Multimedia uploaded content is tagged and recommended by users of collaborative systems, resulting in informal classifications also known as folksonomies. Faceted web ranking has been proved a reasonable alternative to a single ranking which does not take into account a personalized context. In this paper we analyze the online computation of rankings of users associated to facets made up of multiple tags. Possible applications are user reputation evaluation (ego-ranking) and improvement of content quality in case of retrieval. We propose a solution based on PageRank as centrality measure: (i) a ranking for each tag is computed offline on the basis of the corresponding tag-dependent subgraph; (ii) a faceted order is generated by merging rankings corresponding to all the tags in the facet. The fundamental assumption, validated by empirical observations, is that step (i) is scalable. We also present algorithms for part (ii) having time complexity O(k), where k is the number of tags in the facet, well suited to online computation.
Scalability issues were also tackled by Jeh and Widom @cite_3 criticizing offline computation of multiple PageRank vectors for each possible query and preferring another more efficient dynamic programming algorithm for online calculation of the faceted rankings based on offline computation of basis vectors. They found that their algorithm scales well with the size of set @math , the biasing page set, and they criticize previous ideas in @cite_0 : [Richarson and Domingos] suggested that importance scores be precomputed offline for every possible text query, but the enormous number of possibilities makes this approach difficult to scale."
@cite_0 @cite_3
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We study resource-limited online learning, motivated by the problem of conditional-branch outcome prediction in computer architecture. In particular, we consider (parallel) time and space-efficient ensemble learners for online settings, empirically demonstrating benefits similar to those shown previously for offline ensembles. Our learning algorithms are inspired by the previously published “boosting by filtering” framework as well as the offline Arc-x4 boosting-style algorithm. We train ensembles of online decision trees using a novel variant of the ID4 online decision-tree algorithm as the base learner, and show empirical results for both boosting and bagging-style online ensemble methods. Our results evaluate these methods on both our branch prediction domain and online variants of three familiar machine-learning benchmarks. Our data justifies three key claims. First, we show empirically that our extensions to ID4 significantly improve performance for single trees and additionally are critical to achieving performance gains in tree ensembles. Second, our results indicate significant improvements in predictive accuracy with ensemble size for the boosting-style algorithm. The bagging algorithms we tried showed poor performance relative to the boosting-style algorithm (but still improve upon individual base learners). Third, we show that ensembles of small trees are often able to outperform large single trees with the same number of nodes (and similarly outperform smaller ensembles of larger trees that use the same total number of nodes). This makes online boosting particularly useful in domains such as branch prediction with tight space restrictions (i.e., the available real-estate on a microprocessor chip). Developers of rapidly growing applications must be able to anticipate potential scalability problems before they cause performance issues in production environments. A new type of data independence, called scale independence, seeks to address this challenge by guaranteeing a bounded amount of work is required to execute all queries in an application, independent of the size of the underlying data. While optimization strategies have been developed to provide these guarantees for the class of queries that are scale-independent when executed using simple indexes, there are important queries for which such techniques are insufficient. Executing these more complex queries scale-independently requires precomputation using incrementally-maintained materialized views. However, since this precomputation effectively shifts some of the query processing burden from execution time to insertion time, a scale-independent system must be careful to ensure that storage and maintenance costs do not threaten scalability. In this paper, we describe a scale-independent view selection and maintenance system, which uses novel static analysis techniques that ensure that created views do not themselves become scaling bottlenecks. Finally, we present an empirical analysis that includes all the queries from the TPC-W benchmark and validates our implementation's ability to maintain nearly constant high-quantile query and update latency even as an application scales to hundreds of machines. Recommender problems with large and dynamic item pools are ubiquitous in web applications like content optimization, online advertising and web search. Despite the availability of rich item meta-data, excess heterogeneity at the item level often requires inclusion of item-specific "factors" (or weights) in the model. However, since estimating item factors is computationally intensive, it poses a challenge for time-sensitive recommender problems where it is important to rapidly learn factors for new items (e.g., news articles, event updates, tweets) in an online fashion. In this paper, we propose a novel method called FOBFM (Fast Online Bilinear Factor Model) to learn item-specific factors quickly through online regression. The online regression for each item can be performed independently and hence the procedure is fast, scalable and easily parallelizable. However, the convergence of these independent regressions can be slow due to high dimensionality. The central idea of our approach is to use a large amount of historical data to initialize the online models based on offline features and learn linear projections that can effectively reduce the dimensionality. We estimate the rank of our linear projections by taking recourse to online model selection based on optimizing predictive likelihood. Through extensive experiments, we show that our method significantly and uniformly outperforms other competitive methods and obtains relative lifts that are in the range of 10-15 in terms of predictive log-likelihood, 200-300 for a rank correlation metric on a proprietary My Yahoo! dataset; it obtains 9 reduction in root mean squared error over the previously best method on a benchmark MovieLens dataset using a time-based train test data split. We prove the first non-trivial performance ratios strictly above 0.5 for weighted versions of the oblivious matching problem. Even for the unweighted version, since Aronson, Dyer, Frieze, and Suen first proved a non-trivial ratio above 0.5 in the mid-1990s, during the next twenty years several attempts have been made to improve this ratio, until Chan, Chen, Wu and Zhao successfully achieved a significant ratio of 0.523 very recently (SODA 2014). To the best of our knowledge, our work is the first in the literature that considers the node-weighted and edge-weighted versions of the problem in arbitrary graphs (as opposed to bipartite graphs). (1) For arbitrary node weights, we prove that a weighted version of the Ranking algorithm has ratio strictly above 0.5. We have discovered a new structural property of the ranking algorithm: if a node has two unmatched neighbors at the end of algorithm, then it will still be matched even when its rank is demoted to the bottom. This property allows us to form LP constraints for both the node-weighted and the unweighted oblivious matching problems. As a result, we prove that the ratio for the node-weighted case is at least 0.501512. Interestingly via the structural property, we can also improve slightly the ratio for the unweighted case to 0.526823 (from the previous best 0.523166 in SODA 2014). (2) For a bounded number of distinct edge weights, we show that ratio strictly above 0.5 can be achieved by partitioning edges carefully according to the weights, and running the (unweighted) Ranking algorithm on each part. Our analysis is based on a new primal-dual framework known as , in which dual feasibility is bypassed. Instead, only dual constraints corresponding to edges in an optimal matching are satisfied. Using this framework we also design and analyze an algorithm for the edge-weighted online bipartite matching problem with free disposal. We prove that for the case of bounded online degrees, the ratio is strictly above 0.5.