Bayesian nonparametric sparse VAR models

High dimensional vector autoregressive (VAR) models require a large number of parameters to be estimated and may suffer of inferential problems. We propose a new Bayesian nonparametric (BNP) Lasso prior (BNP-Lasso) for high-dimensional VAR models that can improve estimation efficiency and prediction accuracy. Our hierarchical prior overcomes overparametrization and overfitting issues by clustering the VAR coefficients into groups and by shrinking the coefficients of each group toward a common location. Clustering and shrinking effects induced by the BNP-Lasso prior are well suited for the extraction of causal networks from time series, since they account for some stylized facts in real-world networks, which are sparsity, communities structures and heterogeneity in the edges intensity. In order to fully capture the richness of the data and to achieve a better understanding of financial and macroeconomic risk, it is therefore crucial that the model used to extract network accounts for these stylized facts.Comment: Forthcoming in "Journal of Econometrics" ---- Revised Version of the paper "Bayesian nonparametric Seemingly Unrelated Regression Models" ---- Supplementary Material available on reques

Exact reconstruction of gene regulatory networks using compressive sensing.

BackgroundWe consider the problem of reconstructing a gene regulatory network structure from limited time series gene expression data, without any a priori knowledge of connectivity. We assume that the network is sparse, meaning the connectivity among genes is much less than full connectivity. We develop a method for network reconstruction based on compressive sensing, which takes advantage of the network's sparseness.ResultsFor the case in which all genes are accessible for measurement, and there is no measurement noise, we show that our method can be used to exactly reconstruct the network. For the more general problem, in which hidden genes exist and all measurements are contaminated by noise, we show that our method leads to reliable reconstruction. In both cases, coherence of the model is used to assess the ability to reconstruct the network and to design new experiments. We demonstrate that it is possible to use the coherence distribution to guide biological experiment design effectively. By collecting a more informative dataset, the proposed method helps reduce the cost of experiments. For each problem, a set of numerical examples is presented.ConclusionsThe method provides a guarantee on how well the inferred graph structure represents the underlying system, reveals deficiencies in the data and model, and suggests experimental directions to remedy the deficiencies

Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads

A novel deep operator network (DeepONet) with a residual U-Net (ResUNet) as the trunk network is devised to predict full-field highly nonlinear elastic-plastic stress response for complex geometries obtained from topology optimization under variable loads. The proposed DeepONet uses a ResUNet in the trunk to encode complex input geometries, and a fully-connected branch network encodes the parametric loads. Additional information fusion is introduced via an element-wise multiplication of the encoded latent space to improve prediction accuracy further. The performance of the proposed DeepONet was compared to two baseline models, a standalone ResUNet and a DeepONet with fully connected networks as the branch and trunk. The results show that ResUNet and the proposed DeepONet share comparable accuracy; both can predict the stress field and accurately identify stress concentration points. However, the novel DeepONet is more memory efficient and allows greater flexibility with framework architecture modifications. The DeepONet with fully connected networks suffers from high prediction error due to its inability to effectively encode the complex, varying geometry. Once trained, all three networks can predict the full stress distribution orders of magnitude faster than finite element simulations. The proposed network can quickly guide preliminary optimization, designs, sensitivity analysis, uncertainty quantification, and many other nonlinear analyses that require extensive forward evaluations with variable geometries, loads, and other parameters. This work marks the first time a ResUNet is used as the trunk network in the DeepONet architecture and the first time that DeepONet solves problems with complex, varying input geometries under parametric loads and elasto-plastic material behavior

Graph-based learning under perturbations via total least-squares

Graphs are pervasive in different fields unveiling complex relationships between data. Two major graph-based learning tasks are topology identification and inference of signals over graphs. Among the possible models to explain data interdependencies, structural equation models (SEMs) accommodate a gamut of applications involving topology identification. Obtaining conventional SEMs though requires measurements across nodes. On the other hand, typical signal inference approaches “blindly trust” a given nominal topology. In practice however, signal or topology perturbations may be present in both tasks, due to model mismatch, outliers, outages or adversarial behavior. To cope with such perturbations, this work introduces a regularized total least-squares (TLS) approach and iterative algorithms with convergence guarantees to solve both tasks. Further generalizations are also considered relying on structured and/or weighted TLS when extra prior information on the perturbation is available. Analyses with simulated and real data corroborate the effectiveness of the novel TLS-based approaches

Expression data dnalysis and regulatory network inference by means of correlation patterns

With the advance of high-throughput techniques, the amount of available data in the bio-molecular field is rapidly growing. It is now possible to measure genome-wide aspects of an entire biological system as a whole. Correlations that emerge due to internal dependency structures of these systems entail the formation of characteristic patterns in the corresponding data. The extraction of these patterns has become an integral part of computational biology. By triggering perturbations and interventions it is possible to induce an alteration of patterns, which may help to derive the dependency structures present in the system. In particular, differential expression experiments may yield alternate patterns that we can use to approximate the actual interplay of regulatory proteins and genetic elements, namely, the regulatory network of a cell. In this work, we examine the detection of correlation patterns from bio-molecular data and we evaluate their applicability in terms of protein contact prediction, experimental artifact removal, the discovery of unexpected expression patterns and genome-scale inference of regulatory networks. Correlation patterns are not limited to expression data. Their analysis in the context of conserved interfaces among proteins is useful to estimate whether these may have co-evolved. Patterns that hint on correlated mutations would then occur in the associated protein sequences as well. We employ a conceptually simple sampling strategy to decide whether or not two pathway elements share a conserved interface and are thus likely to be in physical contact. We successfully apply our method to a system of ABC-transporters and two-component systems from the phylum of Firmicute bacteria. For spatially resolved gene expression data like microarrays, the detection of artifacts, as opposed to noise, corresponds to the extraction of localized patterns that resemble outliers in a given region. We develop a method to detect and remove such artifacts using a sliding-window approach. Our method is very accurate and it is shown to adapt to other platforms like custom arrays as well. Further, we developed Padesco as a way to reveal unexpected expression patterns. We extract frequent and recurring patterns that are conserved across many experiments. For a specific experiment, we predict whether a gene deviates from its expected behaviour. We show that Padesco is an effective approach for selecting promising candidates from differential expression experiments. In Chapter 5, we then focus on the inference of genome-scale regulatory networks from expression data. Here, correlation patterns have proven useful for the data-driven estimation of regulatory interactions. We show that, for reliable eukaryotic network inference, the integration of prior networks is essential. We reveal that this integration leads to an over-estimate of network-wide quality estimates and suggest a corrective procedure, CoRe, to counterbalance this effect. CoRe drastically improves the false discovery rate of the originally predicted networks. We further suggest a consensus approach in combination with an extended set of topological features to obtain a more accurate estimate of the eukaryotic regulatory network for yeast. In the course of this work we show how correlation patterns can be detected and how they can be applied for various problem settings in computational molecular biology. We develop and discuss competitive approaches for the prediction of protein contacts, artifact repair, differential expression analysis, and network inference and show their applicability in practical setups.Mit der Weiterentwicklung von Hochdurchsatztechniken steigt die Anzahl verfügbarer Daten im Bereich der Molekularbiologie rapide an. Es ist heute möglich, genomweite Aspekte eines ganzen biologischen Systems komplett zu erfassen. Korrelationen, die aufgrund der internen Abhängigkeits-Strukturen dieser Systeme enstehen, führen zu charakteristischen Mustern in gemessenen Daten. Die Extraktion dieser Muster ist zum integralen Bestandteil der Bioinformatik geworden. Durch geplante Eingriffe in das System ist es möglich Muster-Änderungen auszulösen, die helfen, die Abhängigkeits-Strukturen des Systems abzuleiten. Speziell differentielle Expressions-Experimente können Muster-Wechsel bedingen, die wir verwenden können, um uns dem tatsächlichen Wechselspiel von regulatorischen Proteinen und genetischen Elementen anzunähern, also dem regulatorischen Netzwerk einer Zelle. In der vorliegenden Arbeit beschäftigen wir uns mit der Erkennung von Korrelations-Mustern in molekularbiologischen Daten und schätzen ihre praktische Nutzbarkeit ab, speziell im Kontext der Kontakt-Vorhersage von Proteinen, der Entfernung von experimentellen Artefakten, der Aufdeckung unerwarteter Expressions-Muster und der genomweiten Vorhersage regulatorischer Netzwerke. Korrelations-Muster sind nicht auf Expressions-Daten beschränkt. Ihre Analyse im Kontext konservierter Schnittstellen zwischen Proteinen liefert nützliche Hinweise auf deren Ko-Evolution. Muster die auf korrelierte Mutationen hinweisen, würden in diesem Fall auch in den entsprechenden Proteinsequenzen auftauchen. Wir nutzen eine einfache Sampling-Strategie, um zu entscheiden, ob zwei Elemente eines Pathways eine gemeinsame Schnittstelle teilen, berechnen also die Wahrscheinlichkeit für deren physikalischen Kontakt. Wir wenden unsere Methode mit Erfolg auf ein System von ABC-Transportern und Zwei-Komponenten-Systemen aus dem Firmicutes Bakterien-Stamm an. Für räumlich aufgelöste Expressions-Daten wie Microarrays enspricht die Detektion von Artefakten der Extraktion lokal begrenzter Muster. Im Gegensatz zur Erkennung von Rauschen stellen diese innerhalb einer definierten Region Ausreißer dar. Wir entwickeln eine Methodik, um mit Hilfe eines Sliding-Window-Verfahrens, solche Artefakte zu erkennen und zu entfernen. Das Verfahren erkennt diese sehr zuverlässig. Zudem kann es auf Daten diverser Plattformen, wie Custom-Arrays, eingesetzt werden. Als weitere Möglichkeit unerwartete Korrelations-Muster aufzudecken, entwickeln wir Padesco. Wir extrahieren häufige und wiederkehrende Muster, die über Experimente hinweg konserviert sind. Für ein bestimmtes Experiment sagen wir vorher, ob ein Gen von seinem erwarteten Verhalten abweicht. Wir zeigen, dass Padesco ein effektives Vorgehen ist, um vielversprechende Kandidaten eines differentiellen Expressions-Experiments auszuwählen. Wir konzentrieren uns in Kapitel 5 auf die Vorhersage genomweiter regulatorischer Netzwerke aus Expressions-Daten. Hierbei haben sich Korrelations-Muster als nützlich für die datenbasierte Abschätzung regulatorischer Interaktionen erwiesen. Wir zeigen, dass für die Inferenz eukaryotischer Systeme eine Integration zuvor bekannter Regulationen essentiell ist. Unsere Ergebnisse ergeben, dass diese Integration zur Überschätzung netzwerkübergreifender Qualitätsmaße führt und wir schlagen eine Prozedur - CoRe - zur Verbesserung vor, um diesen Effekt auszugleichen. CoRe verbessert die False Discovery Rate der ursprünglich vorhergesagten Netzwerke drastisch. Weiterhin schlagen wir einen Konsensus-Ansatz in Kombination mit einem erweiterten Satz topologischer Features vor, um eine präzisere Vorhersage für das eukaryotische Hefe-Netzwerk zu erhalten. Im Rahmen dieser Arbeit zeigen wir, wie Korrelations-Muster erkannt und wie sie auf verschiedene Problemstellungen der Bioinformatik angewandt werden können. Wir entwickeln und diskutieren Ansätze zur Vorhersage von Proteinkontakten, Behebung von Artefakten, differentiellen Analyse von Expressionsdaten und zur Vorhersage von Netzwerken und zeigen ihre Eignung im praktischen Einsatz