A Noise-Robust Fast Sparse Bayesian Learning Model

This paper utilizes the hierarchical model structure from the Bayesian Lasso in the Sparse Bayesian Learning process to develop a new type of probabilistic supervised learning approach. The hierarchical model structure in this Bayesian framework is designed such that the priors do not only penalize the unnecessary complexity of the model but will also be conditioned on the variance of the random noise in the data. The hyperparameters in the model are estimated by the Fast Marginal Likelihood Maximization algorithm which can achieve sparsity, low computational cost and faster learning process. We compare our methodology with two other popular learning models; the Relevance Vector Machine and the Bayesian Lasso. We test our model on examples involving both simulated and empirical data, and the results show that this approach has several performance advantages, such as being fast, sparse and also robust to the variance in random noise. In addition, our method can give out a more stable estimation of variance of random error, compared with the other methods in the study.Comment: 15 page

Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction

It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron et al. \cite{LARS}), one of the most popular algorithms in sparse learning, cannot be applied. Therefore, most current approaches take indirect ways or have strict settings, which can be inconvenient for applications. In this paper, we proposed the manifold elastic net or MEN for short. MEN incorporates the merits of both the manifold learning based dimensionality reduction and the sparse learning based dimensionality reduction. By using a series of equivalent transformations, we show MEN is equivalent to the lasso penalized least square problem and thus LARS is adopted to obtain the optimal sparse solution of MEN. In particular, MEN has the following advantages for subsequent classification: 1) the local geometry of samples is well preserved for low dimensional data representation, 2) both the margin maximization and the classification error minimization are considered for sparse projection calculation, 3) the projection matrix of MEN improves the parsimony in computation, 4) the elastic net penalty reduces the over-fitting problem, and 5) the projection matrix of MEN can be interpreted psychologically and physiologically. Experimental evidence on face recognition over various popular datasets suggests that MEN is superior to top level dimensionality reduction algorithms.Comment: 33 pages, 12 figure

Classification hardness for supervised learners on 20 years of intrusion detection data

This article consolidates analysis of established (NSL-KDD) and new intrusion detection datasets (ISCXIDS2012, CICIDS2017, CICIDS2018) through the use of supervised machine learning (ML) algorithms. The uniformity in analysis procedure opens up the option to compare the obtained results. It also provides a stronger foundation for the conclusions about the efficacy of supervised learners on the main classification task in network security. This research is motivated in part to address the lack of adoption of these modern datasets. Starting with a broad scope that includes classification by algorithms from different families on both established and new datasets has been done to expand the existing foundation and reveal the most opportune avenues for further inquiry. After obtaining baseline results, the classification task was increased in difficulty, by reducing the available data to learn from, both horizontally and vertically. The data reduction has been included as a stress-test to verify if the very high baseline results hold up under increasingly harsh constraints. Ultimately, this work contains the most comprehensive set of results on the topic of intrusion detection through supervised machine learning. Researchers working on algorithmic improvements can compare their results to this collection, knowing that all results reported here were gathered through a uniform framework. This work's main contributions are the outstanding classification results on the current state of the art datasets for intrusion detection and the conclusion that these methods show remarkable resilience in classification performance even when aggressively reducing the amount of data to learn from