Incremental dimension reduction of tensors with random index

We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low and predictable. Component encoding and decoding are performed on-line without computationally expensive re-analysis of the data set. The range of tensor indices can be extended dynamically without modifying the component representation. This idea originates from a mathematical model of semantic memory and a method known as random indexing in natural language processing. We generalize the random-indexing algorithm to tensors and present signal-to-noise-ratio simulations for representations of vectors and matrices. We present also a mathematical analysis of the approximate orthogonality of high-dimensional ternary vectors, which is a property that underpins this and other similar random-coding approaches to dimension reduction. To further demonstrate the properties of random indexing we present results of a synonym identification task. The method presented here has some similarities with random projection and Tucker decomposition, but it performs well at high dimensionality only (n>10^3). Random indexing is useful for a range of complex practical problems, e.g., in natural language processing, data mining, pattern recognition, event detection, graph searching and search engines. Prototype software is provided. It supports encoding and decoding of tensors of order >= 1 in a unified framework, i.e., vectors, matrices and higher order tensors.Comment: 36 pages, 9 figure

The Inferred Cardiogenic Gene Regulatory Network in the Mammalian Heart

Cardiac development is a complex, multiscale process encompassing cell fate adoption, differentiation and morphogenesis. To elucidate pathways underlying this process, a recently developed algorithm to reverse engineer gene regulatory networks was applied to time-course microarray data obtained from the developing mouse heart. Approximately 200 genes of interest were input into the algorithm to generate putative network topologies that are capable of explaining the experimental data via model simulation. To cull specious network interactions, thousands of putative networks are merged and filtered to generate scale-free, hierarchical networks that are statistically significant and biologically relevant. The networks are validated with known gene interactions and used to predict regulatory pathways important for the developing mammalian heart. Area under the precision-recall curve and receiver operator characteristic curve are 9% and 58%, respectively. Of the top 10 ranked predicted interactions, 4 have already been validated. The algorithm is further tested using a network enriched with known interactions and another depleted of them. The inferred networks contained more interactions for the enriched network versus the depleted network. In all test cases, maximum performance of the algorithm was achieved when the purely data-driven method of network inference was combined with a data-independent, functional-based association method. Lastly, the network generated from the list of approximately 200 genes of interest was expanded using gene-profile uniqueness metrics to include approximately 900 additional known mouse genes and to form the most likely cardiogenic gene regulatory network. The resultant network supports known regulatory interactions and contains several novel cardiogenic regulatory interactions. The method outlined herein provides an informative approach to network inference and leads to clear testable hypotheses related to gene regulation

A Quantitative Study of Pure Parallel Processes

In this paper, we study the interleaving -- or pure merge -- operator that most often characterizes parallelism in concurrency theory. This operator is a principal cause of the so-called combinatorial explosion that makes very hard - at least from the point of view of computational complexity - the analysis of process behaviours e.g. by model-checking. The originality of our approach is to study this combinatorial explosion phenomenon on average, relying on advanced analytic combinatorics techniques. We study various measures that contribute to a better understanding of the process behaviours represented as plane rooted trees: the number of runs (corresponding to the width of the trees), the expected total size of the trees as well as their overall shape. Two practical outcomes of our quantitative study are also presented: (1) a linear-time algorithm to compute the probability of a concurrent run prefix, and (2) an efficient algorithm for uniform random sampling of concurrent runs. These provide interesting responses to the combinatorial explosion problem

Novel metrics for evaluating the functional coherence of protein groups via protein semantic network

Metrics are presented for assessing overall functional coherence of a group of proteins based on the associated biomedical literature

Significance Testing Against the Random Model for Scoring Models on Top k Predictions

Performance at top k predictions, where instances are ranked by a (learned) scoring model, has been used as an evaluation metric in machine learning for various reasons such as where the entire corpus is unknown (e.g., the web) or where the results are to be used by a person with limited time or resources (e.g., ranking financial news stories where the investor only has time to look at relatively few stories per day). This evaluation metric is primarily used to report whether the performance of a given method is significantly better than other (baseline) methods. It has not, however, been used to show whether the result is significant when compared to the simplest of baselines â the random model. If no models outperform the random model at a given confidence interval, then the results may not be worth reporting. This paper introduces a technique to perform an analysis of the expected performance of the top k predictions from the random model given k and a p-value on an evaluation dataset D. The technique is based on the realization that the distribution of the number of positives seen in the top k predictions follows a hypergeometric distribution, which has welldefined statistical density functions. As this distribution is discrete, we show that using parametric estimations based on a binomial distribution are almost always in complete agreement with the discrete distribution and that, if they differ, an interpolation of the discrete bounds gets very close to the parametric estimations. The technique is demonstrated on results from three prior published works, in which it clearly shows that even though performance is greatly increased (sometimes over 100%) with respect to the expected performance of the random model (at p = 0.5), these results, although qualitatively impressive, are not always as significant (p = 0.1) as might be suggested by the impressive qualitative improvements. The technique is used to show, given k, both how many positive instances are needed to achieve a specific significance threshold is as well as how significant a given top k performance is. The technique when used in a more global setting is able to identify the crossover points, with respect to k, when a method becomes significant for a given p. Lastly, the technique is used to generate a complete confidence curve, which shows a general trend over all k and visually shows where a method is significantly better than the random model over all values of k.Information Systems Working Papers Serie

Making Presentation Math Computable

This Open-Access-book addresses the issue of translating mathematical expressions from LaTeX to the syntax of Computer Algebra Systems (CAS). Over the past decades, especially in the domain of Sciences, Technology, Engineering, and Mathematics (STEM), LaTeX has become the de-facto standard to typeset mathematical formulae in publications. Since scientists are generally required to publish their work, LaTeX has become an integral part of today's publishing workflow. On the other hand, modern research increasingly relies on CAS to simplify, manipulate, compute, and visualize mathematics. However, existing LaTeX import functions in CAS are limited to simple arithmetic expressions and are, therefore, insufficient for most use cases. Consequently, the workflow of experimenting and publishing in the Sciences often includes time-consuming and error-prone manual conversions between presentational LaTeX and computational CAS formats. To address the lack of a reliable and comprehensive translation tool between LaTeX and CAS, this thesis makes the following three contributions. First, it provides an approach to semantically enhance LaTeX expressions with sufficient semantic information for translations into CAS syntaxes. Second, it demonstrates the first context-aware LaTeX to CAS translation framework LaCASt. Third, the thesis provides a novel approach to evaluate the performance for LaTeX to CAS translations on large-scaled datasets with an automatic verification of equations in digital mathematical libraries. This is an open access book

Systems approaches to drug repositioning

PhD ThesisDrug discovery has overall become less fruitful and more costly, despite vastly increased biomedical knowledge and evolving approaches to Research and Development (R&D). One complementary approach to drug discovery is that of drug repositioning which focusses on identifying novel uses for existing drugs. By focussing on existing drugs that have already reached the market, drug repositioning has the potential to both reduce the timeframe and cost of getting a disease treatment to those that need it. Many marketed examples of repositioned drugs have been found via serendipitous or rational observations, highlighting the need for more systematic methodologies. Systems approaches have the potential to enable the development of novel methods to understand the action of therapeutic compounds, but require an integrative approach to biological data. Integrated networks can facilitate systems-level analyses by combining multiple sources of evidence to provide a rich description of drugs, their targets and their interactions. Classically, such networks can be mined manually where a skilled person can identify portions of the graph that are indicative of relationships between drugs and highlight possible repositioning opportunities. However, this approach is not scalable. Automated procedures are required to mine integrated networks systematically for these subgraphs and bring them to the attention of the user. The aim of this project was the development of novel computational methods to identify new therapeutic uses for existing drugs (with particular focus on active small molecules) using data integration. A framework for integrating disparate data relevant to drug repositioning, Drug Repositioning Network Integration Framework (DReNInF) was developed as part of this work. This framework includes a high-level ontology, Drug Repositioning Network Integration Ontology (DReNInO), to aid integration and subsequent mining; a suite of parsers; and a generic semantic graph integration platform. This framework enables the production of integrated networks maintaining strict semantics that are important in, but not exclusive to, drug repositioning. The DReNInF is then used to create Drug Repositioning Network Integration (DReNIn), a semantically-rich Resource Description Framework (RDF) dataset. A Web-based front end was developed, which includes a SPARQL Protocol and RDF Query Language (SPARQL) endpoint for querying this dataset. To automate the mining of drug repositioning datasets, a formal framework for the definition of semantic subgraphs was established and a method for Drug Repositioning Semantic Mining (DReSMin) was developed. DReSMin is an algorithm for mining semantically-rich networks for occurrences of a given semantic subgraph. This algorithm allows instances of complex semantic subgraphs that contain data about putative drug repositioning opportunities to be identified in a computationally tractable fashion, scaling close to linearly with network data. The ability of DReSMin to identify novel Drug-Target (D-T) associations was investigated. 9,643,061 putative D-T interactions were identified and ranked, with a strong correlation between highly scored associations and those supported by literature observed. The 20 top ranked associations were analysed in more detail with 14 found to be novel and six found to be supported by the literature. It was also shown that this approach better prioritises known D-T interactions, than other state-of-the-art methodologies. The ability of DReSMin to identify novel Drug-Disease (Dr-D) indications was also investigated. As target-based approaches are utilised heavily in the field of drug discovery, it is necessary to have a systematic method to rank Gene-Disease (G-D) associations. Although methods already exist to collect, integrate and score these associations, these scores are often not a reliable re flection of expert knowledge. Therefore, an integrated data-driven approach to drug repositioning was developed using a Bayesian statistics approach and applied to rank 309,885 G-D associations using existing knowledge. Ranked associations were then integrated with other biological data to produce a semantically-rich drug discovery network. Using this network it was shown that diseases of the central nervous system (CNS) provide an area of interest. The network was then systematically mined for semantic subgraphs that capture novel Dr-D relations. 275,934 Dr-D associations were identified and ranked, with those more likely to be side-effects filtered. Work presented here includes novel tools and algorithms to enable research within the field of drug repositioning. DReNIn, for example, includes data that previous comparable datasets relevant to drug repositioning have neglected, such as clinical trial data and drug indications. Furthermore, the dataset may be easily extended using DReNInF to include future data as and when it becomes available, such as G-D association directionality (i.e. is the mutation a loss-of-function or gain-of-function). Unlike other algorithms and approaches developed for drug repositioning, DReSMin can be used to infer any types of associations captured in the target semantic network. Moreover, the approaches presented here should be more generically applicable to other fields that require algorithms for the integration and mining of semantically rich networks.European and Physical Sciences Research Council (EPSRC) and GS

Categorization of interestingness measures for knowledge extraction

Finding interesting association rules is an important and active research field in data mining. The algorithms of the Apriori family are based on two rule extraction measures, support and confidence. Although these two measures have the virtue of being algorithmically fast, they generate a prohibitive number of rules most of which are redundant and irrelevant. It is therefore necessary to use further measures which filter uninteresting rules. Many synthesis studies were then realized on the interestingness measures according to several points of view. Different reported studies have been carried out to identify "good" properties of rule extraction measures and these properties have been assessed on 61 measures. The purpose of this paper is twofold. First to extend the number of the measures and properties to be studied, in addition to the formalization of the properties proposed in the literature. Second, in the light of this formal study, to categorize the studied measures. This paper leads then to identify categories of measures in order to help the users to efficiently select an appropriate measure by choosing one or more measure(s) during the knowledge extraction process. The properties evaluation on the 61 measures has enabled us to identify 7 classes of measures, classes that we obtained using two different clustering techniques.Comment: 34 pages, 4 figure