Abstract: A disclosed example method involves generating a plurality of wavelet coefficient quantities. Each wavelet coefficient quantity is generated based on items represented by probabilistic data. Each wavelet coefficient quantity represents different ones of the items by multiplying corresponding wavelet vectors. The example method also involves determining an error measure associated with each of the plurality of wavelet coefficient quantities, and selecting at least one of the plurality of wavelet coefficient quantities based on its associated error measure. The method also involves displaying parameter information associated with the one of the plurality of wavelet coefficient quantities to represent the probabilistic data.

Abstract: Example methods and apparatus to construct histogram and wavelet synopses for probabilistic data are disclosed. A disclosed example method involves receiving probabilistic data associated with probability measures and generating a plurality of histograms based on the probabilistic data. Each histogram is generated based on items represented by the probabilistic data. In addition, each histogram is generated using a different quantity of buckets containing different ones of the items. An error measure associated with each of the plurality of histograms is determined and one of the plurality of histograms is selected based on its associated error measure. The method also involves displaying parameter information associated with the one of the plurality of histograms to represent the data.

Abstract: Methods and apparatus for representing probabilistic data using a probabilistic histogram are disclosed. An example method comprises partitioning a plurality of ordered data items into a plurality of buckets, each of the data items capable of having a data value from a plurality of possible data values with a probability characterized by a respective individual probability distribution function (PDF), each bucket associated with a respective subset of the ordered data items bounded by a respective beginning data item and a respective ending data item, and determining a first representative PDF for a first bucket associated with a first subset of the ordered data items by partitioning the plurality of possible data values into a first plurality of representative data ranges and respective representative probabilities based on an error between the first representative PDF and a first plurality of individual PDFs characterizing the first subset of the ordered data items.

Abstract: Methods and apparatus for representing probabilistic data using a probabilistic histogram are disclosed. An example method comprises partitioning a plurality of ordered data items into a plurality of buckets, each of the data items capable of having a data value from a plurality of possible data values with a probability characterized by a respective individual probability distribution function (PDF), each bucket associated with a respective subset of the ordered data items bounded by a respective beginning data item and a respective ending data item, and determining a first representative PDF for a first bucket associated with a first subset of the ordered data items by partitioning the plurality of possible data values into a first plurality of representative data ranges and respective representative probabilities based on an error between the first representative PDF and a first plurality of individual PDFs characterizing the first subset of the ordered data items.

Abstract: The subject matter disclosed herein relates to processing information regarding events. In one particular example, a stabbing query may be formulated in response to an event. One or more sets are associated with and/or mapped to nodes of a tree.

Abstract: Subject matter disclosed herein relates to document classification and/or automated document classifier tuning. In an example embodiment, a document received from a user computing platform in an online database stored in a memory of a server computing platform may be classified based, at least in part, on a training set. Also for an example embodiment, the training set may be modified based, at least in part, on statistics gathered from user browsing behavior.

Abstract: A method and system for allocating inventory in an Internet environment is provided. A method employed by the system may include generating an inventory pool that represents a number of impressions deliverable to all users, then determining, from multiple past orders for booking impressions, a hierarchy of parameters utilized to target users and a number of impressions deliverable to users characterized by the parameters. The inventory pool may then be partitioned into multiple inventory pools according to the hierarchy, where each inventory pool represents a number of impressions deliverable to users characterized by parameters associated with the inventory pool. The hierarchy of pools may then be stored to a database.

Abstract: Example methods and apparatus to construct histogram and wavelet synopses for probabilistic data are disclosed. A disclosed example method involves receiving probabilistic data associated with probability measures and generating a plurality of histograms based on the probabilistic data. Each histogram is generated based on items represented by the probabilistic data. In addition, each histogram is generated using a different quantity of buckets containing different ones of the items. An error measure associated with each of the plurality of histograms is determined and one of the plurality of histograms is selected based on its associated error measure. The method also involves displaying parameter information associated with the one of the plurality of histograms to represent the data.

Abstract: Example embodiments described herein may relate to estimating inventory for a display advertising system utilized, for example, in Web-based advertising.

Abstract: A distinct-count estimate is obtained in a guaranteed small footprint using a two level hash, distinct count sketch. A first hash fills the first-level hash buckets with an exponentially decreasing number of data-elements. These are then uniformly hashed to an array of second-level-hash tables, and have an associated total-element counter and bit-location counters. These counters are used to identify singletons and so provide a distinct-sample and a distinct-count. An estimate of the total distinct-count is obtained by dividing by the distinct-count by the probability of mapping a data-element to that bucket. An estimate of the total distinct-source frequencies of destination address can be found in a similar fashion. By further associating the distinct-count sketch with a list of singletons, a total singleton count and a heap containing the destination addresses ordered by their distinct-source frequencies, a tracking distinct-count sketch may be formed that has considerably improved query time.

Abstract: A method of constructing a score-optimal R-tree to support top-k stabbing queries over a set of scored intervals generates a constraint graph from the set, and determines over each node in the constraint graph that has no other nodes pointing to it the node with the smallest left endpoint; for each of these nodes, the associated interval is added to the tree and the node is removed from the constraint graph.

Abstract: A method of estimating set-expression cardinalities over data streams with guaranteed small maintenance time per data-element update. The method only examines each data element once and uses a limited amount of memory. The time-efficient stream synopsis extends 2-level hash-sketches by randomly, but uniformly, pre-hashing data-elements prior to logarithmically hashing them to a first-level hash-table. This generates a set of independent 2-level hash-sketches. The set-union cardinality can be estimated by determining the smallest hash-bucket index j at which only a predetermined fraction of the b hash-buckets has a non-empty union |A?B|. Once a set-union cardinality is estimated, general set-expression cardinalities may be estimated by counting witness elements for the set-expression, i.e., those first-level hash-buckets that are both a singleton for the set-expression and a set-union singleton.

Abstract: Subject matter disclosed herein relates to document classification and/or automated document classifier tuning.

Abstract: A method of generating a diversified vertical search results listing, including listing attribute values related to search criteria and their frequency of occurrence to create a plurality of listings; creating a plurality of interval bands based on the plurality of listings; generating a random diversity score for each listing over a substantially uniform distribution within each of the plurality of bands; and sorting a set of search results for diversified listing in response to a user searching for the search criteria according to the diversity score of each listing.

Abstract: The subject matter disclosed herein relates to processing information regarding events. In one particular example, a stabbing query may be formulated in response to an event. One or more sets are associated with and/or mapped to nodes of a tree.

Abstract: A method of estimating an aggregate of a join over data-streams in real-time using skimmed sketches, that only examines each data element once and has a worst case space requirement of O(n2/J), where J is the size of the join and n is the number of data elements. The skimmed sketch is an atomic sketch, formed as the inner product of the data-stream frequency vector and a random binary variable, from which the frequency values that exceed a predetermined threshold have been skimmed off and placed in a dense frequency vector. The join size is estimated as the sum of the sub-joins of skimmed sketches and dense frequency vectors. The atomic sketches may be arranged in a hash structure so that processing a data element only requires updating a single sketch per hash table. This keeps the per-element overhead logarithmic in the domain and stream sizes.

Abstract: A method of efficiently providing estimated answers to workloads of aggregate, multi-join SQL-like queries over a number of input data-streams. The method only examines each data elements once and uses a limited amount of computer memory. The method uses join graphs and atomic sketches that are essentially pseudo-random summaries formed using random binary variables. The estimated answer is the product of all the atomic sketches for all the vertices in the query join graph. A query workload is processed efficiently by identifying and sharing atomic sketches common to distinct queries, while ensuring that the join graphs remain well formed. The method may automatically minimize either the average query error or the maximum query error over the workload.

Abstract: A method of distributed approximate query tracking relies on tracking general-purpose randomized sketch summaries of local streams at remote sites along with concise prediction models of local site behavior in order to produce highly communication-efficient and space/time-efficient solutions. A powerful approximate query tracking framework readily incorporates several complex analysis queries, including distributed join and multi-join aggregates and approximate wavelet representations, thus giving the first known low-overhead tracking solution for such queries in the distributed-streams model.

Abstract: The first fast solution to the problem of tracking wavelet representations of one-dimensional and multi-dimensional data streams based on a stream synopsis, the Group-Count Sketch (GCS) is provided. By imposing a hierarchical structure of groups over the data and applying the GCS, our algorithms can quickly recover the most important wavelet coefficients with guaranteed accuracy. A tradeoff between query time and update time is established, by varying the hierarchical structure of groups, allowing the right balance to be found for specific data streams. Experimental analysis confirmed this tradeoff, and showed that all the methods significantly outperformed previously known methods in terms of both update time and query time, while maintaining a high level of accuracy.

Abstract: The invention comprises a method and apparatus for determining a rank of a query value. Specifically, the method comprises receiving a rank query request, determining, for each of the at least one remote monitor, a predicted lower-bound rank value and upper-bound rank value, wherein the predicted lower-bound rank value and upper-bound rank value are determined according to at least one respective prediction model used by each of the at least one remote monitor to compute the at least one local quantile summary, computing a predicted average rank value for each of the at least one remote monitor using the at least one predicted lower-bound rank value and the at least one predicted upper-bound rank value associated with the respective at least one remote monitor, and computing the rank of the query value using the at least one predicted average rank value associated with the respective at least one remote monitor.