arXiv subjects

Emilie Chouzenoux

Publications and source records attributed to Emilie Chouzenoux.

53 records · Page 3Linked to original sources

arXiv2020

DeepVir -- Graphical Deep Matrix Factorization for "In Silico" Antiviral Repositioning: Application to COVID-19

This work formulates antiviral repositioning as a matrix completion problem where the antiviral drugs are along the rows and the viruses along the columns. The input matrix is partially filled, with ones in positions where the antiviral has been known to be effective against a virus. The curated metadata for antivirals (chemical structure and pathways) and viruses (genomic structure and symptoms) is encoded into our matrix completion framework as graph Laplacian regularization. We then frame the resulting multiple graph regularized matrix completion problem as deep matrix factorization. This is solved by using a novel optimization method called HyPALM (Hybrid Proximal Alternating Linearized Minimization). Results on our curated RNA drug virus association (DVA) dataset shows that the proposed approach excels over state-of-the-art graph regularized matrix completion techniques. When applied to "in silico" prediction of antivirals for COVID-19, our approach returns antivirals that are either used for treating patients or are under for trials for the same.

cs.LG↗

arXiv2020

SPOQ $\ell_p$-Over-$\ell_q$ Regularization for Sparse Signal Recovery applied to Mass Spectrometry

Underdetermined or ill-posed inverse problems require additional information for \ldd{d} sound solutions with tractable optimization algorithms. Sparsity yields consequent heuristics to that matter, with numerous applications in signal restoration, image recovery, or machine learning. Since the $\ell_0$ count measure is barely tractable, many statistical or learning approaches have invested in computable proxies, such as the $\ell_1$ norm. However, the latter does not exhibit the desirable property of scale invariance for sparse data. Extending the SOOT Euclidean/Taxicab $\ell_1$-over-$\ell_2$ norm-ratio initially introduced for blind deconvolution, we propose SPOQ, a family of smoothed (approximately) scale-invariant penalty functions. It consists of a Lipschitz-differentiable surrogate for $\ell_p$-over-$\ell_q$ quasi-norm/norm ratios with $p\in\,]0,2[$ and $q\ge 2$. This surrogate is embedded into a novel majorize-minimize trust-region approach, generalizing the variable metric forward-backward algorithm. For naturally sparse mass-spectrometry signals, we show that SPOQ significantly outperforms $\ell_0$, $\ell_1$, Cauchy, Welsch, SCAD and Celo penalties on several performance measures. Guidelines on SPOQ hyperparameters tuning are also provided, suggesting simple data-driven choices.

math.OC↗

arXiv2020

A computational approach to aid clinicians in selecting anti-viral drugs for COVID-19 trials

COVID-19 has fast-paced drug re-positioning for its treatment. This work builds computational models for the same. The aim is to assist clinicians with a tool for selecting prospective antiviral treatments. Since the virus is known to mutate fast, the tool is likely to help clinicians in selecting the right set of antivirals for the mutated isolate. The main contribution of this work is a manually curated database publicly shared, comprising of existing associations between viruses and their corresponding antivirals. The database gathers similarity information using the chemical structure of drugs and the genomic structure of viruses. Along with this database, we make available a set of state-of-the-art computational drug re-positioning tools based on matrix completion. The tools are first analysed on a standard set of experimental protocols for drug target interactions. The best performing ones are applied for the task of re-positioning antivirals for COVID-19. These tools select six drugs out of which four are currently under various stages of trial, namely Remdesivir (as a cure), Ribavarin (in combination with others for cure), Umifenovir (as a prophylactic and cure) and Sofosbuvir (as a cure). Another unanimous prediction is Tenofovir alafenamide, which is a novel tenofovir prodrug developed in order to improve renal safety when compared to the counterpart tenofovir disoproxil. Both are under trail, the former as a cure and the latter as a prophylactic. These results establish that the computational methods are in sync with the state-of-practice. We also demonstrate how the selected drugs change as the SARS-Cov-2 mutates over time, suggesting the importance of such a tool in drug prediction. The dataset and software is available publicly at https://github.com/aanchalMongia/DVA and the prediction tool with a user-friendly interface is available at http://dva.salsa.iiitd.edu.in.

q-bio.QM↗

arXiv2020

Block Distributed Majorize-Minimize Memory Gradient Algorithm and its application to 3D image restoration

Modern 3D image recovery problems require powerful optimization frameworks to handle high dimensionality while providing reliable numerical solutions in a reasonable time. In this perspective, asynchronous parallel optimization algorithms have received an increasing attention by overcoming memory limitation issues and communication bottlenecks. In this work, we propose a block distributed Majorize-Minorize Memory Gradient (BD3MG) optimization algorithm for solving large scale non-convex differentiable optimization problems. Assuming a distributed memory environment, the algorithm casts the efficient 3MG scheme into smaller dimension subproblems where blocks of variables are addressed in an asynchronous manner. Convergence of the sequence built by the proposed BD3MG method is established under mild assumptions. Application to the restoration of 3D images degraded by a depth-variant blur shows that our method yields significant computational time reduction compared to several synchronous and asynchronous competitors, while exhibiting great scalability potential.

math.OC↗

arXiv2020

Deep Unfolding of a Proximal Interior Point Method for Image Restoration

Variational methods are widely applied to ill-posed inverse problems for they have the ability to embed prior knowledge about the solution. However, the level of performance of these methods significantly depends on a set of parameters, which can be estimated through computationally expensive and time-consuming methods. In contrast, deep learning offers very generic and efficient architectures, at the expense of explainability, since it is often used as a black-box, without any fine control over its output. Deep unfolding provides a convenient approach to combine variational-based and deep learning approaches. Starting from a variational formulation for image restoration, we develop iRestNet, a neural network architecture obtained by unfolding a proximal interior point algorithm. Hard constraints, encoding desirable properties for the restored image, are incorporated into the network thanks to a logarithmic barrier, while the barrier parameter, the stepsize, and the penalization weight are learned by the network. We derive explicit expressions for the gradient of the proximity operator for various choices of constraints, which allows training iRestNet with gradient descent and backpropagation. In addition, we provide theoretical results regarding the stability of the network for a common inverse problem example. Numerical experiments on image deblurring problems show that the proposed approach compares favorably with both state-of-the-art variational and machine learning methods in terms of image quality.

math.OC↗

arXiv2019

Transformed Subspace Clustering

Subspace clustering assumes that the data is sepa-rable into separate subspaces. Such a simple as-sumption, does not always hold. We assume that, even if the raw data is not separable into subspac-es, one can learn a representation (transform coef-ficients) such that the learnt representation is sep-arable into subspaces. To achieve the intended goal, we embed subspace clustering techniques (locally linear manifold clustering, sparse sub-space clustering and low rank representation) into transform learning. The entire formulation is jointly learnt; giving rise to a new class of meth-ods called transformed subspace clustering (TSC). In order to account for non-linearity, ker-nelized extensions of TSC are also proposed. To test the performance of the proposed techniques, benchmarking is performed on image clustering and document clustering datasets. Comparison with state-of-the-art clustering techniques shows that our formulation improves upon them.

cs.LG↗

arXiv2019

Deep Latent Factor Model for Collaborative Filtering

Latent factor models have been used widely in collaborative filtering based recommender systems. In recent years, deep learning has been successful in solving a wide variety of machine learning problems. Motivated by the success of deep learning, we propose a deeper version of latent factor model. Experiments on benchmark datasets shows that our proposed technique significantly outperforms all state-of-the-art collaborative filtering techniques.

cs.LG↗

arXiv2019

General risk measures for robust machine learning

A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often estimated from training sets, which may lead to poor out-of-sample performance. In this work, we bring new insights in this problem by using the framework which has been developed in quantitative finance for risk measures. We show that the original min-max problem can be recast as a convex minimization problem under suitable assumptions. We discuss several important examples of robust formulations, in particular by defining ambiguity sets based on $φ$-divergences and the Wasserstein metric.We also propose an efficient algorithm for solving the corresponding convex optimization problems involving complex convex constraints. Through simulation examples, we demonstrate that this algorithm scales well on real data sets.

math.OC↗

arXiv2018

A Two-Stage Subspace Trust Region Approach for Deep Neural Network Training

In this paper, we develop a novel second-order method for training feed-forward neural nets. At each iteration, we construct a quadratic approximation to the cost function in a low-dimensional subspace. We minimize this approximation inside a trust region through a two-stage procedure: first inside the embedded positive curvature subspace, followed by a gradient descent step. This approach leads to a fast objective function decay, prevents convergence to saddle points, and alleviates the need for manually tuning parameters. We show the good performance of the proposed algorithm on benchmark datasets.

cs.CV↗

arXiv2017

A Random Block-Coordinate Douglas-Rachford Splitting Method with Low Computational Complexity for Binary Logistic Regression

In this paper, we propose a new optimization algorithm for sparse logistic regression based on a stochastic version of the Douglas-Rachford splitting method. Our algorithm sweeps the training set by randomly selecting a mini-batch of data at each iteration, and it allows us to update the variables in a block coordinate manner. Our approach leverages the proximity operator of the logistic loss, which is expressed with the generalized Lambert W function. Experiments carried out on standard datasets demonstrate the efficiency of our approach w.r.t. stochastic gradient-like methods.

math.OC↗

arXiv2017

A Fast Algorithm Based on a Sylvester-like Equation for LS Regression with GMRF Prior

This paper presents a fast approach for penalized least squares (LS) regression problems using a 2D Gaussian Markov random field (GMRF) prior. More precisely, the computation of the proximity operator of the LS criterion regularized by different GMRF potentials is formulated as solving a Sylvester-like matrix equation. By exploiting the structural properties of GMRFs, this matrix equation is solved columnwise in an analytical way. The proposed algorithm can be embedded into a wide range of proximal algorithms to solve LS regression problems including a convex penalty. Experiments carried out in the case of a constrained LS regression problem arising in a multichannel image processing application, provide evidence that an alternating direction method of multipliers performs quite efficiently in this context.

cs.CV↗

arXiv2017

A Variational Bayesian Approach for Image Restoration. Application to Image Deblurring with Poisson-Gaussian Noise

In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is reliably estimated from the observations. As the posterior density of the unknown parameters is analytically intractable, the estimation problem is derived in a variational Bayesian framework where the goal is to provide a good approximation to the posterior distribution in order to compute posterior mean estimates. Moreover, a majorization technique is employed to circumvent the difficulties raised by the intricate forms of the non-Gaussian likelihood and of the prior density. We demonstrate the potential of the proposed approach through comparisons with state-of-the-art techniques that are specifically tailored to signal recovery in the presence of mixed Poisson-Gaussian noise. Results show that the proposed approach is efficient and achieves performance comparable with other methods where the regularization parameter is manually tuned from the ground truth.

math.OC↗

arXiv2016

PALMA, an improved algorithm for DOSY signal processing

NMR is a tool of choice for the measure of diffusion coefficients of species in solution. The DOSY experiment, a 2D implementation of this measure, has proven to be particularly useful for the study of complex mixtures, molecular interactions, polymers, etc. However, DOSY data analysis requires to resort to inverse Laplace transform, in particular for polydisperse samples. This is a known difficult numerical task, for which we present here a novel approach. A new algorithm based on a splitting scheme and on the use of proximity operators is introduced. Used in conjunction with a Maximum Entropy and $\ell_1$ hybrid regularisation, this algorithm converges rapidly and produces results robust against experimental noise. This method has been called PALMA. It is able to reproduce faithfully monodisperse as well as polydisperse systems, and numerous simulated and experimental examples are presented. It has been implemented on the server http://palma.labo.igbmc.fr where users can have their datasets processed automatically.

physics.data-an↗

arXiv2016

Convergence Rate Analysis of the Majorize-Minimize Subspace Algorithm -- Extended Version

State-of-the-art methods for solving smooth optimization problems are nonlinear conjugate gradient, low memory BFGS, and Majorize-Minimize (MM) subspace algorithms. The MM subspace algorithm which has been introduced more recently has shown good practical performance when compared with other methods on various optimization problems arising in signal and image processing. However, to the best of our knowledge, no general result exists concerning the theoretical convergence rate of the MM subspace algorithm. This paper aims at deriving such convergence rates both for batch and online versions of the algorithm and, in particular, discusses the influence of the choice of the subspace.

math.OC↗

arXiv2015

A Survey of Stochastic Simulation and Optimization Methods in Signal Processing

Modern signal processing (SP) methods rely very heavily on probability and statistics to solve challenging SP problems. SP methods are now expected to deal with ever more complex models, requiring ever more sophisticated computational inference techniques. This has driven the development of statistical SP methods based on stochastic simulation and optimization. Stochastic simulation and optimization algorithms are computationally intensive tools for performing statistical inference in models that are analytically intractable and beyond the scope of deterministic inference methods. They have been recently successfully applied to many difficult problems involving complex statistical models and sophisticated (often Bayesian) statistical inference techniques. This survey paper offers an introduction to stochastic simulation and optimization methods in signal and image processing. The paper addresses a variety of high-dimensional Markov chain Monte Carlo (MCMC) methods as well as deterministic surrogate methods, such as variational Bayes, the Bethe approach, belief and expectation propagation and approximate message passing algorithms. It also discusses a range of optimization methods that have been adopted to solve stochastic problems, as well as stochastic methods for deterministic optimization. Subsequently, areas of overlap between simulation and optimization, in particular optimization-within-MCMC and MCMC-driven optimization are discussed.

cs.IT↗

arXiv2014

Euclid in a Taxicab: Sparse Blind Deconvolution with Smoothed l1/l2 Regularization

The l1/l2 ratio regularization function has shown good performance for retrieving sparse signals in a number of recent works, in the context of blind deconvolution. Indeed, it benefits from a scale invariance property much desirable in the blind context. However, the l1/l2 function raises some difficulties when solving the nonconvex and nonsmooth minimization problems resulting from the use of such a penalty term in current restoration methods. In this paper, we propose a new penalty based on a smooth approximation to the l1/l2 function. In addition, we develop a proximal-based algorithm to solve variational problems involving this function and we derive theoretical convergence results. We demonstrate the effectiveness of our method through a comparison with a recent alternating optimization strategy dealing with the exact l1/l2 term, on an application to seismic data blind deconvolution.

math.OC↗

arXiv2013

A Majorize-Minimize subspace approach for l2-l0 image regularization

In this work, we consider a class of differentiable criteria for sparse image computing problems, where a nonconvex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes edge-preserving measures or frame-analysis potentials commonly used in image processing. As shown by our asymptotic results, the l2-l0 penalties we consider may be employed to provide approximate solutions to l0-penalized optimization problems. One of the advantages of the proposed approach is that it allows us to derive an efficient Majorize-Minimize subspace algorithm. The convergence of the algorithm is investigated by using recent results in nonconvex optimization. The fast convergence properties of the proposed optimization method are illustrated through image processing examples. In particular, its effectiveness is demonstrated on several data recovery problems.

math.OC↗