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The Gaussian process (GP) is a popular statistical technique for stochastic function approximation and uncertainty quantification from data. GPs have been adopted into the realm of machine learning in the last two decades because of their…

In this abstract paper, we introduce a new kernel learning method by a nonparametric density estimator. The estimator consists of a group of k-centroids clusterings. Each clustering randomly selects data points with randomly selected…

Structural equation models (SEMs) have been widely adopted for inference of causal interactions in complex networks. Recent examples include unveiling topologies of hidden causal networks over which processes such as spreading diseases, or…

Grounded language models use external sources of information, such as knowledge graphs, to meet some of the general challenges associated with pre-training. By extending previous work on compositional generalization in semantic parsing, we…

One of recent trends [30, 31, 14] in network architec- ture design is stacking small filters (e.g., 1x1 or 3x3) in the entire network because the stacked small filters is more ef- ficient than a large kernel, given the same computational…

Recent empirical work has shown that hierarchical convolutional kernels inspired by convolutional neural networks (CNNs) significantly improve the performance of kernel methods in image classification tasks. A widely accepted explanation…

We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework encompasses two key classes: (i) compact kernels, which…

Building spatial process models that capture nonstationary behavior while delivering computationally efficient inference is challenging. Nonstationary spatially varying kernels (see, e.g., Paciorek, 2003) offer flexibility and richness, but…

Sketching and stochastic gradient methods are arguably the most common techniques to derive efficient large scale learning algorithms. In this paper, we investigate their application in the context of nonparametric statistical learning.…

In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal approximation techniques,…

Pre-trained sequence-to-sequence language models have led to widespread success in many natural language generation tasks. However, there has been relatively less work on analyzing their ability to generate structured outputs such as…

Disentangling the encodings of neural models is a fundamental aspect for improving interpretability, semantic control and downstream task performance in Natural Language Processing. Currently, most disentanglement methods are unsupervised…

The general perception is that kernel methods are not scalable, and neural nets are the methods of choice for nonlinear learning problems. Or have we simply not tried hard enough for kernel methods? Here we propose an approach that scales…

The state-of-the-art CNN models give good performance on sentence classification tasks. The purpose of this work is to empirically study desirable properties such as semantic coherence, attention mechanism and reusability of CNNs in these…

Attributed graphs, typically characterized by irregular topologies and a mix of numerical and categorical attributes, are ubiquitous in diverse domains such as social networks, bioinformatics, and cheminformatics. While graph kernels…

The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel…

We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes of the graph. The model is designed to capture various graph signal structures through a highly adaptive kernel that incorporates a flexible…

In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…

In this paper we are concerned with the learnability of nonlocal interaction kernels for first order systems modeling certain social interactions, from observations of realizations of their dynamics. This paper is the first of a series on…

Capturing the compositional process which maps the meaning of words to that of documents is a central challenge for researchers in Natural Language Processing and Information Retrieval. We introduce a model that is able to represent the…