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In spatial statistics, kriging models are often designed using a stationary covariance structure; this translation-invariance produces models which have numerous favorable properties. This assumption can be limiting, though, in…
Text classification is a fundamental task in natural language processing (NLP). Several recent studies show the success of deep learning on text processing. Convolutional neural network (CNN), as a popular deep learning model, has shown…
We propose a generalization of convolutional neural networks (CNNs) to irregular domains, through the use of a translation operator on a graph structure. In regular settings such as images, convolutional layers are designed by translating a…
The ability to accurately represent sentences is central to language understanding. We describe a convolutional architecture dubbed the Dynamic Convolutional Neural Network (DCNN) that we adopt for the semantic modelling of sentences. The…
Learning models of dynamical systems characterized by specific stability properties is of crucial importance in applications. Existing results mainly focus on linear systems or some limited classes of nonlinear systems and stability…
Graphs have become increasingly popular in modeling structures and interactions in a wide variety of problems during the last decade. Graph-based clustering and semi-supervised classification techniques have shown impressive performance.…
Graph-based convolutional model such as non-local block has shown to be effective for strengthening the context modeling ability in convolutional neural networks (CNNs). However, its pixel-wise computational overhead is prohibitive which…
Large language models (LLMs) often hallucinate and lack the ability to provide attribution for their generations. Semi-parametric LMs, such as kNN-LM, approach these limitations by refining the output of an LM for a given prompt using its…
We propose a simple algorithm to train stochastic neural networks to draw samples from given target distributions for probabilistic inference. Our method is based on iteratively adjusting the neural network parameters so that the output…
Statistical machine translation models have made great progress in improving the translation quality. However, the existing models predict the target translation with only the source- and target-side local context information. In practice,…
For the past 30 years or so, machine learning has stimulated a great deal of research in the study of approximation capabilities (expressive power) of a multitude of processes, such as approximation by shallow or deep neural networks,…
An important goal in visual recognition is to devise image representations that are invariant to particular transformations. In this paper, we address this goal with a new type of convolutional neural network (CNN) whose invariance is…
Despite the effectiveness of Convolutional Neural Networks (CNNs) for image classification, our understanding of the relationship between shape of convolution kernels and learned representations is limited. In this work, we explore and…
Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. Current GNN architectures assume ideal scenarios and ignore link…
Kernels on graphs have had limited options for node-level problems. To address this, we present a novel, generalized kernel for graphs with node feature data for semi-supervised learning. The kernel is derived from a regularization…
Constructing the adjacency graph is fundamental to graph-based clustering. Graph learning in kernel space has shown impressive performance on a number of benchmark data sets. However, its performance is largely determined by the chosen…
The last decade has witnessed the success of the traditional feature-based method on exploiting the discrete structures such as words or lexical patterns to extract relations from text. Recently, convolutional and recurrent neural networks…
The thesis presents an attempt at using the syntactic structure in natural language for improved language models for speech recognition. The structured language model merges techniques in automatic parsing and language modeling using an…
In this paper, sparsification techniques aided online prediction algorithms in a reproducing kernel Hilbert space are studied for nonstationary time series. The online prediction algorithms as usual consist of the selection of kernel…
Data-driven neighborhood definitions and graph constructions are often used in machine learning and signal processing applications. k-nearest neighbor~(kNN) and $\epsilon$-neighborhood methods are among the most common methods used for…