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The highly non-linear nature of deep neural networks causes them to be susceptible to adversarial examples and have unstable gradients which hinders interpretability. However, existing methods to solve these issues, such as adversarial…

In this paper, we propose a new randomized second-order optimization algorithm---Stochastic Subspace Cubic Newton (SSCN)---for minimizing a high dimensional convex function $f$. Our method can be seen both as a {\em stochastic} extension of…

We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…

Neural networks (NNs) have emerged as a state-of-the-art method for modeling nonlinear systems in model predictive control (MPC). However, the robustness of NNs, in terms of sensitivity to small input perturbations, remains a critical…

Deep Neural Network (DNN) based super-resolution algorithms have greatly improved the quality of the generated images. However, these algorithms often yield significant artifacts when dealing with real-world super-resolution problems due to…

In this paper, we utilize stochastic optimization to reduce the space complexity of convex composite optimization with a nuclear norm regularizer, where the variable is a matrix of size $m \times n$. By constructing a low-rank estimate of…

This work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of…

Nowadays, graph-structured data are increasingly used to model complex systems. Meanwhile, detecting anomalies from graph has become a vital research problem of pressing societal concerns. Anomaly detection is an unsupervised learning task…

Effectively detecting anomalous nodes in attributed networks is crucial for the success of many real-world applications such as fraud and intrusion detection. Existing approaches have difficulties with three major issues: sparsity and…

Graph Neural Networks (GNNs) have enjoyed wide spread applications in graph-structured data. However, existing graph based applications commonly lack annotated data. GNNs are required to learn latent patterns from a limited amount of…

The success of neural networks over the past decade has established them as effective models for many relevant data generating processes. Statistical theory on neural networks indicates graceful scaling of sample complexity. For example,…

Graph convolutional networks (GCNs) aim at extending deep learning to arbitrary irregular domains, namely graphs. Their success is highly dependent on how the topology of input graphs is defined and most of the existing GCN architectures…

Graph convolutional networks (GCNs) update a node's feature vector by aggregating features from its neighbors in the graph. This ignores potentially useful contributions from distant nodes. Identifying such useful distant contributions is…

The adaptive smoothing method (ASM) is a standard data-driven technique used in traffic state estimation. The ASM has free parameters which, in practice, are chosen to be some generally acceptable values based on intuition. However, we note…

Convolutional Neural Networks (CNNs) have achieved remarkable success across a wide range of machine learning tasks by leveraging hierarchical feature learning through deep architectures. However, the large number of layers and millions of…

Standard deep learning models that employ the categorical cross-entropy loss are known to perform well at image classification tasks. However, many standard models thus obtained often exhibit issues like feature redundancy, low…

This work studies the global convergence and implicit bias of Gauss Newton's (GN) when optimizing over-parameterized one-hidden layer networks in the mean-field regime. We first establish a global convergence result for GN in the…

Stochastic gradient descent (SGD) is a popular stochastic optimization method in machine learning. Traditional parallel SGD algorithms, e.g., SimuParallel SGD, often require all nodes to have the same performance or to consume equal…

Graph structural information such as topologies or connectivities provides valuable guidance for graph convolutional networks (GCNs) to learn nodes' representations. Existing GCN models that capture nodes' structural information weight in-…

A deep neural network of multiple nonlinear layers forms a large function space, which can easily lead to overfitting when it encounters small-sample data. To mitigate overfitting in small-sample classification, learning more discriminative…