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Random feature mapping (RFM) is a popular method for speeding up kernel methods at the cost of losing a little accuracy. We study kernel ridge regression with random feature mapping (RFM-KRR) and establish novel out-of-sample error upper…

Deep reinforcement learning (DRL) has been widely studied in the portfolio management task. However, it is challenging to understand a DRL-based trading strategy because of the black-box nature of deep neural networks. In this paper, we…

We introduce a discriminative regression approach to supervised classification in this paper. It estimates a representation model while accounting for discriminativeness between classes, thereby enabling accurate derivation of categorical…

In the ever-changing and intricate landscape of financial markets, portfolio optimisation remains a formidable challenge for investors and asset managers. Conventional methods often struggle to capture the complex dynamics of market…

Diffusion models have achieved significant progress in image generation. The pre-trained Stable Diffusion (SD) models are helpful for image deblurring by providing clear image priors. However, directly using a blurry image or pre-deblurred…

Robustness to modeling errors and uncertainties remains a central challenge in reinforcement learning (RL). In this work, we address this challenge by leveraging diffusion models to train robust RL policies. Diffusion models have recently…

Incorporating various modes of information into the machine learning procedure is becoming a new trend. And data from various source can provide more information than single one no matter they are heterogeneous or homogeneous. Existing deep…

Efficient tools for predicting the drag of rough walls in turbulent flows would have a tremendous impact. However, methods for drag prediction rely on experiments or numerical simulations which are costly and time-consuming. Data-driven…

The method of occupation kernels has been used to learn ordinary differential equations from data in a non-parametric way. We propose a two-step method for learning the drift and diffusion of a stochastic differential equation given…

The increasing demand for autonomous systems in complex and dynamic environments has driven significant research into intelligent path planning methodologies. For decades, graph-based search algorithms, linear programming techniques, and…

Reinforcement learning (RL) struggles to scale to large, combinatorial action spaces common in many real-world problems. This paper introduces a novel framework for training discrete diffusion models as highly effective policies in these…

We introduce Constr-DRKM, a deep kernel method for the unsupervised learning of disentangled data representations. We propose augmenting the original deep restricted kernel machine formulation for kernel PCA by orthogonality constraints on…

Accurate precipitation forecasting is essential for hydrometeorological risk management, especially for anticipating extreme rainfall that can lead to flash flooding and infrastructure damage. This study introduces a diffusion-based deep…

Kernel-based subspace clustering, which addresses the nonlinear structures in data, is an evolving area of research. Despite noteworthy progressions, prevailing methodologies predominantly grapple with limitations relating to (i) the…

The ability to generalize under distributional shifts is essential to reliable machine learning, while models optimized with empirical risk minimization usually fail on non-$i.i.d$ testing data. Recently, invariant learning methods for…

An active learning algorithm for the classification of high-dimensional images is proposed in which spatially-regularized nonlinear diffusion geometry is used to characterize cluster cores. The proposed method samples from estimated cluster…

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…

We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…

An intelligent radar resource management is an essential milestone in the development of a cognitive radar system. The quality of service based resource allocation model (Q-RAM) is a framework allowing for intelligent decision making but…

Diffusion geometry is a manifold learning framework that uses random walks defined by Markov transition matrices to characterize the geometry of a dataset at multiple scales. We use diffusion geometry for neural representations,…