Constraint-based probabilistic learning of metabolic pathways from tomato volatiles

Clustering and correlation analysis techniques have become popular tools for the analysis of data produced by metabolomics experiments. The results obtained from these approaches provide an overview of the interactions between objects of interest. Often in these experiments, one is more interested in information about the nature of these relationships, e.g., cause-effect relationships, than in the actual strength of the interactions. Finding such relationships is of crucial importance as most biological processes can only be understood in this way. Bayesian networks allow representation of these cause-effect relationships among variables of interest in terms of whether and how they influence each other given that a third, possibly empty, group of variables is known. This technique also allows the incorporation of prior knowledge as established from the literature or from biologists. The representation as a directed graph of these relationship is highly intuitive and helps to understand these processes. This paper describes how constraint-based Bayesian networks can be applied to metabolomics data and can be used to uncover the important pathways which play a significant role in the ripening of fresh tomatoes. We also show here how this methods of reconstructing pathways is intuitive and performs better than classical techniques. Methods for learning Bayesian network models are powerful tools for the analysis of data of the magnitude as generated by metabolomics experiments. It allows one to model cause-effect relationships and helps in understanding the underlying processes

To Compress or Not to Compress -- Self-Supervised Learning and Information Theory: A Review

Deep neural networks have demonstrated remarkable performance in supervised learning tasks but require large amounts of labeled data. Self-supervised learning offers an alternative paradigm, enabling the model to learn from data without explicit labels. Information theory has been instrumental in understanding and optimizing deep neural networks. Specifically, the information bottleneck principle has been applied to optimize the trade-off between compression and relevant information preservation in supervised settings. However, the optimal information objective in self-supervised learning remains unclear. In this paper, we review various approaches to self-supervised learning from an information-theoretic standpoint and present a unified framework that formalizes the \textit{self-supervised information-theoretic learning problem}. We integrate existing research into a coherent framework, examine recent self-supervised methods, and identify research opportunities and challenges. Moreover, we discuss empirical measurement of information-theoretic quantities and their estimators. This paper offers a comprehensive review of the intersection between information theory, self-supervised learning, and deep neural networks

Circumventing the Curse of Dimensionality in Prediction: Causal Rate-Distortion for Infinite-Order Markov Processes

Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on finite sequences cannot capture all of their past dependencies. Spectral arguments show that algorithms which cluster finite-length sequences fail dramatically when the underlying process has long-range temporal correlations and can fail even for processes generated by finite-memory hidden Markov models. We circumvent the curse of dimensionality in rate-distortion analysis of infinite-order processes by casting predictive rate-distortion objective functions in terms of the forward- and reverse-time causal states of computational mechanics. Examples demonstrate that the resulting causal rate-distortion theory substantially improves current predictive rate-distortion analyses.Comment: 25 pages, 14 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/cn.ht

Bayesian networks for omics data analysis

This thesis focuses on two aspects of high throughput technologies, i.e. data storage and data analysis, in particular in transcriptomics and metabolomics. Both technologies are part of a research field that is generally called ‘omics’ (or ‘-omics’, with a leading hyphen), which refers to genomics, transcriptomics, proteomics, or metabolomics. Although these techniques study different entities (genes, gene expression, proteins, or metabolites), they all have in common that they use high-throughput technologies such as microarrays and mass spectrometry, and thus generate huge amounts of data. Experiments conducted using these technologies allow one to compare different states of a living cell, for example a healthy cell versus a cancer cell or the effect of food on cell condition, and at different levels. The tools needed to apply omics technologies, in particular microarrays, are often manufactured by different vendors and require separate storage and analysis software for the data generated by them. Moreover experiments conducted using different technologies cannot be analyzed simultaneously to answer a biological question. Chapter 3 presents MADMAX, our software system which supports storage and analysis of data from multiple microarray platforms. It consists of a vendor-independent database which is tightly coupled with vendor-specific analysis tools. Upcoming technologies like metabolomics, proteomics and high-throughput sequencing can easily be incorporated in this system. Once the data are stored in this system, one obviously wants to deduce a biological relevant meaning from these data and here statistical and machine learning techniques play a key role. The aim of such analysis is to search for relationships between entities of interest, such as genes, metabolites or proteins. One of the major goals of these techniques is to search for causal relationships rather than mere correlations. It is often emphasized in the literature that "correlation is not causation" because people tend to jump to conclusions by making inferences about causal relationships when they actually only see correlations. Statistics are often good in finding these correlations; techniques called linear regression and analysis of variance form the core of applied multivariate statistics. However, these techniques cannot find causal relationships, neither are they able to incorporate prior knowledge of the biological domain. Graphical models, a machine learning technique, on the other hand do not suffer from these limitations. Graphical models, a combination of graph theory, statistics and information science, are one of the most exciting things happening today in the field of machine learning applied to biological problems (see chapter 2 for a general introduction). This thesis deals with a special type of graphical models known as probabilistic graphical models, belief networks or Bayesian networks. The advantage of Bayesian networks over classical statistical techniques is that they allow the incorporation of background knowledge from a biological domain, and that analysis of data is intuitive as it is represented in the form of graphs (nodes and edges). Standard statistical techniques are good in describing the data but are not able to find non-linear relations whereas Bayesian networks allow future prediction and discovering nonlinear relations. Moreover, Bayesian networks allow hierarchical representation of data, which makes them particularly useful for representing biological data, since most biological processes are hierarchical by nature. Once we have such a causal graph made either by a computer program or constructed manually we can predict the effects of a certain entity by manipulating the state of other entities, or make backward inferences from effects to causes. Of course, if the graph is big, doing the necessary calculations can be very difficult and CPU-expensive, and in such cases approximate methods are used. Chapter 4 demonstrates the use of Bayesian networks to determine the metabolic state of feeding and fasting mice to determine the effect of a high fat diet on gene expression. This chapter also shows how selection of genes based on key biological processes generates more informative results than standard statistical tests. In chapter 5 the use of Bayesian networks is shown on the combination of gene expression data and clinical parameters, to determine the effect of smoking on gene expression and which genes are responsible for the DNA damage and the raise in plasma cotinine levels of blood of a smoking population. This study was conducted at Maastricht University where 22 twin smokers were profiled. Chapter 6 presents the reconstruction of a key metabolic pathway which plays an important role in ripening of tomatoes, thus showing the versatility of the use of Bayesian networks in metabolomics data analysis. The general trend in research shows a flood of data emerging from sequencing and metabolomics experiments. This means that to perform data mining on these data one requires intelligent techniques that are computationally feasible and able to take the knowledge of experts into account to generate relevant results. Graphical models fit this paradigm well and we expect them to play a key role in mining the data generated from omics experiments. <br/

Essential hidden variables: an introduction and novel algorithm for detection

It has recently been shown that Bayesian networks with hidden variables represent a wider range of probabilistic distributions than Bayesian networks without hidden variables. After introducing the general concept of a hidden variable and how it can be understood in Bayesian networks, we present a distinction between optimizing and essential hidden variables. We propose that it is only essential hidden variables that add representational power to Bayesian networks. We then explain past research with hidden variables in light of this new distinction and implement an exploratory algorithm to find essential hidden variables and to examine the conditions on the distribution that hint at their existence

The information bottleneck EM algorithm

Learning with hidden variables is a central challenge in probabilistic graphical models that has important implications for many real-life problems. The classical approach is using the Expectation Maximization (EM) algorithm. This algorithm, however, can get trapped in local maxima. In this paper we explore a new approach that is based on the Information Bottleneck principle. In this approach, we view the learning problem as a tradeoff between two information theoretic objectives. The first is to make the hidden variables uninformative about the identity of specific instances. The second is to make the hidden variables informative about the observed attributes. By exploring different tradeoffs between these two objectives, we can gradually converge on a high-scoring solution. As we show, the resulting, Information Bottleneck Expectation Maximization (IB-EM) algorithm, manages to find solutions that are superior to standard EM methods.

The Information Bottleneck EM Algorithm

In this paper, we introduce a new approach to learningBayesian networks with hidden variables. In this approach, we view the learning problem as a tradeoff between twoinformation theoretic objectives. The first objective is to compress information about the training data. The sec-ond objective is to make the hidden variables informativ