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Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

Motivation: Microarray experiments result in large scale data sets that require extensive mining and refining to extract useful information. We have been developing an efficient novel algorithm for nonmetric multidimensional scaling (nMDS)…

The problem of finding a reduced dimensionality representation of categorical variables while preserving their most relevant characteristics is fundamental for the analysis of complex data. Specifically, given a co-occurrence matrix of two…

Sparse signal recovery problems from noisy linear measurements appear in many areas of wireless communications. In recent years, deep learning (DL) based approaches have attracted interests of researchers to solve the sparse linear inverse…

Time series forecasting is often fundamental to scientific and engineering problems and enables decision making. With ever increasing data set sizes, a trivial solution to scale up predictions is to assume independence between interacting…

Most of the existing multi-relational network embedding methods, e.g., TransE, are formulated to preserve pair-wise connectivity structures in the networks. With the observations that significant triangular connectivity structures and…

There are many time series in the literature with high dimension yet limited sample sizes, such as macroeconomic variables, and it is almost impossible to obtain efficient estimation and accurate prediction by using the corresponding…

The human visual system is an intricate network of brain regions that enables us to recognize the world around us. Despite its abundant lateral and feedback connections, object processing is commonly viewed and studied as a feedforward…

Interpretable scientific machine learning often trades predictive performance for structural transparency. When physical targets arise from hierarchical and nonlinear descriptor entanglement, weakly interacting white-box models underfit,…

The iterated learning model is an agent model which simulates the transmission of of language from generation to generation. It is used to study how the language adapts to pressures imposed by transmission. In each iteration, a language…

A major bottleneck for building statistical spoken dialogue systems for new domains and applications is the need for large amounts of training data. To address this problem, we adopt the multi-dimensional approach to dialogue management and…

The objective of this paper is to design novel multi-layer neural network architectures for multiscale simulations of flows taking into account the observed data and physical modeling concepts. Our approaches use deep learning concepts…

Interpretability benefits the theoretical understanding of representations. Existing word embeddings are generally dense representations. Hence, the meaning of latent dimensions is difficult to interpret. This makes word embeddings like a…

Sequence models assign probabilities to variable-length sequences such as natural language texts. The ability of sequence models to capture temporal dependence can be characterized by the temporal scaling of correlation and mutual…

Large language models (LLMs) have numerous real-life applications across various domains, such as natural language translation, sentiment analysis, language modeling, chatbots and conversational agents, creative writing, text…

Recently, Su and Cook proposed a dimension reduction technique called the inner envelope which can be substantially more efficient than the original envelope or existing dimension reduction techniques for multivariate regression. However,…

Several studies have proposed constraints under which a low dimensional representation can be derived from large-scale real-world networks exhibiting complex nonlinear dynamics. Typically, these representations are formulated under certain…

In this paper, we study the information transmission problem under the distributed learning framework, where each worker node is merely permitted to transmit a $m$-dimensional statistic to improve learning results of the target node.…

Large-scale multi-relational embedding refers to the task of learning the latent representations for entities and relations in large knowledge graphs. An effective and scalable solution for this problem is crucial for the true success of…

Many real-world systems can be described by mathematical models that are human-comprehensible, easy to analyze and help explain the system's behavior. Symbolic regression is a method that can automatically generate such models from data.…