Switch Detection in Genetic Regulatory Networks

This paper considers piecewise affine models of genetic regulatory networks and focuses on the problem of detecting switches among different modes of operation in gene expression data. This task constitutes the first step of a procedure for the complete identification of the network and complements the algorithms proposed in (Drulhe et al., 2006). We propose two methods for switch detection. The first one is based on the computation of suitable indexes that emphasize the occurrence of switches in the data. The second one exploits nonlinear identification techniques in order to recast switch detection into an hypothesis testing problem. In both cases we assume that the expression of individual genes obeys to an output-error piecewise affine dynamics and we study the performance of the proposed algorithms for different noise levels. We also illustrate the application of our methods to the reconstruction of switching times in data produced by a piecewise affine model of the network regulating the carbon starvation response in Escherichia coli.

Giancarlo Ferrari Trecate

Springer-Verlag2007

Alignment and Assembly

Lyudmila Yartseva

Over recent years, many large network datasets become available, giving rise to novel and valuable applications of data mining and machine learning techniques. These datasets include social networks, the structure of the Internet, and protein-interaction networks, to name just a few. Graph mining exploits information hidden in these data to shed light on such problems as finding relevant pages on the web, or identifying communities of strongly connected individuals. Clearly, to address such problems, we first need the complete and reliable network graph. In many real-world scenarios, the full graph is not available for free. For example, data-collection processes may be noisy and unreliable or node identifiers may be hidden for privacy protection. Therefore, we cannot rely on the node labels to infer the full graph. In this thesis, we address fundamental and practical questions of inferring a true full network from multiple ambiguous observations. We formulate two variations of this problem: network alignment and network assembly. In each variant, we address two types of questions: first, we characterize how graph features impact the fundamental feasibility of reconstruction; second, we seek efficient algorithms that can scale to very large networks. In the first part of this thesis, we consider network alignment. We assume two large, noisy observations of the true network that are not labeled. Network alignment refers to the problem of aligning the vertices of the two networks using only structural cues and it can be viewed as a generalization of the classic graph-isomorphism problem. We make the following contributions. First, we introduce a random bigraph model with parameters p, t and s that generates two correlated graphs. We characterize conditions on p, t and s for the feasibility of alignment of two graphs. Second, we create an algorithm named percolation graph-matching (PGM) that builds an alignment from a small set of pre-matched nodes S. We prove conditions on the parameters p, t , s and r for which PGM succeeds, and we establish a phase transition in |S|. In the second part of this thesis, we consider network assembly. We assume many small, noisy observations of the true network, called patches. The node labels are either absent or not unique. The network assembly problem consists in reconstructing the true graph from these patches. We make the following contributions. First, we introduce a novel random-graph model with parameters p and q that generates a network with high clustering. We characterize conditions on p and q for feasibility of assembly. Second, we propose a heuristic assembly algorithm to reconstruct the true graph from arbitrary patches with label ambiguity.

EPFL2017

From Classical to Unsupervised-Deep-Learning Methods for Solving Inverse Problems in Imaging.

Harshit Gupta

In this thesis, we propose new algorithms to solve inverse problems in the context of biomedical images. Due to ill-posedness, solving these problems require some prior knowledge of the statistics of the underlying images. The traditional algorithms, in the field, assume prior knowledge related to smoothness or sparsity of these images. Recently, they have been outperformed by the second generation algorithms which harness the power of neural networks to learn required statistics from training data. Even more recently, last generation deep-learning-based methods have emerged which require neither training nor training data. This thesis devises algorithms which progress through these generations. It extends these generations to novel formulations and applications while bringing more robustness. In parallel, it also progresses in terms of complexity, from proposing algorithms for problems with 1D data and an exact known forward model to the ones with 4D data and an unknown parametric forward model. We introduce five main contributions. The last three of them propose deep-learning-based latest-generation algorithms that require no prior training. 1) We develop algorithms to solve the continuous-domain formulation of inverse problems with both classical Tikhonov and total-variation regularizations. We formalize the problems, characterize the solution set, and devise numerical approaches to find the solutions. 2) We propose an algorithm that improves upon end-to-end neural-network-based second generation algorithms. In our method, a neural network is first trained as a projector on a training set, and is then plugged in as a projector inside the projected gradient descent (PGD). Since the problem is nonconvex, we relax the PGD to ensure convergence to a local minimum under some constraints. This method outperforms all the previous generation algorithms for Computed Tomography (CT). 3) We develop a novel time-dependent deep-image-prior algorithm for modalities that involve a temporal sequence of images. We parameterize them as the output of an untrained neural network fed with a sequence of latent variables. To impose temporal directionality, the latent variables are assumed to lie on a 1D manifold. The network is then tuned to minimize the data fidelity. We obtain state-of-the-art results in dynamic magnetic resonance imaging (MRI) and even recover intra-frame images. 4) We propose a novel reconstruction paradigm for cryo-electron-microscopy (CryoEM) called CryoGAN. Motivated by generative adversarial networks (GANs), we reconstruct a biomolecule's 3D structure such that its CryoEM measurements resemble the acquired data in a distributional sense. The algorithm is pose-or-likelihood-estimation-free, needs no ab initio, and is proven to have a theoretical guarantee of recovery of the true structure. 5) We extend CryoGAN to reconstruct continuously varying conformations of a structure from heterogeneous data. We parameterize the conformations as the output of a neural network fed with latent variables on a low-dimensional manifold. The method is shown to recover continuous protein conformations and their energy landscape.