Exploring associations between molecular features and categorical factors, like disease status, is a crucial task in metabolomics data analysis, demanding exceptional rigor. However, data imbalance and crossed factorial design complicate the selection of appropriate analysis settings. This paper presents a comparative study of candidate analysis settings for unbalanced metabolomics data, focusing on Parkinson’s disease with gender as a background factor. The study evaluates two statistical test methods, pairwise t-tests and 2-way ANOVA, combined with two multiple hypothesis correction strategies: global correction and two-stage correction. Additionally, an unconditional analysis setting is examined, which can be easily misapplied due to its disregard for data imbalance and factor interactions. We profile the characteristics of each setting through experiments on real-world datasets from human samples and provide practical guidance for selecting appropriate settings to enhance the reliability of metabolomics studies.

Statistically sound pattern discovery harnesses the rigour of statistical hypothesis testing to overcome many of the issues that have hampered standard data mining approaches to pattern discovery. Most importantly, application of appropriate statistical tests allows precise control over the risk of false discoveries—patterns that are found in the sample data but do not hold in the wider population from which the sample was drawn. Statistical tests can also be applied to filter out patterns that are unlikely to be useful, removing uninformative variations of the key patterns in the data. This tutorial introduces the key statistical and data mining theory and techniques that underpin this fast developing field. We concentrate on two general classes of patterns: dependency rules that express statistical dependencies between condition and consequent parts and dependency sets that express mutual dependence between set elements. We clarify alternative interpretations of statistical dependence and introduce appropriate tests for evaluating statistical significance of patterns in different situations. We also introduce special techniques for controlling the likelihood of spurious discoveries when multitudes of patterns are evaluated. The paper is aimed at a wide variety of audiences. It provides the necessary statistical background and summary of the state-of-the-art for any data mining researcher or practitioner wishing to enter or understand statistically sound pattern discovery research or practice. It can serve as a general introduction to the field of statistically sound pattern discovery for any reader with a general background in data sciences.

We present theoretical analysis and a suite of tests and procedures for addressing a broad class of redundant and misleading association rules we call specious rules. Specious dependencies, also known as spurious, apparent, or illusory associations, refer to a well-known phenomenon where marginal dependencies are merely products of interactions with other variables and disappear when conditioned on those variables. The most extreme example is Yule-Simpson's paradox where two variables present positive dependence in the marginal contingency table but negative in all partial tables defined by different levels of a confounding factor. It is accepted wisdom that in data of any nontrivial dimensionality it is infeasible to control for all of the exponentially many possible confounds of this nature. In this paper, we consider the problem of specious dependencies in the context of statistical association rule mining. We define specious rules and show they offer a unifying framework which covers many types of previously proposed redundant or misleading association rules. After theoretical analysis, we introduce practical algorithms for detecting and pruning out specious association rules efficiently under many key goodness measures, including Mutual information and exact hypergeometric probabilities. We demonstrate that the procedure greatly reduces the number of associations discovered, providing an elegant and effective solution to the problem of association mining discovering large numbers of misleading and redundant rules.

Pattern discovery is a core data mining activity. Initial approaches were dominated by the frequent pattern discovery paradigm -- only patterns that occur frequently in the data were explored. Having been thoroughly researched and its limitations now well understood, this paradigm is giving way to a new one, which can be called statistically sound pattern discovery. In this paradigm, the main impetus is to discover statistically significant patterns, which are unlikely to have occurred by chance and are likely to hold in future data. Thus, the new paradigm provides a strict control over false discoveries and overfitting.

A current trend in activity recognition is to use just one easily carried accelerometer, either integrated into a mobile phone, carried in a pocket, or attached to an animal's collar. The main disadvantage of this approach is that the orientation of the accelerometer is generally unknown. Therefore, one cannot separate body-related accelerations from the gravitational acceleration or determine the real directions of the observed accelerations accurately. As a solution, we introduce a new technique where jerk (changes of accelerations) is analyzed instead of the original acceleration signal. The total jerk magnitude is completely orientation-independent and it reflects only body-related accelerations. If the direction of the gravitation can be approximated even loosely, then the jerk signal can be further enriched with valuable information on jerk angles (direction changes). According to our experiments this kind of jerk-filtered signal produces robust features and can improve the recognition accuracy remarkably.

Dependency analysis is one of the central problems in bioinformatics and all empirical science. In genetics, for example, an important problem is to find which gene alleles are mutually dependent or which alleles and diseases are dependent. In ecology, a similar problem is to find dependencies between different species or groups of species. In both cases a classical solution is to consider all pairwise dependencies between single attributes and evaluate the relationships with some statistical measure like the χ 2 -measure. It is known that the actual dependency structures can involve more attributes, but the existing computational methods are too inefficient for such an exhaustive search. In this paper, we introduce efficient search methods for positive dependencies of the form X → A with typical statistical measures. The efficiency is achieved by a special kind of a branch-and-bound search which also prunes out redundant rules. Redundant attributes are especially harmful in dependency analysis, because they can blur the actual dependencies and even lead to erroneous conclusions. We consider two alternative definitions of redundancy: the classical one and a stricter one. We improve our previous algorithm for searching for the best strictly non-redundant dependency rules and introduce a totally new algorithm for searching for the best classically non-redundant rules. According to our experiments, both algorithms can prune the search space very efficiently, and in practice no minimum frequency thresholds are needed. This is an important benefit, because biological data sets are typically dense, and the alternative search methods would require too large minimum frequency thresholds for any practical purpose.

Statistical dependency analysis is the basis of all empirical science. A commonly occurring problem is to find the most significant dependency rules, which describe either positive or negative dependencies between categorical attributes. For example, in medical science one is interested in genetic factors, which can either predispose or prevent diseases. The requirement of statistical significance is essential, because the discoveries should hold also in the future data. Typically, the significance is estimated either by Fisher's exact test or the χ2-measure. The problem is computationally very difficult, because the number of all possible dependency rules increases exponentially with the number of attributes. As a solution, different kinds of restrictions and heuristics have been applied, but a general, scalable search method has been missing. In this paper, we introduce an efficient algorithm for searching for the top-K globally optimal dependency rules using Fisher's exact test as a measure function. The rules can express either positive or negative dependencies between a set of positive attributes and a single consequent attribute. The algorithm is based on an application of the branch- and-bound search strategy, supplemented by several pruning properties. Especially, we prove a new lower-bound for the Fisher's p, and introduce a new effective pruning principle. The general search algorithm is applicable to other goodness measures, like the χ2-measure, as well. According to our experiments on classical benchmark data, the algorithm is well scalable and can efficiently handle even dense and high dimensional data sets. In addition, the quality of rules is significantly better than with the χ2-measure using the same search algorithm.

Searching statistically significant association rules is an important but neglected problem. Traditional association rules do not capture the idea of statistical dependence and the resulting rules can be spurious, while the most significant rules may be missing. This leads to erroneous models and predictions which often become expensive.The problem is computationally very difficult, because the significance is not a monotonic property. However, in this paper we prove several other properties, which can be used for pruning the search space. The properties are implemented in the StatApriori algorithm, which searches statistically significant, non-redundant association rules. Based on both theoretical and empirical observations, the resulting rules are very accurate compared to traditional association rules. In addition, StatApriori can work with extremely low frequencies, thus finding new interesting rules.