Sparse Nonlinear Feature Selection Algorithm via Local Structure Learning

In this paper, we propose a new unsupervised feature selection algorithm by considering the nonlinear and similarity relationships within the data. To achieve this, we apply the kernel method and local structure learning to consider the nonlinear relationship between features and the local similarity between features. Specifically, we use a kernel function to map each feature of the data into the kernel space. In the high-dimensional kernel space, different features correspond to different weights, and zero weights are unimportant features (e.g. redundant features). Furthermore, we consider the similarity between features through local structure learning, and propose an effective optimization method to solve it. The experimental results show that the proposed algorithm achieves better performance than the comparison algorithm.

Evaluation of Causal Effects and Local Structure Learning of Causal Networks

Causal effect evaluation and causal network learning are two main research areas in causal inference. For causal effect evaluation, we review the two problems of confounders and surrogates. The Yule-Simpson paradox is the idea that the association between two variables may be changed dramatically due to ignoring confounders. We review criteria for confounders and methods of adjustment for observed and unobserved confounders. The surrogate paradox occurs when a treatment has a positive causal effect on a surrogate endpoint, which, in turn, has a positive causal effect on a true endpoint, but the treatment may have a negative causal effect on the true endpoint. Some of the existing criteria for surrogates are subject to the surrogate paradox, and we review criteria for consistent surrogates to avoid the surrogate paradox. Causal networks are used to depict the causal relationships among multiple variables. Rather than discovering a global causal network, researchers are often interested in discovering the causes and effects of a given variable. We review some algorithms for local structure learning of causal networks centering around a given variable.