| 1. |
- Hadj-Selem, Fouad, et al.
(författare)
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Continuation of Nesterov's Smoothing for Regression With Structured Sparsity in High-Dimensional Neuroimaging
- 2018
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Ingår i: IEEE Transactions on Medical Imaging. - : IEEE. - 0278-0062 .- 1558-254X. ; 37:11, s. 2403-2413
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Tidskriftsartikel (refereegranskat)abstract
- Predictive models can be used on high-dimensional brain images to decode cognitive states or diagnosis/prognosis of a clinical condition/evolution. Spatial regularization through structured sparsity offers new perspectives in this context and reduces the risk of overfitting the model while providing interpretable neuroimaging signatures by forcing the solution to adhere to domain-specific constraints. Total variation (TV) is a promising candidate for structured penalization: it enforces spatial smoothness of the solution while segmenting predictive regions from the background. We consider the problem of minimizing the sum of a smooth convex loss, a non-smooth convex penalty (whose proximal operator is known) and a wide range of possible complex, non-smooth convex structured penalties such as TV or overlapping group Lasso. Existing solvers are either limited in the functions they can minimize or in their practical capacity to scale to high-dimensional imaging data. Nesterov’s smoothing technique can be used to minimize a large number of non-smooth convex structured penalties. However, reasonable precision requires a small smoothing parameter, which slows down the convergence speed to unacceptable levels. To benefit from the versatility of Nesterov’s smoothing technique, we propose a first order continuation algorithm, CONESTA, which automatically generates a sequence of decreasing smoothing parameters. The generated sequence maintains the optimal convergence speed toward any globally desired precision. Our main contributions are: gap to probe the current distance to the global optimum in order to adapt the smoothing parameter and the To propose an expression of the duality convergence speed. This expression is applicable to many penalties and can be used with other solvers than CONESTA. We also propose an expression for the particular smoothing parameter that minimizes the number of iterations required to reach a given precision. Furthermore, we provide a convergence proof and its rate, which is an improvement over classical proximal gradient smoothing methods. We demonstrate on both simulated and high-dimensional structural neuroimaging data that CONESTA significantly outperforms many state-of-the-art solvers in regard to convergence speed and precision.
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| 2. |
- Löfstedt, Tommy, et al.
(författare)
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Simulated Data for Linear Regression with Structured and Sparse Penalties: Introducing pylearn-simulate
- 2018
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Ingår i: Journal of Statistical Software. - : Foundation for Open Access Statistics. - 1548-7660. ; 87:3
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Tidskriftsartikel (refereegranskat)abstract
- A currently very active field of research is how to incorporate structure and prior knowledge in machine learning methods. It has lead to numerous developments in the field of non-smooth convex minimization. With recently developed methods it is possible to perform an analysis in which the computed model can be linked to a given structure of the data and simultaneously do variable selection to find a few important features in the data. However, there is still no way to unambiguously simulate data to test proposed algorithms, since the exact solutions to such problems are unknown.The main aim of this paper is to present a theoretical framework for generating simulated data. These simulated data are appropriate when comparing optimization algorithms in the context of linear regression problems with sparse and structured penalties. Additionally, this approach allows the user to control the signal-to-noise ratio, the correlation structure of the data and the optimization problem to which they are the solution.The traditional approach is to simulate random data without taking into account the actual model that will be fit to the data. But when using such an approach it is not possible to know the exact solution of the underlying optimization problem. With our contribution, it is possible to know the exact theoretical solution of a penalized linear regression problem, and it is thus possible to compare algorithms without the need to use, e.g., cross-validation.We also present our implementation, the Python package pylearn-simulate, available at https://github.com/neurospin/pylearn-simulate and released under the BSD 3clause license. We describe the package and give examples at the end of the paper.
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| 3. |
- Löfstedt, Tommy, et al.
(författare)
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Structured Variable Selection for Regularized Generalized Canonical Correlation Analysis
- 2016
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Ingår i: MULTIPLE FACETS OF PARTIAL LEAST SQUARES AND RELATED METHODS. - Cham : SPRINGER INT PUBLISHING AG. - 9783319406435 - 9783319406411 ; , s. 129-139
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Konferensbidrag (refereegranskat)abstract
- Regularized Generalized Canonical Correlation Analysis (RGCCA) extends regularized canonical correlation analysis to more than two sets of variables. Sparse GCCA(SGCCA) was recently proposed to address the issue of variable selection. However, the variable selection scheme offered by SGCCA is limited to the covariance (tau = 1) link between blocks. In this paper we go beyond the covariance link by proposing an extension of SGCCA for the full RGCCA model. (tau epsilon [0; 1]). In addition, we also propose an extension of SGCCA that exploits pre-given structural relationships between variables within blocks. Specifically, we propose an algorithm that allows structured and sparsity-inducing penalties to be included in the RGCCA optimization problem.
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| 4. |
- de Pierrefeu, Amicie, et al.
(författare)
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Structured Sparse Principal Components Analysis With the TV-Elastic Net Penalty
- 2018
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Ingår i: IEEE Transactions on Medical Imaging. - : IEEE. - 0278-0062 .- 1558-254X. ; 37:2, s. 396-407
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Tidskriftsartikel (refereegranskat)abstract
- Principal component analysis (PCA) is an exploratory tool widely used in data analysis to uncover the dominant patterns of variability within a population. Despite its ability to represent a data set in a low-dimensional space, PCA’s interpretability remains limited. Indeed, the components produced by PCA are often noisy or exhibit no visually meaningful patterns. Furthermore, the fact that the components are usually non-sparse may also impede interpretation, unless arbitrary thresholding is applied. However, in neuroimaging, it is essential to uncover clinically interpretable phenotypic markers that would account for the main variability in the brain images of a population. Recently, some alternatives to the standard PCA approach, such as sparse PCA (SPCA), have been proposed, their aim being to limit the density of the components. Nonetheless, sparsity alone does not entirely solve the interpretability problem in neuroimaging, since it may yield scattered andunstable components. We hypothesized that the incorporation of prior information regarding the structure of the data may lead to improved relevance and interpretability of brain patterns. We therefore present a simple extension of the popular PCA framework that adds structured sparsity penalties on the loading vectors in order to identify the few stable regions in the brain images that capture most of the variability. Such structured sparsity can be obtained by combining, e.g., l1 and total variation (TV) penalties, where the TV regularization encodes information on the underlying structure of the data. This paper presents the structured SPCA (denoted SPCA-TV) optimization framework and its resolution. We demonstrate SPCA-TV’s effectiveness and versatility on three different data sets. It can be applied to any kind of structured data, such as, e.g., N-dimensional array images or meshes of cortical surfaces. The gains of SPCA-TV over unstructured approaches (such as SPCA and ElasticNet PCA) or structured approach (such as GraphNet PCA) are significant, since SPCA-TV reveals the variability within a data set in the form of intelligible brain patterns that are easier to interpret and more stable across different samples.
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| 5. |
- Dubois, Mathieu, et al.
(författare)
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Predictive support recovery with TV-Elastic Net penalty and logistic regression: An application to structural MRI
- 2014
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Konferensbidrag (refereegranskat)abstract
- The use of machine-learning in neuroimaging offers new perspectives in early diagnosis and prognosis of brain diseases. Although such multivariate methods can capture complex relationships in the data, traditional approaches provide irregular (l12 penalty) or scattered (l1 penalty) predictive pattern with a very limited relevance. A penalty like Total Variation (TV) that exploits the natural 3D structure of the images can increase the spatial coherence of the weight map. However, TV penalization leads to non-smooth optimization problems that are hard to minimize. We propose an optimization framework that minimizes any combination of l1, l2, and TV penalties while preserving the exact l1 penalty. This algorithm uses Nesterov's smoothing technique to approximate the TV penalty with a smooth function such that the loss and the penalties are minimized with an exact accelerated proximal gradient algorithm. We propose an original continuation algorithm that uses successively smaller values of the smoothing parameter to reach a prescribed precision while achieving the best possible convergence rate. This algorithm can be used with other losses or penalties. The algorithm is applied on a classification problem on the ADNI dataset. We observe that the TV penalty does not necessarily improve the prediction but provides a major breakthrough in terms of support recovery of the predictive brain regions.
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| 6. |
- Ruggeri, Barbara, et al.
(författare)
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Methylation of OPRL1 mediates the effect of psychosocial stress on binge drinking in adolescents
- 2018
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Ingår i: Journal of Child Psychology and Psychiatry. - : Wiley. - 0021-9630 .- 1469-7610. ; 9:6, s. 50-658
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Tidskriftsartikel (refereegranskat)abstract
- BACKGROUND: Nociceptin is a key regulator linking environmental stress and alcohol drinking. In a genome-wide methylation analysis, we recently identified an association of a methylated region in the OPRL1 gene with alcohol-use disorders.METHODS: Here, we investigate the biological basis of this observation by analysing psychosocial stressors, methylation of the OPRL1 gene, brain response during reward anticipation and alcohol drinking in 660 fourteen-year-old adolescents of the IMAGEN study. We validate our findings in marchigian sardinian (msP) alcohol-preferring rats that are genetically selected for increased alcohol drinking and stress sensitivity.RESULTS: We found that low methylation levels in intron 1 of OPRL1 are associated with higher psychosocial stress and higher frequency of binge drinking, an effect mediated by OPRL1 methylation. In individuals with low methylation of OPRL1, frequency of binge drinking is associated with stronger BOLD response in the ventral striatum during reward anticipation. In msP rats, we found that stress results in increased alcohol intake and decreased methylation of OPRL1 in the nucleus accumbens.CONCLUSIONS: Our findings describe an epigenetic mechanism that helps to explain how psychosocial stress influences risky alcohol consumption and reward processing, thus contributing to the elucidation of biological mechanisms underlying risk for substance abuse.
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