A Local Sparse Screening Identification Algorithm with Applications

Extracting nonlinear governing equations from noisy data is a central challenge in the analysis of complicated nonlinear behaviors.Despite researchers follow the sparse identification nonlinear dynamics algorithm(SINDy)rule to restore nonlinear equations,there also exist obstacles.One is the excessive dependence on empirical parameters,which increases the difficulty of data pre-processing.Another one is the coexistence of multiple coefficient vectors,which causes the optimal solution to be drowned in multiple solutions.The third one is the composition of basic function,which is exclusively applicable to specific equations.In this article,a local sparse screening identification algorithm(LSSI)is proposed to identify nonlinear systems.First,we present the k-neighbor parameter to replace all empirical parameters in data filtering.Second,we combine the mean error screening method with the SINDy algorithm to select the optimal one from multiple solutions.Third,the time variable t is introduced to expand the scope of the SINDy algorithm.Finally,the LSSI algorithm is applied to recover a classic ODE and a bi-stable energy harvester system.The results show that the new algorithm improves the ability of noise immunity and optimal parameters identification provides a desired foundation for nonlinear analyses.

A CLASS OF FACTORIZATION UPDATE ALGORITHM FOR SOLVING SYSTEMS OF SPARSE NONLINEAR EQUATIONS

In this paper, we establish a class of sparse update algorithm based on matrix triangular factorizations for solving a system of sparse equations. The local Q-superlinear convergence of the algorithm is proved without introducing an m-step refactorization. We compare the numerical results of the new algorithm with those of the known algorithms, The comparison implies that the new algorithm is satisfactory.

An improved algorithm for noise-robust sparse linear prediction of speech

The performance of linear prediction analysis of speech deteriorates rapidly under noisy environments. To tackle this issue, an improved noise-robust sparse linear prediction algorithm is proposed. First, the linear prediction residual of speech is modeled as Student-t distribution, and the additive noise is incorporated explicitly to increase the robustness, thus a probabilistic model for sparse linear prediction of speech is built, Furthermore, variational Bayesian inference is utilized to approximate the intractable posterior distributions of the model parameters, and then the optimal linear prediction parameters are estimated robustly. The experimental results demonstrate the advantage of the developed algorithm in terms of several different metrics compared with the traditional algorithm and the l1 norm minimization based sparse linear prediction algorithm proposed in recent years. Finally it draws to a conclusion that the proposed algorithm is more robust to noise and is able to increase the speech quality in applications.

Smolyak Type Sparse Grid Collocation Method for Uncertainty Quantification of Nonlinear Stochastic Dynamic Equations

This paper develops a Smolyak-type sparse-grid stochastic collocation method(SGSCM) for uncertainty quantification of nonlinear stochastic dynamic equations.The solution obtained by the method is a linear combination of tensor product formulas for multivariate polynomial interpolation.By choosing the collocation point sets to coincide with cubature point sets of quadrature rules,we derive quadrature formulas to estimate the expectations of the solution.The method does not suffer from the curse of dimensionality in the sense that the computational cost does not increase exponentially with the number of input random variables.Numerical analysis of a nonlinear elastic oscillator subjected to a discretized band-limited white noise process demonstrates the computational efficiency and accuracy of the developed method.

High Accuracy Gene Signature for Chemosensitivity Prediction in Breast Cancer

Neoadjuvant chemotherapy for breast cancer patients with large tumor size is a necessary treatment.After this treatment patients who achieve a pathologic Complete Response（p CR） usually have a favorable prognosis than those without. Therefore, p CR is now considered as the best prognosticator for patients with neoadjuvant chemotherapy. However, not all patients can benefit from this treatment. As a result, we need to find a way to predict what kind of patients can induce p CR. Various gene signatures of chemosensitivity in breast cancer have been identified, from which such predictors can be built. Nevertheless, many of them have their prediction accuracy around 80%. As such, identifying gene signatures that could be employed to build high accuracy predictors is a prerequisite for their clinical tests and applications. Furthermore, to elucidate the importance of each individual gene in a signature is another pressing need before such signature could be tested in clinical settings. In this study, Genetic Algorithm（GA） and Sparse Logistic Regression（SLR） along with t-test were employed to identify one signature. It had 28 probe sets selected by GA from the top 65 probe sets that were highly overexpressed between p CR and Residual Disease（RD） and was used to build an SLR predictor of p CR（SLR-28）. This predictor tested on a training set（n = 81） and validation set（n = 52） had very precise predictions measured by accuracy,specificity, sensitivity, positive predictive value, and negative predictive value with their corresponding P value all zero. Furthermore, this predictor discovered 12 important genes in the 28 probe set signature. Our findings also demonstrated that the most discriminative genes measured by SLR as a group selected by GA were not necessarily those with the smallest P values by t-test as individual genes, highlighting the ability of GA to capture the interacting genes in p CR prediction as multivariate techniques. Our gene signature produced superior performance over a signature found in one previous study with prediction accuracy 92% vs 76%, demonstrating the potential of GA and SLR in identifying robust gene signatures in chemo response prediction in breast cancer.