Multi-Rank Sparse and Functional PCA: Manifold Optimization and Iterative Deflation Techniques

We consider the problem of estimating multiple principal components using the recently-proposed Sparse and Functional Principal Components Analysis (SFPCA) estimator. We first propose an extension of SFPCA which estimates several principal components simultaneously using manifold optimization techniques to enforce orthogonality constraints. While effective, this approach is computationally burdensome so we also consider iterative deflation approaches which take advantage of existing fast algorithms for rank-one SFPCA. We show that alternative deflation schemes can more efficiently extract signal from the data, in turn improving estimation of subsequent components. Finally, we compare the performance of our manifold optimization and deflation techniques in a scenario where orthogonality does not hold and find that they still lead to significantly improved performance.Comment: To appear in IEEE CAMSAP 201

Multivariate Analysis for Multiple Network Data via Semi-Symmetric Tensor PCA

Network data are commonly collected in a variety of applications, representing either directly measured or statistically inferred connections between features of interest. In an increasing number of domains, these networks are collected over time, such as interactions between users of a social media platform on different days, or across multiple subjects, such as in multi-subject studies of brain connectivity. When analyzing multiple large networks, dimensionality reduction techniques are often used to embed networks in a more tractable low-dimensional space. To this end, we develop a framework for principal components analysis (PCA) on collections of networks via a specialized tensor decomposition we term Semi-Symmetric Tensor PCA or SS-TPCA. We derive computationally efficient algorithms for computing our proposed SS-TPCA decomposition and establish statistical efficiency of our approach under a standard low-rank signal plus noise model. Remarkably, we show that SS-TPCA achieves the same estimation accuracy as classical matrix PCA, with error proportional to the square root of the number of vertices in the network and not the number of edges as might be expected. Our framework inherits many of the strengths of classical PCA and is suitable for a wide range of unsupervised learning tasks, including identifying principal networks, isolating meaningful changepoints or outlying observations, and for characterizing the "variability network" of the most varying edges. Finally, we demonstrate the effectiveness of our proposal on simulated data and on an example from empirical legal studies. The techniques used to establish our main consistency results are surprisingly straightforward and may find use in a variety of other network analysis problems

Multivariate Modeling of Natural Gas Spot Trading Hubs Incorporating Futures Market Realized Volatility

Financial markets for Liquified Natural Gas (LNG) are an important and rapidly-growing segment of commodities markets. Like other commodities markets, there is an inherent spatial structure to LNG markets, with different price dynamics for different points of delivery hubs. Certain hubs support highly liquid markets, allowing efficient and robust price discovery, while others are highly illiquid, limiting the effectiveness of standard risk management techniques. We propose a joint modeling strategy, which uses high-frequency information from thickly-traded hubs to improve volatility estimation and risk management at thinly traded hubs. The resulting model has superior in- and out-of-sample predictive performance, particularly for several commonly used risk management metrics, demonstrating that joint modeling is indeed possible and useful. To improve estimation, a Bayesian estimation strategy is employed and data-driven weakly informative priors are suggested. Our model is robust to sparse data and can be effectively used in any market with similar irregular patterns of data availability

The effect of omega-3 fatty acids on central nervous system remyelination in fat-1 mice

Background There is a large body of experimental evidence suggesting that omega-3 (n-3) polyunsaturated fatty acids (PUFAs) are capable of modulating immune function. Some studies have shown that these PUFAs might have a beneficial effect in patients suffering form multiple sclerosis (MS), a chronic inflammatory demyelinating disease of the central nervous system (CNS). This could be due to increased n-3 PUFA-derived anti-inflammatory lipid mediators. In the present study we tested the effect of an endogenously increased n-3 PUFA status on cuprizone-induced CNS demyelination and remyelination in fat-1 mice versus their wild-type (wt) littermates. Fat-1 mice express an n-3 desaturase, which allows them to convert n-6 PUFAs into n-3 PUFAs. Results CNS lipid profiles in fat-1 mice showed a significant increase of eicosapentaenoic acid (EPA) levels but similar docosahexaenoic acid levels compared to wt littermates. This was also reflected in significantly higher levels of monohydroxy EPA metabolites such as 18-hydroxyeicosapentaenoic acid (18-HEPE) in fat-1 brain tissue. Feeding fat-1 mice and wt littermates 0.2% cuprizone for 5 weeks caused a similar degree of CNS demyelination in both groups; remyelination was increased in the fat-1 group after a recovery period of 2 weeks. However, at p = 0.07 this difference missed statistical significance. Conclusions These results indicate that n-3 PUFAs might have a role in promotion of remyelination after toxic injury to CNS oligodendrocytes. This might occur either via modulation of the immune system or via a direct effect on oligodendrocytes or neurons through EPA- derived lipid metabolites such as 18-HEPE

Quantitative profiling of hydroxy lipid metabolites in mouse organs reveals distinct lipidomic profiles and modifications due to elevated n-3 fatty acid levels

Polyunsaturated fatty acids (PUFA) are precursors of bioactive metabolites and mediators. In this study, the profile of hydroxyeicosatetraenoic (HETE), hydroxyeicosapentaenoic (HEPE) and hydroxydocosahexaenoic (HDHA) acids derived from arachidonic acid (AA), eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) in colon, liver, lung, spleen, muscle, heart and kidney tissue of healthy wildtype mice were characterized, and compared to profiles in organs from transgenic fat-1 mice engineered to express the Caenorhabditis elegans fat-1 gene encoding an n-3 desaturase and thereby with endogenously elevated n-3 PUFA levels. PUFAs were measured using gas chromatography. The lipid metabolites were assayed using LC-MS/MS. AA and DHA were the prominent PUFAs in wildtype and fat-1 mice. EPA levels were low in both groups even though there was a significant increase in fat-1 organs with an up to 12-fold increase in fat-1 spleen and kidney. DHA levels increased by approximately 1.5-fold in fat-1 as compared to wildtype mice. While HETEs remained the same or decreased moderately and HDHAs increased 1- to 3-fold, HEPE formation in fat-1 tissues increased from 8- (muscle) to 44-fold (spleen). These findings indicate distinct profiles of monohydroxy lipid metabolites in different organs and strong utilization of EPA for HEPE formation, by which moderate EPA supplementation might trigger formation of biologically active EPA-derived resolvins