New estimations on the upper bounds for the nuclear norm of a tensor.
Ontology highlight
ABSTRACT:
SUBMITTER: Kong X
PROVIDER: S-EPMC6208618 | biostudies-other | 2018
REPOSITORIES: biostudies-other
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Project description:The notion of a fuzzy upper bound over a groupoid is introduced and some properties of it are investigated. We also define the notions of an either-or subset of a groupoid and a strong either-or subset of a groupoid and study some of their related properties. In particular, we consider fuzzy upper bounds in Bin(X), where Bin(X) is the collection of all groupoids. Finally, we define a fuzzy-d-subset of a groupoid and investigate some of its properties.
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Project description:MotivationComputational drug repositioning is a cost-effective strategy to identify novel indications for existing drugs. Drug repositioning is often modeled as a recommendation system problem. Taking advantage of the known drug-disease associations, the objective of the recommendation system is to identify new treatments by filling out the unknown entries in the drug-disease association matrix, which is known as matrix completion. Underpinned by the fact that common molecular pathways contribute to many different diseases, the recommendation system assumes that the underlying latent factors determining drug-disease associations are highly correlated. In other words, the drug-disease matrix to be completed is low-rank. Accordingly, matrix completion algorithms efficiently constructing low-rank drug-disease matrix approximations consistent with known associations can be of immense help in discovering the novel drug-disease associations.ResultsIn this article, we propose to use a bounded nuclear norm regularization (BNNR) method to complete the drug-disease matrix under the low-rank assumption. Instead of strictly fitting the known elements, BNNR is designed to tolerate the noisy drug-drug and disease-disease similarities by incorporating a regularization term to balance the approximation error and the rank properties. Moreover, additional constraints are incorporated into BNNR to ensure that all predicted matrix entry values are within the specific interval. BNNR is carried out on an adjacency matrix of a heterogeneous drug-disease network, which integrates the drug-drug, drug-disease and disease-disease networks. It not only makes full use of available drugs, diseases and their association information, but also is capable of dealing with cold start naturally. Our computational results show that BNNR yields higher drug-disease association prediction accuracy than the current state-of-the-art methods. The most significant gain is in prediction precision measured as the fraction of the positive predictions that are truly positive, which is particularly useful in drug design practice. Cases studies also confirm the accuracy and reliability of BNNR.Availability and implementationThe code of BNNR is freely available at https://github.com/BioinformaticsCSU/BNNR.Supplementary informationSupplementary data are available at Bioinformatics online.
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Project description:We propose an adaptive nuclear norm penalization approach for low-rank matrix approximation, and use it to develop a new reduced rank estimation method for high-dimensional multivariate regression. The adaptive nuclear norm is defined as the weighted sum of the singular values of the matrix, and it is generally non-convex under the natural restriction that the weight decreases with the singular value. However, we show that the proposed non-convex penalized regression method has a global optimal solution obtained from an adaptively soft-thresholded singular value decomposition. The method is computationally efficient, and the resulting solution path is continuous. The rank consistency of and prediction/estimation performance bounds for the estimator are established for a high-dimensional asymptotic regime. Simulation studies and an application in genetics demonstrate its efficacy.
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Project description:BackgroundPremature discontinuation and other forms of noncompliance with treatment assignment can complicate causal inference of treatment effects in randomized trials. The intent-to-treat analysis gives unbiased estimates for causal effects of treatment assignment on outcome, but may understate potential benefit or harm of actual treatment. The corresponding upper confidence limit can also be underestimated.PurposeTo compare estimates of the hazard ratio and upper bound of the two-sided 95% confidence interval from causal inference methods that account for noncompliance with those from the intent-to-treat analysis.MethodsWe used simulations with parameters chosen to reflect cardiovascular safety trials of diabetes drugs, with a focus on upper bound estimates relative to 1.3, based on regulatory guidelines. A total of 1000 simulations were run under each parameter combination for a hypothetical trial of 10,000 total subjects randomly assigned to active treatment or control at 1:1 ratio. Noncompliance was considered in the form of treatment discontinuation and cross-over at specified proportions, with an assumed true hazard ratio of 0.9, 1, and 1.3, respectively. Various levels of risk associated with being a non-complier (independent of treatment status) were evaluated. Hazard ratio and upper bound estimates from causal survival analysis and intent-to-treat were obtained from each simulation and summarized under each parameter setting.ResultsCausal analysis estimated the true hazard ratio with little bias in almost all settings examined. Intent-to-treat was unbiased only when the true hazard ratio = 1; otherwise it underestimated both benefit and harm. When upper bound estimates from intent-to-treat were ≥1.3, corresponding estimates from causal analysis were also ≥1.3 in almost 100% of the simulations, regardless of the true hazard ratio. When upper bound estimates from intent-to-treat were <1.3 and the true hazard ratio = 1, corresponding upper bound estimates from causal analysis were ≥1.3 in up to 66% of the simulations under some settings.LimitationsSimulations cannot cover all scenarios for noncompliance in real randomized trials.ConclusionCausal survival analysis was superior to intent-to-treat in estimating the true hazard ratio with respect to bias in the presence of noncompliance. However, its large variance should be considered for safety upper bound exclusion especially when the true hazard ratio = 1. Our simulations provided a broad reference for practical considerations of bias-variance trade-off in dealing with noncompliance in cardiovascular safety trials of diabetes drugs. Further research is warranted for the development and application of causal inference methods in the evaluation of safety upper bounds.
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Project description:BACKGROUND: Enumeration of chemical graphs satisfying given constraints is one of the fundamental problems in chemoinformatics and bioinformatics since it leads to a variety of useful applications including structure determination of novel chemical compounds and drug design. RESULTS: In this paper, we consider the problem of enumerating all tree-like chemical graphs from a given set of feature vectors, which is specified by a pair of upper and lower feature vectors, where a feature vector represents the frequency of prescribed paths in a chemical compound to be constructed. This problem can be solved by applying the algorithm proposed by Ishida et al. to each single feature vector in the given set, but this method may take much computation time because in general there are many feature vectors in a given set. We propose a new exact branch-and-bound algorithm for the problem so that all the feature vectors in a given set are handled directly. Since we cannot use the bounding operation proposed by Ishida et al. due to upper and lower constraints, we introduce new bounding operations based on upper and lower feature vectors, a bond constraint, and a detachment condition. CONCLUSIONS: Our proposed algorithm is useful for enumerating tree-like chemical graphs with given upper and lower bounds on path frequencies.
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Project description:MotivationReticulate network is a model for displaying and quantifying the effects of complex reticulate processes on the evolutionary history of species undergoing reticulate evolution. A central computational problem on reticulate networks is: given a set of phylogenetic trees (each for some region of the genomes), reconstruct the most parsimonious reticulate network (called the minimum reticulate network) that combines the topological information contained in the given trees. This problem is well-known to be NP-hard. Thus, existing approaches for this problem either work with only two input trees or make simplifying topological assumptions.ResultsWe present novel results on the minimum reticulate network problem. Unlike existing approaches, we address the fully general problem: there is no restriction on the number of trees that are input, and there is no restriction on the form of the allowed reticulate network. We present lower and upper bounds on the minimum number of reticulation events in the minimum reticulate network (and infer an approximately parsimonious reticulate network). A program called PIRN implements these methods, which also outputs a graphical representation of the inferred network. Empirical results on simulated and biological data show that our methods are practical for a wide range of data. More importantly, the lower and upper bounds match for many datasets (especially when the number of trees is small or reticulation level is low), and this allows us to solve the minimum reticulate network problem exactly for these datasets.AvailabilityA software tool, PIRN, is available for download from the web page: http://www.engr.uconn.edu/~ywu.Supplementary informationSupplementary data is available at Bioinformatics online.
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