A Stochastic Tensor Method for Non-convex Optimization

We present a stochastic optimization method that uses a fourth-order regularized model to find local minima of smooth and potentially non-convex objective functions with a finite-sum structure. This algorithm uses sub-sampled derivatives instead of exact quantities. The proposed approach is shown to find an $(\epsilon_1,\epsilon_2,\epsilon_3)$-third-order critical point in at most \bigO\left(\max\left(\epsilon_1^{-4/3}, \epsilon_2^{-2}, \epsilon_3^{-4}\right)\right) iterations, thereby matching the rate of deterministic approaches. In order to prove this result, we derive a novel tensor concentration inequality for sums of tensors of any order that makes explicit use of the finite-sum structure of the objective function

Anomaly Detection in Sequential Data: A Deep Learning-Based Approach

Anomaly Detection has been researched in various domains with several applications in intrusion detection, fraud detection, system health management, and bio-informatics. Conventional anomaly detection methods analyze each data instance independently (univariate or multivariate) and ignore the sequential characteristics of the data. Anomalies in the data can be detected by grouping the individual data instances into sequential data and hence conventional way of analyzing independent data instances cannot detect anomalies. Currently: (1) Deep learning-based algorithms are widely used for anomaly detection purposes. However, significant computational overhead time is incurred during the training process due to static constant batch size and learning rate parameters for each epoch, (2) the threshold to decide whether an event is normal or malicious is often set as static. This can drastically increase the false alarm rate if the threshold is set low or decrease the True Alarm rate if it is set to a remarkably high value, (3) Real-life data is messy. It is impossible to learn the data features by training just one algorithm. Therefore, several one-class-based algorithms need to be trained. The final output is the ensemble of the output from all the algorithms. The prediction accuracy can be increased by giving a proper weight to each algorithm\u27s output. By extending the state-of-the-art techniques in learning-based algorithms, this dissertation provides the following solutions: (i) To address (1), we propose a hybrid, dynamic batch size and learning rate tuning algorithm that reduces the overall training time of the neural network. (ii) As a solution for (2), we present an adaptive thresholding algorithm that reduces high false alarm rates. (iii) To overcome (3), we propose a multilevel hybrid ensemble anomaly detection framework that increases the anomaly detection rate of the high dimensional dataset