Feature selection aims to identify the most pattern-discriminative feature subset. In prior literature, filter (e.g., backward elimination) and embedded (e.g., Lasso) methods have hyperparameters (e.g., top-K, score thresholding) and tie to specific models, thus, hard to generalize; wrapper methods search a feature subset in a huge discrete space and is computationally costly. To transform the way of feature selection, we regard a selected feature subset as a selection decision token sequence and reformulate feature selection as a deep sequential generative learning task that distills feature knowledge and generates decision sequences. Our method includes three steps: (1) We develop a deep variational transformer model over a joint of sequential reconstruction, variational, and performance evaluator losses. Our model can distill feature selection knowledge and learn a continuous embedding space to map feature selection decision sequences into embedding vectors associated with utility scores. (2) We leverage the trained feature subset utility evaluator as a gradient provider to guide the identification of the optimal feature subset embedding;(3) We decode the optimal feature subset embedding to autoregressively generate the best feature selection decision sequence with autostop. Extensive experimental results show this generative perspective is effective and generic, without large discrete search space and expert-specific hyperparameters.

This work concentrates on optimization on Riemannian manifolds. The Limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm is a commonly used quasi-Newton method for numerical optimization in Euclidean spaces. Riemannian LBFGS (RLBFGS) is an extension of this method to Riemannian manifolds. RLBFGS involves computationally expensive vector transports as well as unfolding recursions using adjoint vector transports. In this article, we propose two mappings in the tangent space using the inverse second root and Cholesky decomposition. These mappings make both vector transport and adjoint vector transport identity and therefore isometric. Identity vector transport makes RLBFGS less computationally expensive and its isometry is also very useful in convergence analysis of RLBFGS. Moreover, under the proposed mappings, the Riemannian metric reduces to Euclidean inner product, which is much less computationally expensive. We focus on the Symmetric Positive Definite (SPD) manifolds which are beneficial in various fields such as data science and statistics. This work opens a research opportunity for extension of the proposed mappings to other well-known manifolds.