T + <NUM> - c], where T is a last time point in the sequence of time points. The third time interval can include [b,T + <NUM> - d].

In some implementations, for each node in the tree model, the value associated with the node can be based on a difference between: (i) a number of users that satisfy a first node-specific selection criterion based on the time intervals specified by the key for the node, and (ii) a number of users that satisfy a second node-specific selection criterion based on the time intervals specified by the key for the node. In such cases, for one or more nodes in the tree model, the key for the node can specify at least a first time interval, a second time interval, a third time interval, and a fourth time interval that are each different. For one or more leaf nodes in the tree model: a user can satisfy the first node-specific selection criterion for the node only if the user: (i) accesses the digital resource in the first time interval, and (ii) accesses the digital resource a target number of times in the second time interval, and a user can satisfy the second node-specific selection criterion for the node only if: (i) the user accesses the digital resource in the third time interval, and (ii) accesses the digital resource the target number of times in the fourth time interval. In some cases, the target number of times can be zero.

In some cases, the tree model can be a one-dimensional tree model. In such cases, for each node in the tree model, the key for the node can be parametrized by a set of parameters that define a region of a one-dimensional space. For example, for each parent node in the tree model: the region of the one-dimensional space defined by the key of the parent node is partitioned by regions of the one-dimensional space defined by keys of child nodes of the parent node. As a particular example, for one or more leaf nodes of the tree model: the key for the node can be parameterized by parameter t. The parameters can define the region of one-dimensional space given by t. The first time interval can include t - <NUM>. The second time interval can include [t,t + W - <NUM>], where W is a predefined hyper-parameter. The third time interval can include t + W - <NUM>. The fourth time interval can include [t - <NUM>, t + W - <NUM>].

The system receives a request to determine a number of users that accessed the digital resource at least a predefined number of times within a time window (<NUM>).

In response to the request, the system processes the tree model to generate an estimate for the number of users that accessed the digital resource at least the predefined number of times within the time window (<NUM>). The system can process the tree model by identifying multiple nodes in the tree model that each have a respective key which satisfies an identification criterion based on the time window. For example, the system can identify that one or more leaf nodes of the tree model and one or more internal nodes of the tree model each have a respective key which satisfies the identification criterion based on the time window.

As a particular example, the system can process the one-dimensional (1D) tree model to identify nodes having keys which satisfy the identification criterion according to "Differential Privacy Fixed Window Reach Query" algorithm outlined in more detail below, where Si is a set of users that accessed the digital resource at time step i, Si+W-<NUM> is a set of users that accessed the digital resource at time step i + W - <NUM>, W is a time window length, n[a,b] is the value of the node associated with interval [a,b], and lsbit(i) denotes the index of the least significant bit of i. In particular, the input to the process is a time index i, and the output is an estimate of the number of users that accessed the digital resources at least once in the time interval [i,i + W - <NUM>]. It will be appreciated that the Differential Privacy Fixed Window Reach Query requires combining at most log T nodes in the tree model, where T is the overall time range covered by the access data.

As another particular example, the system can process the two-dimensional (2D) tree model to identify nodes having keys which satisfy the identification criterion according to "Differential Privacy Time Window Reach Query" algorithm outlined in more detail below, where Si is a set of users that accessed the digital resource at time step i, Sj is a set of users that accessed the digital resource at time step j, T is a total number of time steps, d is the total number of users, n is a number of users, lsbit(i) denotes the index of the least significant bit of i, and lsbit(j) denotes the index of the least significant bit of j. In particular, the input to the process is a time range [i,j], and the output of the process is an estimate for the number of users that accessed the digital resource at least once in the time interval [i,j]. It will be appreciated that the Differential Privacy Time Window Reach Query algorithm requires combining at most log<NUM> T nodes, where T is the overall time range covered by the access data.

The system can determine a combination of the values associated with the identified nodes, e.g., as a sum of the values associated with the identified nodes. Then, the system can generate the estimate for the number of users based at least in part on the combination of the values associated with the identified nodes. In some cases, the system can output the estimate for the number of users that accessed the digital resource at least the predefined number of times within the time window.

An example environment in which digital components are distributed is described in more detail next.

<FIG> is a block diagram of an example environment <NUM> in which digital components are transmitted for presentation with electronic documents. This specification describes techniques that can be used for privacy sensitive estimation of a number of users that received at least a threshold number of transmissions of a digital component within a time window.

The environment <NUM> can include an access frequency estimation system <NUM> (e.g., the access frequency estimation system <NUM> described above with reference to <FIG>). The access frequency estimation system <NUM> can obtain access data for a digital resource, where the access data includes, for each time point in a sequence of time points, data identifying a set of users that accessed the digital resource (e.g., the digital component) at the time point. The system <NUM> can process the access data to perform access frequency estimation, e.g., generate an estimate for the number of users that accessed the digital resource (e.g., the digital component) at least the predefined number of times within a time window. The system <NUM> can use the estimate in a variety of different ways. For example, if users access the digital resource by receiving transmissions of a digital component, the system <NUM> can modify distribution parameters controlling when the digital resource is transmitted to users based on an access frequency estimate, e.g., to cause the digital component to be transmitted to more or fewer users.

The example environment <NUM> includes a network <NUM>, such as a local area network (LAN), a wide area network (WAN), the Internet, or a combination thereof. The network <NUM> connects electronic document servers <NUM>, client devices <NUM>, digital component servers <NUM>, and a digital component distribution system <NUM> (also referred to as a "distribution system" <NUM>). The example environment <NUM> may include many different electronic document servers <NUM>, client devices <NUM>, and digital component servers <NUM>.

A client device <NUM> is an electronic device that is capable of requesting and receiving resources over the network <NUM>. Example client devices <NUM> include personal computers, mobile communication devices (e.g., mobile phones), and other devices that can send and receive data over the network <NUM>. A client device <NUM> typically includes a user application, such as a web browser, to facilitate the sending and receiving of data over the network <NUM>, but native applications executed by the client device <NUM> can also facilitate the sending and receiving of data over the network <NUM>.

An electronic document is data that presents a set of content at a client device <NUM>. Examples of electronic documents include webpages, word processing documents, portable document format (PDF) documents, images, videos, search results pages, and feed sources. Native applications (e.g., "apps"), such as applications installed on mobile, tablet, or desktop computing devices are also examples of electronic documents. Electronic documents can be provided to client devices <NUM> by electronic document servers <NUM> ("Electronic Doc Servers"). For example, the electronic document servers <NUM> can include servers that host publisher websites. In this example, the client device <NUM> can initiate a request for a given publisher webpage, and the electronic server <NUM> that hosts the given publisher webpage can respond to the request by sending machine executable instructions that initiate presentation of the given webpage at the client device <NUM>.

In another example, the electronic document servers <NUM> can include app servers from which client devices <NUM> can download apps. In this example, the client device <NUM> can download files required to install an app at the client device <NUM>, and then execute the downloaded app locally.

Electronic documents can include a variety of content. For example, an electronic document can include static content (e.g., text or other specified content) that is within the electronic document itself and/or does not change over time. Electronic documents can also include dynamic content that may change over time or on a per-request basis. For example, a publisher of a given electronic document can maintain a data source that is used to populate portions of the electronic document. In this example, the given electronic document can include one or more tags or scripts that cause the client device <NUM> to request content from the data source when the given electronic document is processed (e.g., rendered or executed) by a client device <NUM>. The client device <NUM> integrates the content obtained from the data source into the given electronic document to create a composite electronic document including the content obtained from the data source.

In some situations, a given electronic document can include one or more digital component tags or digital component scripts that reference the digital component distribution system <NUM>. In these situations, the digital component tags or digital component scripts are executed by the client device <NUM> when the given electronic document is processed by the client device <NUM>. Execution of the digital component tags or digital component scripts configures the client device <NUM> to generate a request for one or more digital components <NUM> (referred to as a "component request"), which is transmitted over the network <NUM> to the digital component distribution system <NUM>. For example, a digital component tag or digital component script can enable the client device <NUM> to generate a packetized data request including a header and payload data. The component request <NUM> can include event data specifying features such as a name (or network location) of a server from which the digital component is being requested, a name (or network location) of the requesting device (e.g., the client device <NUM>), and/or information that the digital component distribution system <NUM> can use to select one or more digital components provided in response to the request. The component request <NUM> is transmitted, by the client device <NUM>, over the network <NUM> (e.g., a telecommunications network) to a server of the digital component distribution system <NUM>.

The component request <NUM> can include event data specifying other event features, such as the electronic document being requested and characteristics of locations of the electronic document at which digital component can be presented. For example, event data specifying a reference (e.g., URL) to an electronic document (e.g., webpage) in which the digital component will be presented, available locations of the electronic documents that are available to present digital components, sizes of the available locations, and/or media types that are eligible for presentation in the locations can be provided to the digital component distribution system <NUM>. Similarly, event data specifying keywords associated with the electronic document ("document keywords") or entities (e.g., people, places, or things) that are referenced by the electronic document can also be included in the component request <NUM> (e.g., as payload data) and provided to the digital component distribution system <NUM> to facilitate identification of digital components that are eligible for presentation with the electronic document. The event data can also include a search query that was submitted from the client device <NUM> to obtain a search results page, and/or data specifying search results and/or textual, audible, or other visual content that is included in the search results.

Component requests <NUM> can also include event data related to other information, such as information that a user of the client device has provided, geographic information indicating a state or region from which the component request was submitted, or other information that provides context for the environment in which the digital component will be displayed (e.g., a time of day of the component request, a day of the week of the component request, a type of device at which the digital component will be displayed, such as a mobile device or tablet device). Component requests <NUM> can be transmitted, for example, over a packetized network, and the component requests <NUM> themselves can be formatted as packetized data having a header and payload data. The header can specify a destination of the packet and the payload data can include any of the information discussed above.

The component distribution system <NUM> chooses digital components that will be presented with the given electronic document in response to receiving the component request <NUM> and/or using information included in the component request <NUM>. In some implementations, a digital component is selected (using the techniques described herein) in less than a second to avoid errors that could be caused by delayed selection of the digital component. For example, delays in providing digital components in response to a component request <NUM> can result in page load errors at the client device <NUM> or cause portions of the electronic document to remain unpopulated even after other portions of the electronic document are presented at the client device <NUM>. Also, as the delay in providing the digital component to the client device <NUM> increases, it is more likely that the electronic document will no longer be presented at the client device <NUM> when the digital component is delivered to the client device <NUM>, thereby negatively impacting a user's experience with the electronic document. Further, delays in providing the digital component can result in a failed delivery of the digital component, for example, if the electronic document is no longer presented at the client device <NUM> when the digital component is provided.

In some implementations, the digital component distribution system <NUM> is implemented in a distributed computing system that includes, for example, a server and a set of multiple computing devices <NUM> that are interconnected and identify and distribute digital components in response to requests <NUM>. The set of multiple computing devices <NUM> operate together to identify a set of digital components that are eligible to be presented in the electronic document from a corpus of millions of available digital components (DC1-x). The millions of available digital components can be indexed, for example, in a digital component database <NUM>. Each digital component index entry can reference the corresponding digital component and/or include distribution parameters (DP1-DPx) that contribute to (e.g., condition or limit) the distribution/transmission of the corresponding digital component. For example, the distribution parameters can contribute to the transmission of a digital component by requiring that a component request include at least one criterion that matches (e.g., either exactly or with some pre-specified level of similarity) one of the distribution parameters of the digital component.

In some implementations, the distribution parameters for a particular digital component can include distribution keywords that must be matched (e.g., by electronic documents, document keywords, or terms specified in the component request <NUM>) in order for the digital component to be eligible for presentation. In other words, the distribution parameters are used to trigger distribution (e.g., transmission) of the digital components over the network <NUM>. The distribution parameters can also require that the component request <NUM> include information specifying a particular geographic region (e.g., country or state) and/or information specifying that the component request <NUM> originated at a particular type of client device (e.g., mobile device or tablet device) in order for the digital component to be eligible for presentation.

The distribution parameters can also specify an eligibility value (e.g., ranking score, bid, or some other specified value) that is used for evaluating the eligibility of the digital component for distribution/transmission (e.g., among other available digital components), for example, by the component evaluation process. In some situations, the eligibility value can specify a maximum amount of compensation that a provider of the digital component is willing to submit in response to the transmission of the digital component (e.g., for each instance of specific events attributed to the presentation of the digital component, such as user interaction with the digital component).

The identification of the eligible digital component can be segmented into multiple tasks 517a-517c that are then assigned among computing devices within the set of multiple computing devices <NUM>. For example, different computing devices in the set <NUM> can each analyze a different portion of the digital component database <NUM> to identify various digital components having distribution parameters that match information included in the component request <NUM>. In some implementations, each given computing device in the set <NUM> can analyze a different data dimension (or set of dimensions) and pass (e.g., transmit) results (Res <NUM>-Res <NUM>) 518a-518c of the analysis back to the digital component distribution system <NUM>. For example, the results 518a-518c provided by each of the computing devices in the set <NUM> may identify a subset of digital components that are eligible for distribution in response to the component request and/or a subset of the digital components that have certain distribution parameters. The identification of the subset of digital components can include, for example, comparing the event data to the distribution parameters, and identifying the subset of digital components having distribution parameters that match at least some features of the event data.

The digital component distribution system <NUM> aggregates the results 518a-518c received from the set of multiple computing devices <NUM> and uses information associated with the aggregated results to: (i) select one or more digital components that will be provided in response to the request <NUM>, and (ii) determine transmission requirements for the one or more digital components. For example, the digital component distribution system <NUM> can select a set of winning digital components (one or more digital components) based on the outcome of one or more component evaluation processes. In turn, the digital component distribution system <NUM> can generate and transmit, over the network <NUM>, reply data <NUM> (e.g., digital data representing a reply) that enables the client device <NUM> to integrate the set of winning digital components into the given electronic document, such that the set of winning digital components and the content of the electronic document are presented together at a display of the client device <NUM>.

In some implementations, the client device <NUM> executes instructions included in the reply data <NUM>, which configures and enables the client device <NUM> to obtain the set of winning digital components from one or more digital component servers. For example, the instructions in the reply data <NUM> can include a network location (e.g., a Uniform Resource Locator (URL)) and a script that causes the client device <NUM> to transmit a server request (SR) <NUM> to the digital component server <NUM> to obtain a given winning digital component from the digital component server <NUM>. In response to the request, the digital component server <NUM> will identify the given winning digital component specified in the server request <NUM> (e.g., within a database storing multiple digital components) and transmit, to the client device <NUM>, digital component data (DC Data) <NUM> that presents the given winning digital component in the electronic document at the client device <NUM>.

To facilitate searching of electronic documents, the environment <NUM> can include a search system <NUM> that identifies the electronic documents by crawling and indexing the electronic documents (e.g., indexed based on the crawled content of the electronic documents). Data about the electronic documents can be indexed based on the electronic document with which the data are associated. The indexed and, optionally, cached copies of the electronic documents are stored in a search index <NUM> (e.g., hardware memory device(s)). Data that are associated with an electronic document is data that represents content included in the electronic document and/or metadata for the electronic document.

Client devices <NUM> can submit search queries to the search system <NUM> over the network <NUM>. In response, the search system <NUM> accesses the search index <NUM> to identify electronic documents that are relevant to the search query. The search system <NUM> identifies the electronic documents in the form of search results and returns the search results to the client device <NUM> in a search results page. A search result is data generated by the search system <NUM> that identifies an electronic document that is responsive (e.g., relevant) to a particular search query, and includes an active link (e.g., hypertext link) that causes a client device to request data from a specified network location (e.g., URL) in response to user interaction with the search result. An example search result can include a web page title, a snippet of text or a portion of an image extracted from the web page, and the URL of the web page. Another example search result can include a title of a downloadable application, a snippet of text describing the downloadable application, an image depicting a user interface of the downloadable application, and/or a URL to a location from which the application can be downloaded to the client device <NUM>. In some situations, the search system <NUM> can be part of, or interact with, an application store (or an online portal) from which applications can be downloaded for install at a client device <NUM> in order to present information about downloadable applications that are relevant to a submitted search query. Like other electronic documents, search results pages can include one or more slots in which digital components (e.g., advertisements, video clips, audio clips, images, or other digital components) can be presented.

To select a digital component to be transmitted in response to a component request, the distribution system <NUM> may identify a set of digital components that are eligible to be transmitted in response to the component request. The distribution system <NUM> may then select one or more of the eligible digital components to be transmitted through, e.g., an auction procedure. In some implementations, the distribution system <NUM> performs an auction procedure by ranking the eligible digital components in accordance with their respective eligibility values, and selecting one or more highest-ranked digital components to be transmitted in response to the component request.

For example, the distribution system <NUM> may identify digital components A, B, and C as eligible to be transmitted in response to a component request. In this example, digital component A has an eligibility value of <NUM>, digital component B has an eligibility value of <NUM>, and digital component C has an eligibility value of <NUM>, where the eligibility values of the digital components represent bids associated with the digital components. The distribution system <NUM> may rank (e.g., in descending order) the digital components in accordance with their respective eligibility values as: C, A, B. Finally, the distribution system <NUM> may select the highest ranked digital component C for transmission in response to the component request
After selecting a digital component to be transmitted in response to a digital component request, the distribution system <NUM> determines a transmission requirement for the selected digital component. A transmission requirement specifies an action to be performed by the provider of a digital component in response to a transmission of the digital component. For example, the transmission requirement may specify that the provider of the digital component submit an amount of compensation in response to the transmission of the digital component. In some cases, the amount of compensation specifies an amount to be submitted for each instance of specific events attributed to the presentation of the digital component (e.g., user interactions with the digital component).

The distribution system <NUM> may determine the transmission requirement of the selected digital component based on the eligibility value of the selected digital component and/or the eligibility values of the other digital components that were determined as eligible to be transmitted in response to the component request. For example, the distribution system <NUM> may identify digital components A, B, and C as eligible for transmission in response to a digital component request, where A, B, and C have respective eligibility values of <NUM>, <NUM>, and <NUM>. The distribution system <NUM> may select digital component C for transmission (since it has the highest eligibility value), and may determine the transmission requirement for digital component C to be the next highest eligibility value from amongst the eligibility values of the eligible digital components. In this example, next highest eligibility value is $<NUM> (i.e., the eligibility value of digital component A), and therefore the distribution system <NUM> may determine the transmission requirement of digital component C to be $<NUM>.

As described above, the distribution system <NUM> may identify a set of digital components that are eligible to be transmitted for presentation in an electronic document in response to a digital component request based on distribution parameters corresponding to each digital component. In some cases, the distribution parameters corresponding to a digital component may include a keyword cluster (i.e., a set of multiple keywords). The distribution system <NUM> may determine that one or more keywords from the keyword cluster must be matched (e.g., by electronic documents, document keywords, or terms specified in a digital component request) in order for the digital component to be eligible for transmission.

For example, the distribution system <NUM> may receive a digital component request which includes a specific keyword. In this example, the distribution system <NUM> may determine that a particular digital component with distribution parameters specifying a keyword cluster is eligible for transmission in response to the digital component request only if the specific keyword is included in the keyword cluster.

In some implementations, the distribution system <NUM> enables providers of digital components to set distribution parameters specifying keyword clusters from a predetermined set of keyword clusters. The keyword clusters output by the clustering system <NUM> may define a grouping of keywords into semantically related keyword clusters. For example, a keyword cluster can define an assignment of the keywords "shoes", "shoe", "footwear", "boots", "cleats", "heels", "slippers", "sneakers", and the like, to the same cluster.

<FIG> is a block diagram of an example computer system <NUM> that can be used to perform operations described above. The system <NUM> includes a processor <NUM>, a memory <NUM>, a storage device <NUM>, and an input/output device <NUM>. Each of the components <NUM>, <NUM>, <NUM>, and <NUM> can be interconnected, for example, using a system bus <NUM>. The processor <NUM> is capable of processing instructions for execution within the system <NUM>. In one implementation, the processor <NUM> is a single-threaded processor. In another implementation, the processor <NUM> is a multi-threaded processor. The processor <NUM> is capable of processing instructions stored in the memory <NUM> or on the storage device <NUM>.

In one implementation, the input/output device <NUM> can include one or more network interface devices, e.g., an Ethernet card, a serial communication device, e.g., and RS-<NUM> port, and/or a wireless interface device, e.g., and <NUM> card. In another implementation, the input/output device can include driver devices configured to receive input data and send output data to other input/output devices, e.g., keyboard, printer and display devices <NUM>.

Machine learning models can be implemented and deployed using a machine learning framework, e.g., a TensorFlow framework.

Claim 1:
A method (<NUM>) performed by one or more computers, the method comprising:
obtaining (<NUM>) access data (<NUM>) for a digital resource, wherein the access data (<NUM>) comprises, for each time point in a sequence of time points, data identifying a set of users that accessed the digital resource at the time point;
processing (<NUM>) the access data (<NUM>) to generate data defining a tree model (<NUM>, <NUM>, <NUM>), wherein the tree model comprises a set of nodes (<NUM>, <NUM>), and each node in the set of nodes (<NUM>, <NUM>) is associated with:
(i) a key that specifies a plurality of time intervals in a time span comprising the sequence of time points, and
(ii) a value that is based on a respective number of users that satisfy a node-specific selection criterion based on the plurality of time intervals specified by the key for the node;
receiving (<NUM>) a request to determine a number of users that accessed the digital resource at least a predefined number of times within a time window; and
in response to the request:
processing (<NUM>) the tree model (<NUM>, <NUM>, <NUM>) to generate an estimate for the number of users (<NUM>) that accessed the digital resource at least the predefined number of times within the time window; and
outputting the estimate for the number of users (<NUM>) that accessed the digital resource at least the predefined number of times within the time window.