Konstantinos Sechidis

Information Theoretic Feature Selection in Multi-label Data through Composite Likelihood

In this paper we present a framework to unify information theoretic feature selection criteria for multi-label data. Our framework combines two different ideas; expressing multi-label decomposition methods as composite likelihoods and then showing how feature selection criteria can be derived by maximizing these likelihood expressions. Many existing criteria, until now proposed as heuristics, can be reproduced from a single basis under the proposed framework. Furthermore we can derive new problem-specific criteria by making different independence assumptions over the feature and label spaces. One such derived criterion is shown experimentally to outperform other approaches proposed in the literature on real-world datasets.

Statistical hypothesis testing in positive unlabelled data

We propose a set of novel methodologies which enable valid statistical hypothesis testing when we have only positive and unlabelled (PU) examples. This type of problem, a special case of semi-supervised data, is common in text mining, bioinformatics, and computer vision. Focusing on a generalised likelihood ratio test, we have 3 key contributions: (1) a proof that assuming all unlabelled examples are negative cases is sufficient for independence testing, but not for power analysis activities; (2) a new methodology that compensates this and enables power analysis, allowing sample size determination for observing an effect with a desired power; and finally, (3) a new capability, supervision determination, which can determine a-priori the number of labelled examples the user must collect before being able to observe a desired statistical effect. Beyond general hypothesis testing, we suggest the tools will additionally be useful for information theoretic feature selection, and Bayesian Network structure learning.

Simple strategies for semi-supervised feature selection

What is the simplest thing you can do to solve a problem? In the context of semi-supervised feature selection, we tackle exactly this—how much we can gain from two simple classifier-independent strategies. If we have some binary labelled data and some unlabelled, we could assume the unlabelled data are all positives, or assume them all negatives. These minimalist, seemingly naive, approaches have not previously been studied in depth. However, with theoretical and empirical studies, we show they provide powerful results for feature selection, via hypothesis testing and feature ranking. Combining them with some “soft” prior knowledge of the domain, we derive two novel algorithms (Semi-JMI, Semi-IAMB) that outperform significantly more complex competing methods, showing particularly good performance when the labels are missing-not-at-random. We conclude that simple approaches to this problem can work surprisingly well, and in many situations we can provably recover the exact feature selection dynamics, as if we had labelled the entire dataset.

Exploring the consequences of distributed feature selection in DNA microarray data

Microarray data classification has been typically seen as a difficult challenge for machine learning researchers mainly due to its high dimension in features while sample size is small. Because of this particularity, feature selection is usually applied trying to reduce its high dimensionality. However, existing algorithms may not scale well when dealing with this amount of features, and a possible solution is to distribute the features into several nodes. In this work we explore the process of distribution on microarray data — which has recently gained attention — and we evaluate to what extent it is possible to obtain similar results as those obtained with the whole dataset. We performed experiments with different aggregation methods, feature rankers and also evaluated the effect of distributing the feature ranking process in the subsequent classification performance.

Markov blanket discovery in positive-unlabelled and semi-supervised data

The importance of Markov blanket discovery algorithms is twofold: as the main building block in constraint-based structure learning of Bayesian network algorithms and as a technique to derive the optimal set of features in filter feature selection approaches. Equally, learning from partially labelled data is a crucial and demanding area of machine learning, and extending techniques from fully to partially supervised scenarios is a challenging problem. While there are many different algorithms to derive the Markov blanket of fully supervised nodes, the partially-labelled problem is far more challenging, and there is a lack of principled approaches in the literature. Our work derives a generalization of the conditional tests of independence for partially labelled binary target variables, which can handle the two main partially labelled scenarios: positive-unlabelled and semi-supervised. The result is a significantly deeper understanding of how to control false negative errors in Markov Blanket discovery procedures and how unlabelled data can help.

Dealing with under-reported variables

Under-reporting occurs in survey data when there is a reason for participants to give a false negative response to a question, e.g. maternal smoking in epidemiological studies. Failing to correct this misreporting introduces biases and it may lead to misinformed decision making. Our work provides methods of correcting for this bias, by reinterpreting it as a missing data problem, and particularly learning from positive and unlabelled data. Focusing on information theoretic approaches we have three key contributions: (1) we provide a method to perform valid independence tests with known power by incorporating prior knowledge over misreporting; (2) we derive corrections for point/interval estimates of the mutual information that capture both relevance and redundancy; and finally, (3) we derive different ways for ranking under-reported risk factors. Furthermore, we show how to use our results in real-world problems and machine learning tasks. Information theoretic testing, estimation and ranking in under-reported scenarios.Valid tests with known power by incorporating prior knowledge.Corrections for point/interval estimates of the mutual information.Estimates that capture both relevance and redundancy.Different ways for ranking under-reported.

On the Use of Spearman’s Rho to Measure the Stability of Feature Rankings

Producing stable feature rankings is critical in many areas, such as in bioinformatics where the robustness of a list of ranked genes is crucial to interpretation by a domain expert. In this paper, we study Spearman’s rho as a measure of stability to training data perturbations - not just as a heuristic, but here proving that it is the natural measure of stability when using mean rank aggregation. We provide insights on the properties of this stability measure, allowing a useful interpretation of stability values - e.g. how close a stability value is to that of a purely random feature ranking process, and concepts such as the expected value of a stability estimator.

Distinguishing prognostic and predictive biomarkers: An information theoretic approach

Abstract Motivation The identification of biomarkers to support decision-making is central to personalized medicine, in both clinical and research scenarios. The challenge can be seen in two halves: identifying predictive markers, which guide the development/use of tailored therapies; and identifying prognostic markers, which guide other aspects of care and clinical trial planning, i.e. prognostic markers can be considered as covariates for stratification. Mistakenly assuming a biomarker to be predictive, when it is in fact largely prognostic (and vice-versa) is highly undesirable, and can result in financial, ethical and personal consequences. We present a framework for data-driven ranking of biomarkers on their prognostic/predictive strength, using a novel information theoretic method. This approach provides a natural algebra to discuss and quantify the individual predictive and prognostic strength, in a self-consistent mathematical framework. Results Our contribution is a novel procedure, INFO+, which naturally distinguishes the prognostic versus predictive role of each biomarker and handles higher order interactions. In a comprehensive empirical evaluation INFO+ outperforms more complex methods, most notably when noise factors dominate, and biomarkers are likely to be falsely identified as predictive, when in fact they are just strongly prognostic. Furthermore, we show that our methods can be 1–3 orders of magnitude faster than competitors, making it useful for biomarker discovery in ‘big data’ scenarios. Finally, we apply our methods to identify predictive biomarkers on two real clinical trials, and introduce a new graphical representation that provides greater insight into the prognostic and predictive strength of each biomarker. Availability and implementation R implementations of the suggested methods are available at https://github.com/sechidis. Supplementary information Supplementary data are available at Bioinformatics online.

Disentangling Prognostic and Predictive Biomarkers Through Mutual Information

We study information theoretic methods for ranking biomarkers. In clinical trials, there are two, closely related, types of biomarkers: predictive and prognostic, and disentangling them is a key challenge. Our first step is to phrase biomarker ranking in terms of optimizing an information theoretic quantity. This formalization of the problem will enable us to derive rankings of predictive/prognostic biomarkers, by estimating different, high dimensional, conditional mutual information terms. To estimate these terms, we suggest efficient low dimensional approximations. Finally, we introduce a new visualisation tool that captures the prognostic and the predictive strength of a set of biomarkers. We believe this representation will prove to be a powerful tool in biomarker discovery.