We consider the optimization problem of minimizing an objective functional, which admits a variational form and is defined over probability distributions on the constrained domain, which poses challenges to both theoretical analysis and algorithmic design. Inspired by the mirror descent algorithm for constrained optimization, we propose an iterative particle-based algorithm, named Mirrored Variational Transport (mirrorVT), extended from the Variational Transport framework [7] for dealing with the constrained domain. In particular, for each iteration, mirrorVT maps particles to an unconstrained dual domain induced by a mirror map and then approximately perform Wasserstein gradient descent on the manifold of distributions defined over the dual space by pushing particles. At the end of iteration, particles are mapped back to the original constrained domain. Through simulated experiments, we demonstrate the effectiveness of mirrorVT for minimizing the functionals over probability distributions on the simplex- and Euclidean ball-constrained domains. We also analyze its theoretical properties and characterize its convergence to the global minimum of the objective functional.

One of the most important problems arising in time series analysis is that of bifurcation, or change point detection. That is, given a collection of time series over a varying parameter, when has the structure of the underlying dynamical system changed? For this task, we turn to the field of topological data analysis (TDA), which encodes information about the shape and structure of data. The idea of utilizing tools from TDA for signal processing tasks, known as topological signal processing (TSP), has gained much attention in recent years, largely through a standard pipeline that computes the persistent homology of the point cloud generated by the Takens' embedding. However, this procedure is limited by computation time since the simplicial complex generated in this case is large, but also has a great deal of redundant data. For this reason, we turn to a more recent method for encoding the structure of the attractor, which constructs an ordinal partition network (OPN) representing information about when the dynamical system has passed between certain regions of state space. The result is a weighted graph whose structure encodes information about the underlying attractor. Our previous work began to find ways to package the information of the OPN in a manner that is amenable to TDA; however, that work only used the network structure and did nothing to encode the additional weighting information. In this paper, we take the next step: building a pipeline to analyze the weighted OPN with TDA and showing that this framework provides more resilience to noise or perturbations in the system and improves the accuracy of the dynamic state detection.

Systems biology seeks to create math models of biological systems to reduce inherent biological complexity and provide predictions for applications such as therapeutic development. However, it remains a challenge to determine which math model is correct and how to arrive optimally at the answer. We present an algorithm for automated biological model selection using mathematical models of systems biology and likelihood free inference methods. Our algorithm shows improved performance in arriving at correct models without a priori information over conventional heuristics used in experimental biology and random search. This method shows promise to accelerate biological basic science and drug discovery.

Stochastic gradient descent (SGD) algorithm is an effective learning strategy to build a latent factor analysis (LFA) model on a high-dimensional and incomplete (HDI) matrix. A particle swarm optimization (PSO) algorithm is commonly adopted to make an SGD-based LFA model's hyper-parameters, i.e, learning rate and regularization coefficient, self-adaptation. However, a standard PSO algorithm may suffer from accuracy loss caused by premature convergence. To address this issue, this paper incorporates more historical information into each particle's evolutionary process for avoiding premature convergence following the principle of a generalized-momentum (GM) method, thereby innovatively achieving a novel GM-incorporated PSO (GM-PSO). With it, a GM-PSO-based LFA (GMPL) model is further achieved to implement efficient self-adaptation of hyper-parameters. The experimental results on three HDI matrices demonstrate that the GMPL model achieves a higher prediction accuracy for missing data estimation in industrial applications.

Recently, graph neural networks have shown the superiority of modeling the complex topological structures in heterogeneous network-based recommender systems. Due to the diverse interactions among nodes and abundant semantics emerging from diverse types of nodes and edges, there is a bursting research interest in learning expressive node representations in multiplex heterogeneous networks. One of the most important tasks in recommender systems is to predict the potential connection between two nodes under a specific edge type (i.e., relationship). Although existing studies utilize explicit metapaths to aggregate neighbors, practically they only consider intra-relationship metapaths and thus fail to leverage the potential uplift by inter-relationship information. Moreover, it is not always straightforward to exploit inter-relationship metapaths comprehensively under diverse relationships, especially with the increasing number of node and edge types. In addition, contributions of different relationships between two nodes are difficult to measure. To address the challenges, we propose HybridGNN, an end-to-end GNN model with hybrid aggregation flows and hierarchical attentions to fully utilize the heterogeneity in the multiplex scenarios. Specifically, HybridGNN applies a randomized inter-relationship exploration module to exploit the multiplexity property among different relationships. Then, our model leverages hybrid aggregation flows under intra-relationship metapaths and randomized exploration to learn the rich semantics. To explore the importance of different aggregation flow and take advantage of the multiplexity property, we bring forward a novel hierarchical attention module which leverages both metapath-level attention and relationship-level attention. Extensive experimental results suggest that HybridGNN achieves the best performance compared to several state-of-the-art baselines.

In this paper, we propose SGEM, Stochastic Gradient with Energy and Momentum, to solve a large class of general non-convex stochastic optimization problems, based on the AEGD method that originated in the work [AEGD: Adaptive Gradient Descent with Energy. arXiv: 2010.05109]. SGEM incorporates both energy and momentum at the same time so as to inherit their dual advantages. We show that SGEM features an unconditional energy stability property, and derive energy-dependent convergence rates in the general nonconvex stochastic setting, as well as a regret bound in the online convex setting. A lower threshold for the energy variable is also provided. Our experimental results show that SGEM converges faster than AEGD and generalizes better or at least as well as SGDM in training some deep neural networks.

Area under the ROC curve, a.k.a. AUC, is a measure of choice for assessing the performance of a classifier for imbalanced data. AUC maximization refers to a learning paradigm that learns a predictive model by directly maximizing its AUC score. It has been studied for more than two decades dating back to late 90s and a huge amount of work has been devoted to AUC maximization since then. Recently, stochastic AUC maximization for big data and deep AUC maximization for deep learning have received increasing attention and yielded dramatic impact for solving real-world problems. However, to the best our knowledge there is no comprehensive survey of related works for AUC maximization. This paper aims to address the gap by reviewing the literature in the past two decades. We not only give a holistic view of the literature but also present detailed explanations and comparisons of different papers from formulations to algorithms and theoretical guarantees. We also identify and discuss remaining and emerging issues for deep AUC maximization, and provide suggestions on topics for future work.

Machine learning based malware detection techniques rely on grayscale images of malware and tends to classify malware based on the distribution of textures in graycale images. Albeit the advancement and promising results shown by machine learning techniques, attackers can exploit the vulnerabilities by generating adversarial samples. Adversarial samples are generated by intelligently crafting and adding perturbations to the input samples. There exists majority of the software based adversarial attacks and defenses. To defend against the adversaries, the existing malware detection based on machine learning and grayscale images needs a preprocessing for the adversarial data. This can cause an additional overhead and can prolong the real-time malware detection. So, as an alternative to this, we explore RRAM (Resistive Random Access Memory) based defense against adversaries. Therefore, the aim of this thesis is to address the above mentioned critical system security issues. The above mentioned challenges are addressed by demonstrating proposed techniques to design a secure and robust cognitive system. First, a novel technique to detect stealthy malware is proposed. The technique uses malware binary images and then extract different features from the same and then employ different ML-classifiers on the dataset thus obtained. Results demonstrate that this technique is successful in differentiating classes of malware based on the features extracted. Secondly, I demonstrate the effects of adversarial attacks on a reconfigurable RRAM-neuromorphic architecture with different learning algorithms and device characteristics. I also propose an integrated solution for mitigating the effects of the adversarial attack using the reconfigurable RRAM architecture.

This paper proves that robustness implies generalization via data-dependent generalization bounds. As a result, robustness and generalization are shown to be connected closely in a data-dependent manner. Our bounds improve previous bounds in two directions, to solve an open problem that has seen little development since 2010. The first is to reduce the dependence on the covering number. The second is to remove the dependence on the hypothesis space. We present several examples, including ones for lasso and deep learning, in which our bounds are provably preferable. The experiments on real-world data and theoretical models demonstrate near-exponential improvements in various situations. To achieve these improvements, we do not require additional assumptions on the unknown distribution; instead, we only incorporate an observable and computable property of the training samples. A key technical innovation is an improved concentration bound for multinomial random variables that is of independent interest beyond robustness and generalization.

Federated learning, as a privacy-preserving collaborative machine learning paradigm, has been gaining more and more attention in the industry. With the huge rise in demand, there have been many federated learning platforms that allow federated participants to set up and build a federated model from scratch. However, exiting platforms are highly intrusive, complicated, and hard to integrate with built machine learning models. For many real-world businesses that already have mature serving models, existing federated learning platforms have high entry barriers and development costs. This paper presents a simple yet practical federated learning plug-in inspired by ensemble learning, dubbed WrapperFL, allowing participants to build/join a federated system with existing models at minimal costs. The WrapperFL works in a plug-and-play way by simply attaching to the input and output interfaces of an existing model, without the need of re-development, significantly reducing the overhead of manpower and resources. We verify our proposed method on diverse tasks under heterogeneous data distributions and heterogeneous models. The experimental results demonstrate that WrapperFL can be successfully applied to a wide range of applications under practical settings and improves the local model with federated learning at a low cost.