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With the growth of interest in the attack and defense of deep neural networks, researchers are focusing more on the robustness of applying them to devices with limited memory. Thus, unlike adversarial training, which only considers the…

Bayesian method is capable of capturing real world uncertainties/incompleteness and properly addressing the over-fitting issue faced by deep neural networks. In recent years, Bayesian Neural Networks (BNNs) have drawn tremendous attentions…

In recent years Deep Neural Networks (DNNs) have been rapidly developed in various applications, together with increasingly complex architectures. The performance gain of these DNNs generally comes with high computational costs and large…

Alternating Direction Method of Multipliers (ADMM) has been used successfully in many conventional machine learning applications and is considered to be a useful alternative to Stochastic Gradient Descent (SGD) as a deep learning optimizer.…

Recently proposed numerical algorithms for solving high-dimensional nonlinear partial differential equations (PDEs) based on neural networks have shown their remarkable performance. We review some of them and study their convergence…

Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…

This paper considers distributed average consensus using finite-bit bounded quantizer with possibly unbounded data. Under the framework of the alternating direction method of multipliers (ADMM), we develop distributed averaging algorithms…

We propose several novel methods for enhancing the multi-class SVMs by applying the generalization performance of binary classifiers as the core idea. This concept will be applied on the existing algorithms, i.e., the Decision Directed…

Binary embeddings provide efficient and powerful ways to perform operations on large scale data. However binary embedding typically requires long codes in order to preserve the discriminative power of the input space. Thus binary coding…

Over the past decade, decision diagrams (DDs) have been used to model and solve integer programming and combinatorial optimization problems. Despite successful performance of DDs in solving various discrete optimization problems, their…

This paper focuses on distributed constrained optimization over time-varying directed networks, where all agents cooperate to optimize the sum of their locally accessible objective functions subject to a coupled inequality constraint…

We address the extraction of mathematical statements and their proofs from scholarly PDF articles as a multimodal classification problem, utilizing text, font features, and bitmap image renderings of PDFs as distinct modalities. We propose…

Sparse variable selection improves interpretability and generalization in high-dimensional learning by selecting a small subset of informative features. Recent advances in Mixed Integer Programming (MIP) have enabled solving large-scale…

Breadth-first search (BFS) is known as a basic search strategy for learning graph properties. As the scales of graph databases have increased tremendously in recent years, large-scale graphs G are often disk-resident. Obtaining the BFS…

A buffer k-d tree is a k-d tree variant for massively-parallel nearest neighbor search. While providing valuable speed-ups on modern many-core devices in case both a large number of reference and query points are given, buffer k-d trees are…

Modern 3D image recovery problems require powerful optimization frameworks to handle high dimensionality while providing reliable numerical solutions in a reasonable time. In this perspective, asynchronous parallel optimization algorithms…

Approximate nearest neighbour (ANN) search has become a central task in modern data-intensive applications, particularly when operating on large, heterogeneous, or high-dimensional datasets. However, many existing ANN methods struggle in…

Efficient exact algorithms for Discrete Optimization (DO) rely heavily on strong primal and dual bounds. Relaxed Decision Diagrams (DDs) provide a versatile mechanism for deriving such dual bounds by compactly over-approximating the…

Despite significant recent advances in deep neural networks, training them remains a challenge due to the highly non-convex nature of the objective function. State-of-the-art methods rely on error backpropagation, which suffers from several…

Efficient Nearest Neighbor (NN) search in high-dimensional spaces is a foundation of many multimedia retrieval systems. A common approach is to rely on Product Quantization, which allows the storage of large vector databases in memory and…