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Deep learning has achieved remarkable success across many domains, but it has also created a growing demand for interpretability in model predictions. Although many explainable machine learning methods have been proposed, post-hoc…

Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…

Non-exhaustive learning (NEL) is an emerging machine-learning paradigm designed to confront the challenge of non-stationary environments characterized by anon-exhaustive training sets lacking full information about the available…

Most deep anomaly detection models are based on learning normality from datasets due to the difficulty of defining abnormality by its diverse and inconsistent nature. Therefore, it has been a common practice to learn normality under the…

Quantifying uncertainty in predictions or, more generally, estimating the posterior conditional distribution, is a core challenge in machine learning and statistics. We introduce Convex Nonparanormal Regression (CNR), a conditional…

The present study proposes incorporating non-parametric knowledge into the diffusion least-mean-squares algorithm in the framework of a maximum a posteriori (MAP) estimation. The proposed algorithm leads to a robust estimation of an unknown…

The estimation of unknown values of parameters (or hidden variables, control variables) that characterise a physical system often relies on the comparison of measured data with synthetic data produced by some numerical simulator of the…

We propose an approach to multivariate nonparametric regression that generalizes reduced rank regression for linear models. An additive model is estimated for each dimension of a $q$-dimensional response, with a shared $p$-dimensional…

Deep neural networks have gained tremendous success in a broad range of machine learning tasks due to its remarkable capability to learn semantic-rich features from high-dimensional data. However, they often require large-scale labelled…

To better understand complexity in neural networks, we theoretically investigate the idealised phenomenon of lossless network compressibility, whereby an identical function can be implemented with fewer hidden units. In the setting of…

Pattern recognition constitutes a particularly important task underlying a great deal of scientific and technologica activities. At the same time, pattern recognition involves several challenges, including the choice of features to…

Inferring properties of graph-structured data, e.g., the solubility of molecules, essentially involves learning the implicit mapping from graphs to their properties. This learning process is often costly for graph property learners like…

Transformers have achieved great success in recent years. Interestingly, transformers have shown particularly strong in-context learning capability -- even without fine-tuning, they are still able to solve unseen tasks well purely based on…

We study the theory of neural network (NN) from the lens of classical nonparametric regression problems with a focus on NN's ability to adaptively estimate functions with heterogeneous smoothness -- a property of functions in Besov or…

Kernel Density Estimation (KDE) is a nonparametric method for estimating the shape of a density function, given a set of samples from the distribution. Recently, locality-sensitive hashing, originally proposed as a tool for nearest neighbor…

Feature correspondence selection is pivotal to many feature-matching based tasks in computer vision. Searching for spatially k-nearest neighbors is a common strategy for extracting local information in many previous works. However, there is…

Recursive Neural Networks are non-linear adaptive models that are able to learn deep structured information. However, these models have not yet been broadly accepted. This fact is mainly due to its inherent complexity. In particular, not…

Timely detection of abrupt anomalies is crucial for real-time monitoring and security of modern systems producing high-dimensional data. With this goal, we propose effective and scalable algorithms. Proposed algorithms are nonparametric as…

ML models are typically trained using large datasets of high quality. However, training datasets often contain inconsistent or incomplete data. To tackle this issue, one solution is to develop algorithms that can check whether a prediction…

Learning hierarchical structures in sequential data -- from simple algorithmic patterns to natural language -- in a reliable, generalizable way remains a challenging problem for neural language models. Past work has shown that recurrent…