In many regression tasks, in addition to an accurate estimate of the conditional mean of the target distribution, an indication of the predictive uncertainty is also required. There are two principal sources of this uncertainty: the noise process contaminating the data and the uncertainty in estimating the model parameters based on a limited sample of training data. Both of them can be summaris...

Ridge regression is an algorithm that takes as input a large number of data points and finds the best-fit linear curve through these points. It is a building block for many machine-learning operations. This report presents a system for privacy-preserving ridge regression. The system outputs the best-fit curve in the clear, but exposes no other information about the input data. This problem was ...

Based on the feature map principle, Sparse Kernel Ridge Regression (SKRR) model is proposed. SKRR obtains the sparseness by backward deletion feature selection procedure that recursively removes the feature with the smallest leave-one-out score until the stop criterion is satisfied. Besides good generalization performance, the most compelling property of SKRR is rather sparse, and moreover, the...

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Traditional methods of assessing chemical toxicity of various compounds require tests on animals, which raises ethical concerns and is expensive. Current legislation may lead to a further increase of demand for laboratory animals in the next years. As a result, automatically generated predictions using Quantitative Structure–Activity Relationship (QSAR) modelling approaches appear as an attract...

A multiple regression model has got the standard assumptions. If the data can not satisfy these assumptions some problems which have some serious undesired effects on the parameter estimates arise. One of the problems is called multicollinearity which means that there is a nearly perfect linear relationship between explanatory variables used in a multiple regression model. This undesirable prob...

Ridge regression, being based on the minimization of a quadratic loss function, is sensitive to outliers. Current proposals for robust ridge regression estimators are sensitive to “bad leverage observations”, cannot be employed when the number of predictors p is larger than the number of observations n; and have a low robustness when the ratio p=n is large. In this paper a ridge regression esti...

It is widely believed that both common and rare variants contribute to the risks of common diseases or complex traits and the cumulative effects of multiple rare variants can explain a significant proportion of trait variances. Advances in high-throughput DNA sequencing technologies allow us to genotype rare causal variants and investigate the effects of such rare variants on complex traits. We...

In this material, we provide the theoretical analyses to show that the trivial coefficients always correspond to the codes over errors. Lemmas 1–3 show that our errors-removing strategy will perform well when the lp-norm is enforced over the representation, where p = {1, 2,∞}. Let x 6= 0 be a data point in the union of subspaces SD that is spanned by D = [Dx D−x], where Dx and D−x consist of th...

Fisher linear discriminant analysis (FDA) and its kernel extension—kernel discriminant analysis (KDA)—are well known methods that consider dimensionality reduction and classification jointly. While widely deployed in practical problems, there are still unresolved issues surrounding their efficient implementation and their relationship with least mean squares procedures. In this paper we address...