367 research outputs found
A convex pseudo-likelihood framework for high dimensional partial correlation estimation with convergence guarantees
Sparse high dimensional graphical model selection is a topic of much interest
in modern day statistics. A popular approach is to apply l1-penalties to either
(1) parametric likelihoods, or, (2) regularized regression/pseudo-likelihoods,
with the latter having the distinct advantage that they do not explicitly
assume Gaussianity. As none of the popular methods proposed for solving
pseudo-likelihood based objective functions have provable convergence
guarantees, it is not clear if corresponding estimators exist or are even
computable, or if they actually yield correct partial correlation graphs. This
paper proposes a new pseudo-likelihood based graphical model selection method
that aims to overcome some of the shortcomings of current methods, but at the
same time retain all their respective strengths. In particular, we introduce a
novel framework that leads to a convex formulation of the partial covariance
regression graph problem, resulting in an objective function comprised of
quadratic forms. The objective is then optimized via a coordinate-wise
approach. The specific functional form of the objective function facilitates
rigorous convergence analysis leading to convergence guarantees; an important
property that cannot be established using standard results, when the dimension
is larger than the sample size, as is often the case in high dimensional
applications. These convergence guarantees ensure that estimators are
well-defined under very general conditions, and are always computable. In
addition, the approach yields estimators that have good large sample properties
and also respect symmetry. Furthermore, application to simulated/real data,
timing comparisons and numerical convergence is demonstrated. We also present a
novel unifying framework that places all graphical pseudo-likelihood methods as
special cases of a more general formulation, leading to important insights
Machine Learning and Integrative Analysis of Biomedical Big Data.
Recent developments in high-throughput technologies have accelerated the accumulation of massive amounts of omics data from multiple sources: genome, epigenome, transcriptome, proteome, metabolome, etc. Traditionally, data from each source (e.g., genome) is analyzed in isolation using statistical and machine learning (ML) methods. Integrative analysis of multi-omics and clinical data is key to new biomedical discoveries and advancements in precision medicine. However, data integration poses new computational challenges as well as exacerbates the ones associated with single-omics studies. Specialized computational approaches are required to effectively and efficiently perform integrative analysis of biomedical data acquired from diverse modalities. In this review, we discuss state-of-the-art ML-based approaches for tackling five specific computational challenges associated with integrative analysis: curse of dimensionality, data heterogeneity, missing data, class imbalance and scalability issues
Distributionally Robust Skeleton Learning of Discrete Bayesian Networks
We consider the problem of learning the exact skeleton of general discrete
Bayesian networks from potentially corrupted data. Building on distributionally
robust optimization and a regression approach, we propose to optimize the most
adverse risk over a family of distributions within bounded Wasserstein distance
or KL divergence to the empirical distribution. The worst-case risk accounts
for the effect of outliers. The proposed approach applies for general
categorical random variables without assuming faithfulness, an ordinal
relationship or a specific form of conditional distribution. We present
efficient algorithms and show the proposed methods are closely related to the
standard regularized regression approach. Under mild assumptions, we derive
non-asymptotic guarantees for successful structure learning with logarithmic
sample complexities for bounded-degree graphs. Numerical study on synthetic and
real datasets validates the effectiveness of our method. Code is available at
https://github.com/DanielLeee/drslbn.Comment: NeurIPS 2O23 Spotlight. More empirical results adde
Improved genome-scale multitarget virtual screening via a novel collaborative filtering approach to cold-start problem
Conventional one-drug-one-gene approach has been of limited success in modern drug discovery. Polypharmacology, which focuses on searching for multi-targeted drugs to perturb disease-causing networks instead of designing selective ligands to target individual proteins, has emerged as a new drug discovery paradigm. Although many methods for single-target virtual screening have been developed to improve the efficiency of drug discovery, few of these algorithms are designed for polypharmacology. Here, we present a novel theoretical framework and a corresponding algorithm for genome-scale multitarget virtual screening based on the one-class collaborative filtering technique. Our method overcomes the sparseness of the protein-chemical interaction data by means of interaction matrix weighting and dual regularization from both chemicals and proteins. While the statistical foundation behind our method is general enough to encompass genome-wide drug off-target prediction, the program is specifically tailored to find protein targets for new chemicals with little to no available interaction data. We extensively evaluate our method using a number of the most widely accepted gene-specific and cross-gene family benchmarks and demonstrate that our method outperforms other state-of-the-art algorithms for predicting the interaction of new chemicals with multiple proteins. Thus, the proposed algorithm may provide a powerful tool for multi-target drug design
Unsupervised multiple kernel learning approaches for integrating molecular cancer patient data
Cancer is the second leading cause of death worldwide. A characteristic of this disease is its complexity leading to a wide variety of genetic and molecular aberrations in the tumors. This heterogeneity necessitates personalized therapies for the patients. However, currently defined cancer subtypes used in clinical practice for treatment decision-making are based on relatively few selected markers and thus provide only a coarse classifcation of tumors. The increased availability in multi-omics data measured for cancer patients now offers the possibility of defining more informed cancer subtypes. Such a more fine-grained characterization of cancer subtypes harbors the potential of substantially expanding treatment options in personalized cancer therapy. In this thesis, we identify comprehensive cancer subtypes using multidimensional data. For this purpose, we apply and extend unsupervised multiple kernel learning methods. Three challenges of unsupervised multiple kernel learning are addressed: robustness, applicability, and interpretability. First, we show that regularization of the multiple kernel graph embedding framework, which enables the implementation of dimensionality reduction techniques, can increase the stability of the resulting patient subgroups. This improvement is especially beneficial for data sets with a small number of samples. Second, we adapt the objective function of kernel principal component analysis to enable the application of multiple kernel learning in combination with this widely used dimensionality reduction technique. Third, we improve the interpretability of kernel learning procedures by performing feature clustering prior to integrating the data via multiple kernel learning. On the basis of these clusters, we derive a score indicating the impact of a feature cluster on a patient cluster, thereby facilitating further analysis of the cluster-specific biological properties. All three procedures are successfully tested on real-world cancer data. Comparing our newly derived methodologies to established methods provides evidence that our work offers novel and beneficial ways of identifying patient subgroups and gaining insights into medically relevant characteristics of cancer subtypes.Krebs ist eine der häufigsten Todesursachen weltweit. Krebs ist gekennzeichnet durch seine Komplexität, die zu vielen verschiedenen genetischen und molekularen Aberrationen im Tumor führt. Die Unterschiede zwischen Tumoren erfordern personalisierte Therapien für die einzelnen Patienten. Die Krebssubtypen, die derzeit zur Behandlungsplanung in der klinischen Praxis verwendet werden, basieren auf relativ wenigen, genetischen oder molekularen Markern und können daher nur eine grobe Unterteilung der Tumoren liefern. Die zunehmende Verfügbarkeit von Multi-Omics-Daten für Krebspatienten ermöglicht die Neudefinition von fundierteren Krebssubtypen, die wiederum zu spezifischeren Behandlungen für Krebspatienten führen könnten. In dieser Dissertation identifizieren wir neue, potentielle Krebssubtypen basierend auf Multi-Omics-Daten. Hierfür verwenden wir unüberwachtes Multiple Kernel Learning, welches in der Lage ist mehrere Datentypen miteinander zu kombinieren. Drei Herausforderungen des unüberwachten Multiple Kernel Learnings werden adressiert: Robustheit, Anwendbarkeit und Interpretierbarkeit. Zunächst zeigen wir, dass die zusätzliche Regularisierung des Multiple Kernel Learning Frameworks zur Implementierung verschiedener Dimensionsreduktionstechniken die Stabilität der identifizierten Patientengruppen erhöht. Diese Robustheit ist besonders vorteilhaft für Datensätze mit einer geringen Anzahl von Proben. Zweitens passen wir die Zielfunktion der kernbasierten Hauptkomponentenanalyse an, um eine integrative Version dieser weit verbreiteten Dimensionsreduktionstechnik zu ermöglichen. Drittens verbessern wir die Interpretierbarkeit von kernbasierten Lernprozeduren, indem wir verwendete Merkmale in homogene Gruppen unterteilen bevor wir die Daten integrieren. Mit Hilfe dieser Gruppen definieren wir eine Bewertungsfunktion, die die weitere Auswertung der biologischen Eigenschaften von Patientengruppen erleichtert. Alle drei Verfahren werden an realen Krebsdaten getestet. Den Vergleich unserer Methodik mit etablierten Methoden weist nach, dass unsere Arbeit neue und nützliche Möglichkeiten bietet, um integrative Patientengruppen zu identifizieren und Einblicke in medizinisch relevante Eigenschaften von Krebssubtypen zu erhalten
Probabilistic analysis of the human transcriptome with side information
Understanding functional organization of genetic information is a major
challenge in modern biology. Following the initial publication of the human
genome sequence in 2001, advances in high-throughput measurement technologies
and efficient sharing of research material through community databases have
opened up new views to the study of living organisms and the structure of life.
In this thesis, novel computational strategies have been developed to
investigate a key functional layer of genetic information, the human
transcriptome, which regulates the function of living cells through protein
synthesis. The key contributions of the thesis are general exploratory tools
for high-throughput data analysis that have provided new insights to
cell-biological networks, cancer mechanisms and other aspects of genome
function.
A central challenge in functional genomics is that high-dimensional genomic
observations are associated with high levels of complex and largely unknown
sources of variation. By combining statistical evidence across multiple
measurement sources and the wealth of background information in genomic data
repositories it has been possible to solve some the uncertainties associated
with individual observations and to identify functional mechanisms that could
not be detected based on individual measurement sources. Statistical learning
and probabilistic models provide a natural framework for such modeling tasks.
Open source implementations of the key methodological contributions have been
released to facilitate further adoption of the developed methods by the
research community.Comment: Doctoral thesis. 103 pages, 11 figure
Network Inference via the Time-Varying Graphical Lasso
Many important problems can be modeled as a system of interconnected
entities, where each entity is recording time-dependent observations or
measurements. In order to spot trends, detect anomalies, and interpret the
temporal dynamics of such data, it is essential to understand the relationships
between the different entities and how these relationships evolve over time. In
this paper, we introduce the time-varying graphical lasso (TVGL), a method of
inferring time-varying networks from raw time series data. We cast the problem
in terms of estimating a sparse time-varying inverse covariance matrix, which
reveals a dynamic network of interdependencies between the entities. Since
dynamic network inference is a computationally expensive task, we derive a
scalable message-passing algorithm based on the Alternating Direction Method of
Multipliers (ADMM) to solve this problem in an efficient way. We also discuss
several extensions, including a streaming algorithm to update the model and
incorporate new observations in real time. Finally, we evaluate our TVGL
algorithm on both real and synthetic datasets, obtaining interpretable results
and outperforming state-of-the-art baselines in terms of both accuracy and
scalability
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