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Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool…

Vertical Federated Learning (VFL), which has a broad range of real-world applications, has received much attention in both academia and industry. Enterprises aspire to exploit more valuable features of the same users from diverse…

While deep networks have been enormously successful over the last decade, they rely on flat-feature vector representations, which makes them unsuitable for richly structured domains such as those arising in applications like social network…

Deep Neural Networks (DNNs) are popularly used for implementing autonomy related tasks in automotive Cyber-Physical Systems (CPSs). However, these networks have been shown to make erroneous predictions to anomalous inputs, which manifests…

This paper develops a randomized approach for incrementally building deep neural networks, where a supervisory mechanism is proposed to constrain the random assignment of the weights and biases, and all the hidden layers have direct links…

We present a simple linear regression based approach for learning the weights and biases of a neural network, as an alternative to standard gradient based backpropagation. The present work is exploratory in nature, and we restrict the…

Function approximation has been an indispensable component in modern reinforcement learning algorithms designed to tackle problems with large state spaces in high dimensions. This paper reviews recent results on error analysis for these…

The exponential growth in scale and relevance of social networks enable them to provide expansive insights. Predicting missing links in social networks efficiently can help in various modern-day business applications ranging from generating…

Regression neural networks (NNs) are most commonly trained by minimizing the mean squared prediction error, which is highly sensitive to outliers and data contamination. Existing robust training methods for regression NNs are often limited…

Large Language Models (LLMs) have shown promising results on various language and vision tasks. Recently, there has been growing interest in applying LLMs to graph-based tasks, particularly on Text-Attributed Graphs (TAGs). However, most…

Recently, link prediction has attracted more attentions from various disciplines such as computer science, bioinformatics and economics. In this problem, unknown links between nodes are discovered based on numerous information such as…

This paper provides a comprehensive error analysis of learning with vector-valued random features (RF). The theory is developed for RF ridge regression in a fully general infinite-dimensional input-output setting, but nonetheless applies to…

Inferring missing links or detecting spurious ones based on observed graphs, known as link prediction, is a long-standing challenge in graph data analysis. With the recent advances in deep learning, graph neural networks have been used for…

Markov Random Fields (MRFs), a formulation widely used in generative image modeling, have long been plagued by the lack of expressive power. This issue is primarily due to the fact that conventional MRFs formulations tend to use simplistic…

Complex networks are graphs representing real-life systems that exhibit unique characteristics not found in purely regular or completely random graphs. The study of such systems is vital but challenging due to the complexity of the…

In recent years, deep perceptual loss has been widely and successfully used to train machine learning models for many computer vision tasks, including image synthesis, segmentation, and autoencoding. Deep perceptual loss is a type of loss…

We introduce a Banach space-valued extension of random feature learning, a data-driven supervised machine learning technique for large-scale kernel approximation. By randomly initializing the feature maps, only the linear readout needs to…

Relational data are ubiquitous in real-world data applications, e.g., in social network analysis or biological modeling, but networks are nearly always incompletely observed. The state-of-the-art for predicting missing links in the hard…

Kernel and linear regression have been recently explored in the prediction of graph signals as the output, given arbitrary input signals that are agnostic to the graph. In many real-world problems, the graph expands over time as new nodes…

Diagonal linear networks are neural networks with linear activation and diagonal weight matrices. Their theoretical interest is that their implicit regularization can be rigorously analyzed: from a small initialization, the training of…