Knowledge tracing aims to predict students’ probability of correctly answering the next question based on their interaction history. Previous methods employ left-to-right unidirectional transformers to encode the historical behaviors into hidden representations, especially with contrastive learning methods. Using uni-directional models to model student behaviors can only learn the hidden representation from its previous items, which restricts the power of the representation capability. Inspired by the success of BERT in text understanding, we propose a novel Bidirectional Transformer encoder guided Contrastive Learning framework for deep Knowledge Tracing system, named as Bi-CL4KT to generate the accurate response predictions for the next question. We incorporate the Cloze task and carefully design data augmentation methods to generate high-quality positive and negative instances for contrastive learning. Extensive experiments conducted on three real-world education datasets show that the proposed method significantly outperforms the state-of-the-art methods.

Knowledge tracing aims to estimate knowledge states of students over a set of skills based on students' past learning activities. Deep learning based knowledge tracing models show superior performance to traditional knowledge tracing approaches. Early works like DKT use skill IDs and student responses only. Recent works also incorporate questions IDs into their models and achieve much improved performance in the next question correctness prediction task. However, predictions made by these models are thus on specific questions, and it is not straightforward to translate them to estimation of students' knowledge states over skills. In this paper, we propose to replace question IDs with question difficulty levels in deep knowledge tracing models. The predictions made by our model can be more readily translated to students' knowledge states over skills. Furthermore, by using question difficulty levels to replace question IDs, we can also alleviate the cold-start problem in knowledge tracing as online learning platforms are updated frequently with new questions. We further use two techniques to smooth the predicted scores. One is to combine embeddings of nearby difficulty levels using the Hann function. The other is to constrain the predicted probabilities to be consistent with question difficulties by imposing a penalty if they are not consistent. We conduct extensive experiments to study the performance of the proposed model. Our experimental results show that our model outperforms the state-of-the-art knowledge tracing models in terms of both accuracy and consistency with question difficulty levels.

Matrix factorization has been widely adopted for recommendation by learning latent embeddings of users and items from observed user-item interaction data. However, previous methods usually assume the learned embeddings are static or homogeneously evolving with the same diffusion rate. This is not valid in most scenarios, where users’ preferences and item attributes heterogeneously drift over time. To remedy this issue, we have proposed a novel dynamic matrix factorization model, named Dynamic Bayesian Logistic Matrix Factorization (DBLMF), which aims to learn heterogeneous user and item embeddings that are drifting with inconsistent diffusion rates. More specifically, DBLMF extends logistic matrix factorization to model the probability a user would like to interact with an item at a given timestamp, and a diffusion process to connect latent embeddings over time. In addition, an efficient Bayesian inference algorithm has also been proposed to make DBLMF scalable on large datasets. The effectiveness of the proposed method has been demonstrated by extensive experiments on real datasets, compared with the state-of-the-art methods.

A large number of new buyers are often acquired by merchants during promotions. However, many of the attracted buyers are one-time deal hunters, and the promotions may have little long-lasting impact on sales. It is important for merchants to identify who can be converted to regular loyal buyers and then target them to reduce promotion cost and increase the return on investment (ROI). At International Joint Conferences on Artificial Intelligence (IJCAI) 2015, Alibaba hosted an international competition for repeat buyer prediction based on the sales data of the ``Double 11" shopping event in 2014 at Tmall.com. We won the first place at stage 1 of the competition out of 753 teams. In this paper, we present our winning solution, which consists of comprehensive feature engineering and model training. We created profiles for users, merchants, brands, categories, items and their interactions via extensive feature engineering. These profiles are not only useful for this particular prediction task, but can also be used for other important tasks in e-commerce, such as customer segmentation, product recommendation, and customer base augmentation for brands. Feature engineering is often the most important factor for the success of a prediction task, but not much work can be found in the literature on feature engineering for prediction tasks in e-commerce. Our work provides some useful hints and insights for data science practitioners in e-commerce.

Conventional hypothesis testing is carried out in a hypothesis-driven manner. A scientist must first formulate a hypothesis based on what he or she sees and then devise a variety of experiments to test it. Given the rapid growth of data, it has become virtually impossible for a person to manually inspect all data to find all of the interesting hypotheses for testing. In this article, we propose and develop a data-driven framework for automatic hypothesis testing and analysis. We define a hypothesis as a comparison between two or more subpopulations. We find subpopulations for comparison using frequent pattern mining techniques and then pair them up for statistical hypothesis testing. We also generate additional information for further analysis of the hypotheses that are deemed significant. The number of hypotheses generated can be very large, and many of them are very similar. We develop algorithms to remove redundant hypotheses and present a succinct set of significant hypotheses to users. We conducted a set of experiments to show the efficiency and effectiveness of the proposed algorithms. The results show that our system can help users (1) identify significant hypotheses efficiently, (2) isolate the reasons behind significant hypotheses efficiently, and (3) find confounding factors that form Simpson’s paradoxes with discovered significant hypotheses.

Frequent pattern mining often produces an enormous number of frequent patterns, which imposes a great challenge on visualizing, understanding and further analysis of the generated patterns. This calls for finding a small number of representative patterns to best approximate all other patterns. In this paper, we develop an algorithm called MinRPset to find a minimum representative pattern set with error guarantee. MinRPset produces the smallest solution that we can possibly have in practice under the given problem setting, and it takes a reasonable amount of time to finish when the number of frequent closed patterns is below one million. MinRPset is very space-consuming and time-consuming on some dense datasets when the number of frequent closed patterns is large. To solve this problem, we propose another algorithm called FlexRPset, which provides one extra parameter K to allow users to make a trade-off between result size and efficiency. We adopt an incremental approach to let the users make the trade-off conveniently. Our experiment results show that MinRPset and FlexRPset produce fewer representative patterns than RPlocal-an efficient algorithm that is developed for solving the same problem.

Frequent itemset mining is an important problem in the data mining area. Extensive efforts have been devoted to developing efficient algorithms for mining frequent itemsets. However, not much attention is paid on managing the large collection of frequent itemsets produced by these algorithms for subsequent analysis and for user exploration. In this paper, we study three structures for indexing and querying frequent itemsets: inverted files, signature files and CFP-tree. The first two structures have been widely used for indexing general set-valued data. We make some modifications to make them more suitable for indexing frequent itemsets. The CFP-tree structure is specially designed for storing frequent itemsets. We add a pruning technique based on length-2 frequent itemsets to make it more efficient for processing superset queries. We study the performance of the three structures in supporting five types of containment queries: exact match, subset/superset search and immediate subset/superset search. Our results show that no structure can outperform other structures for all the five types of queries on all the datasets. CFP-tree shows better overall performance than the other two structures.

We present a system called AssocExplorer to support exploratory data analysis via association rule visualization and exploration. AssocExplorer is designed by following the visual information-seeking mantra: overview first, zoom and filter, then details on demand. It effectively uses coloring to deliver information so that users can easily detect things that are interesting to them. If users find a rule interesting, they can explore related rules for further analysis, which allows users to find interesting phenomenon that are difficult to detect when rules are examined separately. Our system also allows users to compare rules and inspect rules with similar item composition but different statistics so that the key factors that contribute to the difference can be isolated.

Frequent pattern mining often produces an enormous number of frequent patterns, which imposes a great challenge on understanding and further analysis of the generated patterns. This calls for finding a small number of representative patterns to best approximate all other patterns. An ideal approach should 1) produce a minimum number of representative patterns; 2) restore the support of all patterns with error guarantee; and 3) have good efficiency. Few existing approaches can satisfy all the three requirements. In this paper, we develop two algorithms, MinRPset and FlexRPset, for finding minimum representative pattern sets. Both algorithms provide error guarantee. MinRPset produces the smallest solution that we can possibly have in practice under the given problem setting, and it takes a reasonable amount of time to finish. FlexRPset is developed based on MinRPset. It provides one extra parameter K to allow users to make a trade-off between result size and efficiency. Our experiment results show that MinRPset and FlexRPset produce fewer representative patterns than RPlocal---an efficient algorithm that is developed for solving the same problem. FlexRPset can be slightly faster than RPlocal when K is small.

Abstract Contact: [email protected]

Hypothesis testing is a well-established tool for scientific discovery. Conventional hypothesis testing is carried out in a hypothesis-driven manner. A scientist must first formulate a hypothesis based on his/her knowledge and experience, and then devise a variety of experiments to test it. Given the rapid growth of data, it has become virtually impossible for a person to manually inspect all the data to find all the interesting hypotheses for testing. In this paper, we propose and develop a data-driven system for automatic hypothesis testing and analysis. We define a hypothesis as a comparison between two or more sub-populations. We find sub-populations for comparison using frequent pattern mining techniques and then pair them up for statistical testing. We also generate additional information for further analysis of the hypotheses that are deemed significant. We conducted a set of experiments to show the efficiency of the proposed algorithms, and the usefulness of the generated hypotheses. The results show that our system can help users (1) identify significant hypotheses; (2) isolate the reasons behind significant hypotheses; and (3) find confounding factors that form Simpson's Paradoxes with discovered significant hypotheses.

MOTIVATION: Many new methods have recently been proposed for detecting epistatic interactions in GWAS data. There is, however, no in-depth independent comparison of these methods yet. RESULTS: Five recent methods-TEAM, BOOST, SNPHarvester, SNPRuler and Screen and Clean (SC)-are evaluated here in terms of power, type-1 error rate, scalability and completeness. In terms of power, TEAM performs best on data with main effect and BOOST performs best on data without main effect. In terms of type-1 error rate, TEAM and BOOST have higher type-1 error rates than SNPRuler and SNPHarvester. SC does not control type-1 error rate well. In terms of scalability, we tested the five methods using a dataset with 100 000 SNPs on a 64 bit Ubuntu system, with Intel (R) Xeon(R) CPU 2.66 GHz, 16 GB memory. TEAM takes ~36 days to finish and SNPRuler reports heap allocation problems. BOOST scales up to 100 000 SNPs and the cost is much lower than that of TEAM. SC and SNPHarvester are the most scalable. In terms of completeness, we study how frequently the pruning techniques employed by these methods incorrectly prune away the most significant epistatic interactions. We find that, on average, 20% of datasets without main effect and 60% of datasets with main effect are pruned incorrectly by BOOST, SNPRuler and SNPHarvester. AVAILABILITY: The software for the five methods tested are available from the URLs below. TEAM: http://csbio.unc.edu/epistasis/download.php BOOST: http://ihome.ust.hk/~eeyang/papers.html. SNPHarvester: http://bioinformatics.ust.hk/SNPHarvester.html. SNPRuler: http://bioinformatics.ust.hk/SNPRuler.zip. Screen and Clean: http://wpicr.wpic.pitt.edu/WPICCompGen/. CONTACT: [email protected].

Association rule mining is an important problem in the data mining area. It enumerates and tests a large number of rules on a dataset and outputs rules that satisfy user-specified constraints. Due to the large number of rules being tested, rules that do not represent real systematic effect in the data can satisfy the given constraints purely by random chance. Hence association rule mining often suffers from a high risk of false positive errors. There is a lack of comprehensive study on controlling false positives in association rule mining. In this paper, we adopt three multiple testing correction approaches---the direct adjustment approach, the permutation-based approach and the holdout approach---to control false positives in association rule mining, and conduct extensive experiments to study their performance. Our results show that (1) Numerous spurious rules are generated if no correction is made. (2) The three approaches can control false positives effectively. Among the three approaches, the permutation-based approach has the highest power of detecting real association rules, but it is very computationally expensive. We employ several techniques to reduce its cost effectively.

Protein complexes are important for understanding principles of cellular organization and functions. With the availability of large amounts of high-throughput proteinprotein interactions (PPI), many algorithms have been proposed to discover protein complexes from PPI networks. However, none of existing algorithms takes into consideration the fact that not all the interactions in a PPI network take place at the same time. As a result, predicted complexes often contain many spuriously included proteins, precluding them from matching true complexes. We propose two methods to tackle this problem: (1) We utilize cellular component Gene Ontology (GO) terms to decompose PPI networks into several smaller networks such that the proteins in each decomposed network are annotated with the same cellular component GO term. (2) Hub proteins are more likely to fuse clusters that correspond to different complexes. To avoid this, we remove hub proteins from PPI networks, and then apply a complex discovery algorithm on the remaining PPI network. The removed hub proteins are added back to the generated clusters afterwards. We tested the two methods on the yeast PPI network downloaded from BioGRID. Our results show that these methods can improve the performance of several complex discovery algorithms significantly. Further improvement in performance is achieved when we apply them in tandem.

BACKGROUND: Human genome contains millions of common single nucleotide polymorphisms (SNPs) and these SNPs play an important role in understanding the association between genetic variations and human diseases. Many SNPs show correlated genotypes, or linkage disequilibrium (LD), thus it is not necessary to genotype all SNPs for association study. Many algorithms have been developed to find a small subset of SNPs called tag SNPs that are sufficient to infer all the other SNPs. Algorithms based on the r2 LD statistic have gained popularity because r2 is directly related to statistical power to detect disease associations. Most of existing r2 based algorithms use pairwise LD. Recent studies show that multi-marker LD can help further reduce the number of tag SNPs. However, existing tag SNP selection algorithms based on multi-marker LD are both time-consuming and memory-consuming. They cannot work on chromosomes containing more than 100 k SNPs using length-3 tagging rules. RESULTS: We propose an efficient algorithm called FastTagger to calculate multi-marker tagging rules and select tag SNPs based on multi-marker LD. FastTagger uses several techniques to reduce running time and memory consumption. Our experiment results show that FastTagger is several times faster than existing multi-marker based tag SNP selection algorithms, and it consumes much less memory at the same time. As a result, FastTagger can work on chromosomes containing more than 100 k SNPs using length-3 tagging rules.FastTagger also produces smaller sets of tag SNPs than existing multi-marker based algorithms, and the reduction ratio ranges from 3%-9% when length-3 tagging rules are used. The generated tagging rules can also be used for genotype imputation. We studied the prediction accuracy of individual rules, and the average accuracy is above 96% when r2 >/= 0.9. CONCLUSIONS: Generating multi-marker tagging rules is a computation intensive task, and it is the bottleneck of existing multi-marker based tag SNP selection methods. FastTagger is a practical and scalable algorithm to solve this problem.

MOTIVATION: Protein complexes are important for understanding principles of cellular organization and function. High-throughput experimental techniques have produced a large amount of protein interactions, which makes it possible to predict protein complexes from protein-protein interaction (PPI) networks. However, protein interaction data produced by high-throughput experiments are often associated with high false positive and false negative rates, which makes it difficult to predict complexes accurately. RESULTS: We use an iterative scoring method to assign weight to protein pairs, and the weight of a protein pair indicates the reliability of the interaction between the two proteins. We develop an algorithm called CMC (clustering-based on maximal cliques) to discover complexes from the weighted PPI network. CMC first generates all the maximal cliques from the PPI networks, and then removes or merges highly overlapped clusters based on their interconnectivity. We studied the performance of CMC and the impact of our iterative scoring method on CMC. Our results show that: (i) the iterative scoring method can improve the performance of CMC considerably; (ii) the iterative scoring method can effectively reduce the impact of random noise on the performance of CMC; (iii) the iterative scoring method can also improve the performance of other protein complex prediction methods and reduce the impact of random noise on their performance; and (iv) CMC is an effective approach to protein complex prediction from protein interaction network. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

The rigid all-versus-all adjacency required by a maximal biclique for its two vertex sets is extremely vulnerable to missing data. In the past, several types of quasi-bicliques have been proposed to tackle this problem, however their noise tolerance is usually unbalanced and can be very skewed. In this paper, we improve the noise tolerance of maximal quasi-bicliques by allowing every vertex to tolerate up to the same number, or the same percentage, of missing edges. This idea leads to a more natural interaction between the two vertex sets—a balanced most-versus-most adjacency. This generalization is also non-trivial, as many large-size maximal quasi-biclique subgraphs do not contain any maximal bicliques. This observation implies that direct expansion from maximal bicliques may not guarantee a complete enumeration of all maximal quasi-bicliques. We present important properties of maximal quasi-bicliques such as a bounded closure property and a fixed point property to design efficient algorithms. Maximal quasi-bicliques are closely related to co-clustering problems such as documents and words co-clustering, images and features co-clustering, stocks and financial ratios co-clustering, etc. Here, we demonstrate the usefulness of our concepts using a new application—a bioinformatics example—where prediction of true protein interactions is investigated.

Traditional similarity or distance measurements usually become meaningless when the dimensions of the datasets increase, which has detrimental effects on clustering performance. In this paper, we propose a distance-based subspace clustering model, called nCluster, to find groups of objects that have similar values on subsets of dimensions. Instead of using a grid based approach to partition the data space into non-overlapping rectangle cells as in the density based subspace clustering algorithms, the nCluster model uses a more flexible method to partition the dimensions to preserve meaningful and significant clusters. We develop an efficient algorithm to mine only maximal nClusters. A set of experiments are conducted to show the efficiency of the proposed algorithm and the effectiveness of the new model in preserving significant clusters.

With the increasing service-oriented applications, efficient service data management is becoming a practical and important issue. Currently, most exchange messages among different Web services is SOAP, which is represented by XML-formatted data. So, the main task of service data management is to manage XML format message files in order to provide efficient store and query for service requestors. Storing XML documents in relational databases has drawn much attention in recent years because it can leverage existing investments in relational database technologies. However, most former work defines relational schema for XML files based on heuristics without considering application characteristics, hence fails to produce efficient relational schema for various applications. In this paper, we propose an autonomic, workload-aware approach to generate relational schema according to dynamic application characteristics or user specified workload. Our approach adopts the genetic algorithm to find optimal mappings, and an elegant encoding method and related operations are proposed to manipulate mappings using bit strings. We implemented the proposed algorithm and our preliminary experiment results showed that our algorithm was more robust, more suitable for dynamic SOA applications and produced better relational schema than existing work

The support-confidence framework is the most common measure used in itemset mining algorithms, for its antimonotonicity that effectively simplifies the search lattice. This computational convenience brings both quality and statistical flaws to the results as observed by many previous studies. In this paper, we introduce a novel algorithm that produces itemsets with ranked statistical merits under sophisticated test statistics such as chi-square, risk ratio, odds ratio, etc. Our algorithm is based on the concept of equivalence classes. An equivalence class is a set of frequent itemsets that always occur together in the same set of transactions. Therefore, itemsets within an equivalence class all share the same level of statistical significance regardless of the variety of test statistics. As an equivalence class can be uniquely determined and concisely represented by a closed pattern and a set of generators, we just mine closed patterns and generators, taking a simultaneous depth-first search scheme. This parallel approach has not been exploited by any prior work. We evaluate our algorithm on two aspects. In general, we compare to LCM and FPclose which are the best algorithms tailored for mining only closed patterns. In particular, we compare to epMiner which is the most recent algorithm for mining a type of relative risk patterns, known as minimal emerging patterns. Experimental results show that our algorithm is faster than all of them, sometimes even multiple orders of magnitude faster. These statistically ranked patterns and the efficiency have a high potential for real-life applications, especially in biomedical and financial fields where classical test statistics are of dominant interest.

Maximal biclique (also known as complete bipartite) subgraphs can model many applications in Web mining, business, and bioinformatics. Enumerating maximal biclique subgraphs from a graph is a computationally challenging problem, as the size of the output can become exponentially large with respect to the vertex number when the graph grows. In this paper, we efficiently enumerate them through the use of closed patterns of the adjacency matrix of the graph. For an undirected graph G without self-loops, we prove that 1) the number of closed patterns in the adjacency matrix of G is even, 2) the number of the closed patterns is precisely double the number of maximal biclique subgraphs of G, and 3) for every maximal biclique subgraph, there always exists a unique pair of closed patterns that matches the two vertex sets of the subgraph. Therefore, the problem of enumerating maximal bicliques can be solved by using efficient algorithms for mining closed patterns, which are algorithms extensively studied in the data mining field. However, this direct use of existing algorithms causes a duplicated enumeration. To achieve high efficiency, we propose an O(mn) time delay algorithm for a nonduplicated enumeration, in particular, for enumerating those maximal bicliques with a large size, where m and n. are the number of edges and vertices of the graph, respectively. We evaluate the high efficiency of our algorithm by comparing it to state- of-the-art algorithms on three categories of graphs: randomly generated graphs, benchmarks, and a real-life protein interaction network. In this paper, we also prove that if self-loops are allowed in a graph, then the number of closed patterns in the adjacency matrix is not necessarily even, but the maximal bicliques are exactly the same as those of the graph after removing all the self-loops.

We introduce an unsupervised process to co-cluster groups of stocks and financial ratios, so that investors can gain more insight on how they are correlated. Our idea for the co-clustering is based on a graph concept called maximal quasi-bicliques, which can tolerate erroneous or/and missing information that are common in the stock and financial ratio data. Compared to previous works, our maximal quasi-bicliques require the errors to be evenly distributed, which enable us to capture more meaningful co-clusters. We develop a new algorithm that can efficiently enumerate maximal quasi-bicliques from an undirected graph. The concept of maximal quasi-bicliques is domain-independent; it can be extended to perform co-clustering on any set of data that are modeled by graphs.

A complete set of frequent itemsets can get undesirably large due to redundancy. Several representations have been proposed to eliminate the redundancy. Existing generator based representations rely on a negative border to make the representation lossless. However, negative borders of generators are often very large. The number of itemsets on a negative border sometimes even exceeds the total number of frequent itemsets. In this paper, we propose to use a positive border together with frequent generators to form a lossless representation. A set of frequent generators plus its positive border is always no larger than the corresponding complete set of frequent itemsets, thus it is a true concise representation. The generalized form of this representation is also proposed. We develop an efficient algorithm, called GrGrowth, to mine generators and positive borders as well as their generalizations.

Mining frequent patterns is a fundamental and important problem in many data mining applications. Many of the algorithms adopt the pattern growth approach, which is shown to be superior to the candidate generate-and-test approach significantly. We identify the key factors that influence the performance of the pattern growth approach, and optimize them to further improve the performance. Our algorithm uses a simple while compact data structure-ascending frequency ordered prefixtree (AFOPT) to organize the conditional databases, in which we use arrays to store single branches to further save space. We traverse our prefix-tree structure using a top-down strategy. Our experiment results show that the combination of the top-down traversal strategy and the ascending frequency item ordering method achieves significant performance improvement over previous works.

Extensive efforts have been devoted to developing efficient algorithms for mining frequent patterns. However, frequent pattern mining remains a time-consuming process, especially for very large datasets. It is therefore desirable to adopt a "mining once and using many times" strategy. Unfortunately, there has been little work reported on managing and organizing a large set of patterns for future use. In this paper, we propose a disk-based data structure, CFP-tree (Condensed Frequent Pattern Tree), for organizing frequent patterns discovered from transactional databases. In addition to an efficient algorithm for CFP-tree construction, we also developed algorithms to efficiently support two important types of queries, namely queries with minimum support constraints and queries with item constraints, against the stored patterns, as these two types of queries are basic building blocks for complex frequent pattern related mining tasks. Comprehensive experimental study has been conducted to demonstrate the effectiveness of CFP-tree and efficiency of related algorithms.

We propose a framework for mining frequent patterns from large transactional databases. The core of the framework is a coded prefix-path tree with two representations, namely, a memory-based prefix-path tree and a disk-based prefix-path tree. The disk-based prefix-path tree is simple in its data structure yet rich in information contained, and is small in size. The memory-based prefix-path tree is simple and compact. Based on the memory-based prefix-path tree, a new depth-first frequent pattern discovery algorithm, called PP-Mine, is proposed that outperforms FP-growth significantly. The memory-based prefix-path tree can be stored on disk using a disk-based prefix-path tree with assistance of the new coding scheme. We present loading algorithms to load the minimal required disk-based prefix-path tree into main memory. Our technique is to push constraints into the loading process, which has not been well studied yet.