Penalized weighted low-rank approximation for robust recovery of recurrent copy number variations

2015-2016 UNCG University Libraries Open Access Publishing Fund Grant Winner. BackgroundCopy number variation (CNV) analysis has become one of the most important researchareas for understanding complex disease. With increasing resolution of array-basedcomparative genomic hybridization (aCGH) arrays, more and more raw copy numberdata are collected for multiple arrays. It is natural to realize the co-existence of bothrecurrent and individual-specific CNVs, together with the possible data contaminationduring the data generation process. Therefore, there is a great need for an efficient androbust statistical model for simultaneous recovery of both recurrent and individualspecificCNVs.ResultWe develop a penalized weighted low-rank approximation method (WPLA) for robustrecovery of recurrent CNVs. In particular, we formulate multiple aCGH arrays into arealization of a hidden low-rank matrix with some random noises and let an additionalweight matrix account for those individual-specific effects. Thus, we do not restrict therandom noise to be normally distributed, or even homogeneous. We show itsperformance through three real datasets and twelve synthetic datasets from different typesof recurrent CNV regions associated with either normal random errors or heavilycontaminated errors.ConclusionOur numerical experiments have demonstrated that the WPLA can successfully recoverthe recurrent CNV patterns from raw data under different scenarios. Compared with twoother recent methods, it performs the best regarding its ability to simultaneously detectboth recurrent and individual-specific CNVs under normal random errors. Moreimportantly, the WPLA is the only method which can effectively recover the recurrentCNVs region when the data is heavily contaminated

Optimization for Probabilistic Machine Learning

We have access to great variety of datasets more than any time in the history. Everyday, more data is collected from various natural resources and digital platforms. Great advances in the area of machine learning research in the past few decades have relied strongly on availability of these datasets. However, analyzing them imposes significant challenges that are mainly due to two factors. First, the datasets have complex structures with hidden interdependencies. Second, most of the valuable datasets are high dimensional and are largely scaled. The main goal of a machine learning framework is to design a model that is a valid representative of the observations and develop a learning algorithm to make inference about unobserved or latent data based on the observations. Discovering hidden patterns and inferring latent characteristics in such datasets is one of the greatest challenges in the area of machine learning research. In this dissertation, I will investigate some of the challenges in modeling and algorithm design, and present my research results on how to overcome these obstacles. Analyzing data generally involves two main stages. The first stage is designing a model that is flexible enough to capture complex variation and latent structures in data and is robust enough to generalize well to the unseen data. Designing an expressive and interpretable model is one of crucial objectives in this stage. The second stage involves training learning algorithm on the observed data and measuring the accuracy of model and learning algorithm. This stage usually involves an optimization problem whose objective is to tune the model to the training data and learn the model parameters. Finding global optimal or sufficiently good local optimal solution is one of the main challenges in this step. Probabilistic models are one of the best known models for capturing data generating process and quantifying uncertainties in data using random variables and probability distributions. They are powerful models that are shown to be adaptive and robust and can scale well to large datasets. However, most probabilistic models have a complex structure. Training them could become challenging commonly due to the presence of intractable integrals in the calculation. To remedy this, they require approximate inference strategies that often results in non-convex optimization problems. The optimization part ensures that the model is the best representative of data or data generating process. The non-convexity of an optimization problem take away the general guarantee on finding a global optimal solution. It will be shown later in this dissertation that inference for a significant number of probabilistic models require solving a non-convex optimization problem. One of the well-known methods for approximate inference in probabilistic modeling is variational inference. In the Bayesian setting, the target is to learn the true posterior distribution for model parameters given the observations and prior distributions. The main challenge involves marginalization of all the other variables in the model except for the variable of interest. This high-dimensional integral is generally computationally hard, and for many models there is no known polynomial time algorithm for calculating them exactly. Variational inference deals with finding an approximate posterior distribution for Bayesian models where finding the true posterior distribution is analytically or numerically impossible. It assumes a family of distribution for the estimation, and finds the closest member of that family to the true posterior distribution using a distance measure. For many models though, this technique requires solving a non-convex optimization problem that has no general guarantee on reaching a global optimal solution. This dissertation presents a convex relaxation technique for dealing with hardness of the optimization involved in the inference. The proposed convex relaxation technique is based on semidefinite optimization that has a general applicability to polynomial optimization problem. I will present theoretical foundations and in-depth details of this relaxation in this work. Linear dynamical systems represent the functionality of many real-world physical systems. They can describe the dynamics of a linear time-varying observation which is controlled by a controller unit with quadratic cost function objectives. Designing distributed and decentralized controllers is the goal of many of these systems, which computationally, results in a non-convex optimization problem. In this dissertation, I will further investigate the issues arising in this area and develop a convex relaxation framework to deal with the optimization challenges. Setting the correct number of model parameters is an important aspect for a good probabilistic model. If there are only a few parameters, model may lack capturing all the essential relations and components in the observations while too many parameters may cause significant complications in learning or overfit to the observations. Non-parametric models are suitable techniques to deal with this issue. They allow the model to learn the appropriate number of parameters to describe the data and make predictions. In this dissertation, I will present my work on designing Bayesian non-parametric models as powerful tools for learning representations of data. Moreover, I will describe the algorithm that we derived to efficiently train the model on the observations and learn the number of model parameters. Later in this dissertation, I will present my works on designing probabilistic models in combination with deep learning methods for representing sequential data. Sequential datasets comprise a significant portion of resources in the area of machine learning research. Designing models to capture dependencies in sequential datasets are of great interest and have a wide variety of applications in engineering, medicine and statistics. Recent advances in deep learning research has shown exceptional promises in this area. However, they lack interpretability in their general form. To remedy this, I will present my work on mixing probabilistic models with neural network models that results in better performance and expressiveness of the results

Hypothesis testing and causal inference with heterogeneous medical data

Learning from data which associations hold and are likely to hold in the future is a fundamental part of scientific discovery. With increasingly heterogeneous data collection practices, exemplified by passively collected electronic health records or high-dimensional genetic data with only few observed samples, biases and spurious correlations are prevalent. These are called spurious because they do not contribute to the effect being studied. In this context, the modelling assumptions of existing statistical tests and causal inference methods are often found inadequate and their practical utility diminished even though these models are increasingly used as decision-support tools in practice. This thesis investigates how modern computational techniques may broaden the fields of hypothesis testing and causal inference to handle the subtleties of large heterogeneous data sets, as well as simultaneously improve the robustness and theoretical understanding of machine learning algorithms using insights from causality and statistics. The first part of this thesis is concerned with hypothesis testing. We develop a framework for hypothesis testing on set-valued data, a representation that faithfully describes many real-world phenomena including patient biomarker trajectories in the hospital. Using similar techniques, we develop next a two-sample test for making inference on selection-biased data, in the sense that not all individuals are equally likely to be included in the study, a fact that biases tests if not accounted for and if the desideratum is to obtain conclusions that are generally applicable. We conclude this section with an investigation of conditional independence in high-dimensional data, such as found in gene expression data, and propose a test using generative adversarial networks. The second part of this thesis is concerned with causal inference and discovery, with a special focus on the influence of unobserved confounders that distort the observed associations between variables and yet may not be ruled out or adjusted for using data alone. We start by demonstrating that unobserved confounders may bias substantially the generalization performance of machine learning algorithms trained with conventional learning paradigms such as empirical risk minimization. Acknowledging this spurious effect, we develop a new learning principle inspired by causal insights that provably generalizes to test data sampled from a larger set of distributions different from the training distribution. In the last chapter we consider the influence of unobserved confounders for causal discovery. We show that with some assumptions on the type and influence on the nature of unobserved confounding one may develop provably consistent causal discovery algorithms, formulated as a solution to a continuous optimization program

Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain

The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio

Finding regions of aberrant DNA copy number associated with tumor phenotype

DNA copy number alterations are a hallmark of cancer. Understanding their role in tumor progression can help improve diagnosis, prognosis and therapy selection for cancer patients. High-resolution, genome-wide measurements of DNA copy number changes for large cohorts of tumors are currently available, owing to technologies like microarray-based array comparative hybridization (arrayCGH). In this thesis, we present a computational pipeline for statistical analysis of tumor cohorts, which can help extract relevant patterns of copy number aberrations and infer their association with various phenotypical indicators. The main challenges are the instability of classification models due to the high dimensionality of the arrays compared to the small number of tumor samples, as well as the large correlations between copy number estimates measured at neighboring loci. We show that the feature ranking given by several widely-used methods for feature selection is biased due to the large correlations between features. In order to correct for the bias and instability of the feature ranking, we introduce methods for consensus segmentation of the set of arrays. We present three algorithms for consensus segmentation, which are based on identifying recurrent DNA breakpoints or DNA regions of constant copy number profile. The segmentation constitutes the basis for computing a set of super-features, corresponding to the regions. We use the super-features for supervised classification and we compare the models to baseline models trained on probe data. We validated the methods by training models for prediction of the phenotype of breast cancers and neuroblastoma tumors. We show that the multivariate segmentation affords higher model stability, in general improves prediction accuracy and facilitates model interpretation. One of our most important biological results refers to the classification of neuroblastoma tumors. We show that patients belonging to different age subgroups are characterized by distinct copy number patterns, with largest discrepancy when the subgroups are defined as older or younger than 16-18 months. We thereby confirm the recommendation for a higher age cutoff than 12 months (current clinical practice) for differential diagnosis of neuroblastoma.Die abnormale Multiplizität bestimmter Segmente der DNS (copy number aberrations) ist eines der hervorstechenden Merkmale von Krebs. Das Verständnis der Rolle dieses Merkmals für das Tumorwachstum könnte massgeblich zur Verbesserung von Krebsdiagnose,-prognose und -therapie beitragen und somit bei der Auswahl individueller Therapien helfen. Micoroarray-basierte Technologien wie 'Array Comparative Hybridization' (array-CGH) erlauben es, hochauflösende, genomweite Kopiezahl-Karten von Tumorgeweben zu erstellen. Gegenstand dieser Arbeit ist die Entwicklung einer Software-Pipeline für die statistische Analyse von Tumorkohorten, die es ermöglicht, relevante Muster abnormaler Kopiezahlen abzuleiten und diese mit diversen phänotypischen Merkmalen zu assoziieren. Dies geschieht mithilfe maschineller Lernmethoden für Klassifikation und Merkmalselektion mit Fokus auf die Interpretierbarkeit der gelernten Modelle (regularisierte lineare Methoden sowie Entscheidungsbaum-basierte Modelle). Herausforderungen an die Methoden liegen vor allem in der hohen Dimensionalität der Daten, denen lediglich eine vergleichsweise geringe Anzahl von gemessenen Tumorproben gegenüber steht, sowie der hohen Korrelation zwischen den gemessenen Kopiezahlen in benachbarten genomischen Regionen. Folglich hängen die Resultate der Merkmalselektion stark von der Auswahl des Trainingsdatensatzes ab, was die Reproduzierbarkeit bei unterschiedlichen klinischen Datensätzen stark einschränkt. Diese Arbeit zeigt, dass die von diversen gängigen Methoden bestimmte Rangfolge von Features in Folge hoher Korrelationskoefizienten einzelner Prädiktoren stark verfälscht ist. Um diesen 'Bias' sowie die Instabilität der Merkmalsrangfolge zu korrigieren, führen wir in unserer Pipeline einen dimensions-reduzierenden Schritt ein, der darin besteht, die Arrays gemeinsam multivariat zu segmentieren. Wir präsentieren drei Algorithmen für diese multivariate Segmentierung,die auf der Identifikation rekurrenter DNA Breakpoints oder genomischer Regionen mit konstanten Kopiezahl-Profilen beruhen. Durch Zusammenfassen der DNA Kopiezahlwerte innerhalb einer Region bildet die multivariate Segmentierung die Grundlage für die Berechnung einer kleineren Menge von 'Super-Merkmalen'. Im Vergleich zu Klassifikationsverfahren,die auf Ebene einzelner Arrayproben beruhen, verbessern wir durch überwachte Klassifikation basierend auf den Super-Merkmalen die Interpretierbarkeit sowie die Stabilität der Modelle. Wir validieren die Methoden in dieser Arbeit durch das Trainieren von Vorhersagemodellen auf Brustkrebs und Neuroblastoma Datensätzen. Hier zeigen wir, dass der multivariate Segmentierungsschritt eine erhöhte Modellstabilität erzielt, wobei die Vorhersagequalität nicht abnimmt. Die Dimension des Problems wird erheblich reduziert (bis zu 200-fach weniger Merkmale), welches die multivariate Segmentierung nicht nur zu einem probaten Mittel für die Vorhersage von Phänotypen macht.Vielmehr eignet sich das Verfahren darüberhinaus auch als Vorverarbeitungschritt für spätere integrative Analysen mit anderen Datentypen. Auch die Interpretierbarkeit der Modelle wird verbessert. Dies ermöglicht die Identifikation von wichtigen Relationen zwischen Änderungen der Kopiezahl und Phänotyp. Beispielsweise zeigen wir, dass eine Koamplifikation in direkter Nachbarschaft des ERBB2 Genlokus einen höchst informativen Prädiktor für die Unterscheidung von entzündlichen und nicht-entzündlichen Brustkrebsarten darstellt. Damit bestätigen wir die in der Literatur gängige Hypothese, dass die Grösse eines Amplikons mit dem Krebssubtyp zusammenhängt. Im Fall von Neuroblastoma Tumoren zeigen wir, dass Untergruppen, die durch das Alter des Patienten deniert werden, durch Kopiezahl-Muster charakterisiert werden können. Insbesondere ist dies möglich, wenn ein Altersschwellenwert von 16 bis 18 Monaten zur Definition der Gruppen verwandt wird, bei dem ausserdem auch die höchste Vorhersagegenauigkeit vorliegt. Folglich geben wir weitere Evidenz für die Empfehlung, einen höheren Schwellenwert als zwölf Monate für die differentielle Diagnose von Neuroblastoma zu verwenden

Book of Abstracts XVIII Congreso de Biometría CEBMADRID

Abstracts of the XVIII Congreso de Biometría CEBMADRID held from 25 to 27 May in MadridInteractive modelling and prediction of patient evolution via multistate models / Leire Garmendia Bergés, Jordi Cortés Martínez and Guadalupe Gómez Melis : This research was funded by the Ministerio de Ciencia e Innovación (Spain) [PID2019104830RBI00]; and the Generalitat de Catalunya (Spain) [2017SGR622 and 2020PANDE00148].Operating characteristics of a model-based approach to incorporate non-concurrent controls in platform trials / Pavla Krotka, Martin Posch, Marta Bofill Roig : EU-PEARL (EU Patient-cEntric clinicAl tRial pLatforms) project has received funding from the Innovative Medicines Initiative (IMI) 2 Joint Undertaking (JU) under grant agreement No 853966. This Joint Undertaking receives support from the European Union’s Horizon 2020 research and innovation programme and EFPIA and Children’s Tumor Foundation, Global Alliance for TB Drug Development non-profit organisation, Spring works Therapeutics Inc.Modeling COPD hospitalizations using variable domain functional regression / Pavel Hernández Amaro, María Durbán Reguera, María del Carmen Aguilera Morillo, Cristobal Esteban Gonzalez, Inma Arostegui : This work is supported by the grant ID2019-104901RB-I00 from the Spanish Ministry of Science, Innovation and Universities MCIN/AEI/10.13039/501100011033.Spatio-temporal quantile autoregression for detecting changes in daily temperature in northeastern Spain / Jorge Castillo-Mateo, Alan E. Gelfand, Jesús Asín, Ana C. Cebrián / Spatio-temporal quantile autoregression for detecting changes in daily temperature in northeastern Spain : This work was partially supported by the Ministerio de Ciencia e Innovación under Grant PID2020-116873GB-I00; Gobierno de Aragón under Research Group E46_20R: Modelos Estocásticos; and JC-M was supported by Gobierno de Aragón under Doctoral Scholarship ORDEN CUS/581/2020.Estimation of the area under the ROC curve with complex survey data / Amaia Iparragirre, Irantzu Barrio, Inmaculada Arostegui : This work was financially supported in part by IT1294-19, PID2020-115882RB-I00, KK-2020/00049. The work of AI was supported by PIF18/213.INLAMSM: Adjusting multivariate lattice models with R and INLA / Francisco Palmí Perales, Virgilio Gómez Rubio and Miguel Ángel Martínez Beneito : This work has been supported by grants PPIC-2014-001-P and SBPLY/17/180501/000491, funded by Consejería de Educación, Cultura y Deportes (Junta de Comunidades de Castilla-La Mancha, Spain) and FEDER, grant MTM2016-77501-P, funded by Ministerio de Economía y Competitividad (Spain), grant PID2019-106341GB-I00 from Ministerio de Ciencia e Innovación (Spain) and a grant to support research groups by the University of Castilla-La Mancha (Spain). F. Palmí-Perales has been supported by a Ph.D. scholarship awarded by the University of Castilla-La Mancha (Spain)

Learning to process with spikes and to localise pulses

In the last few decades, deep learning with artificial neural networks (ANNs) has emerged as one of the most widely used techniques in tasks such as classification and regression, achieving competitive results and in some cases even surpassing human-level performance. Nonetheless, as ANN architectures are optimised towards empirical results and departed from their biological precursors, how exactly human brains process information using these short electrical pulses called spikes remains a mystery. Hence, in this thesis, we explore the problem of learning to process with spikes and to localise pulses. We first consider spiking neural networks (SNNs), a type of ANN that more closely mimic biological neural networks in that neurons communicate with one another using spikes. This unique architecture allows us to look into the role of heterogeneity in learning. Since it is conjectured that the information is encoded by the timing of spikes, we are particularly interested in the heterogeneity of time constants of neurons. We then trained SNNs for classification tasks on a range of visual and auditory neuromorphic datasets, which contain streams of events (spike times) instead of the conventional frame-based data, and show that the overall performance is improved by allowing the neurons to have different time constants, especially on tasks with richer temporal structure. We also find that the learned time constants are distributed similarly to those experimentally observed in some mammalian cells. Besides, we demonstrate that learning with heterogeneity improves robustness against hyperparameter mistuning. These results suggest that heterogeneity may be more than the byproduct of noisy processes and perhaps serves a key role in learning in changing environments, yet heterogeneity has been overlooked in basic artificial models. While neuromorphic datasets, which are often captured by neuromorphic devices that closely model the corresponding biological systems, have enabled us to explore the more biologically plausible SNNs, there still exists a gap in understanding how spike times encode information in actual biological neural networks like human brains, as such data is difficult to acquire due to the trade-off between the timing precision and the number of cells simultaneously recorded electrically. Instead, what we usually obtain is the low-rate discrete samples of trains of filtered spikes. Hence, in the second part of the thesis, we focus on a different type of problem involving pulses, that is to retrieve the precise pulse locations from these low-rate samples. We make use of the finite rate of innovation (FRI) sampling theory, which states that perfect reconstruction is possible for classes of continuous non-bandlimited signals that have a small number of free parameters. However, existing FRI methods break down under very noisy conditions due to the so-called subspace swap event. Thus, we present two novel model-based learning architectures: Deep Unfolded Projected Wirtinger Gradient Descent (Deep Unfolded PWGD) and FRI Encoder-Decoder Network (FRIED-Net). The former is based on the existing iterative denoising algorithm for subspace-based methods, while the latter models directly the relationship between the samples and the locations of the pulses using an autoencoder-like network. Using a stream of K Diracs as an example, we show that both algorithms are able to overcome the breakdown inherent in the existing subspace-based methods. Moreover, we extend our FRIED-Net framework beyond conventional FRI methods by considering when the shape is unknown. We show that the pulse shape can be learned using backpropagation. This coincides with the application of spike detection from real-world calcium imaging data, where we achieve competitive results. Finally, we explore beyond canonical FRI signals and demonstrate that FRIED-Net is able to reconstruct streams of pulses with different shapes.Open Acces

Statistical learning methods for multi-omics data integration in dimension reduction, supervised and unsupervised machine learning

Over the decades, many statistical learning techniques such as supervised learning, unsupervised learning, dimension reduction technique have played ground breaking roles for important tasks in biomedical research. More recently, multi-omics data integration analysis has become increasingly popular to answer to many intractable biomedical questions, to improve statistical power by exploiting large size samples and different types omics data, and to replicate individual experiments for validation. This dissertation covers the several analytic methods and frameworks to tackle with practical problems in multi-omics data integration analysis. Supervised prediction rules have been widely applied to high-throughput omics data to predict disease diagnosis, prognosis or survival risk. The top scoring pair (TSP) algorithm is a supervised discriminant rule that applies a robust simple rank-based algorithm to identify rank-altered gene pairs in case/control classes. TSP usually generates greatly reduced accuracy in inter-study prediction (i.e., the prediction model is established in the training study and applied to an independent test study). In the first part, we introduce a MetaTSP algorithm that combines multiple transcriptomic studies and generates a robust prediction model applicable to independent test studies. One important objective of omics data analysis is clustering unlabeled patients in order to identify meaningful disease subtypes. In the second part, we propose a group structured integrative clustering method to incorporate a sparse overlapping group lasso technique and a tight clustering via regularization to integrate inter-omics regulation flow, and to encourage outlier samples scattering away from tight clusters. We show by two real examples and simulated data that our proposed methods improve the existing integrative clustering in clustering accuracy, biological interpretation, and are able to generate coherent tight clusters. Principal component analysis (PCA) is commonly used for projection to low-dimensional space for visualization. In the third part, we introduce two meta-analysis frameworks of PCA (Meta-PCA) for analyzing multiple high-dimensional studies in common principal component space. Theoretically, Meta-PCA specializes to identify meta principal component (Meta-PC) space; (1) by decomposing the sum of variances and (2) by minimizing the sum of squared cosines. Applications to various simulated data shows that Meta-PCAs outstandingly identify true principal component space, and retain robustness to noise features and outlier samples. We also propose sparse Meta-PCAs that penalize principal components in order to selectively accommodate significant principal component projections. With several simulated and real data applications, we found Meta-PCA efficient to detect significant transcriptomic features, and to recognize visual patterns for multi-omics data sets. In the future, the success of data integration analysis will play an important role in revealing the molecular and cellular process inside multiple data, and will facilitate disease subtype discovery and characterization that improve hypothesis generation towards precision medicine, and potentially advance public health research