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We propose kernel sequential Monte Carlo (KSMC), a framework for sampling from static target densities. KSMC is a family of sequential Monte Carlo algorithms that are based on building emulator models of the current particle system in a…
This paper introduces a discrete diffusion model (DDM) framework for text-aligned speech tokenization and reconstruction. By replacing the auto-regressive speech decoder with a discrete diffusion counterpart, our model achieves…
This work proposes a Stochastic Variational Deep Kernel Learning method for the data-driven discovery of low-dimensional dynamical models from high-dimensional noisy data. The framework is composed of an encoder that compresses…
Deep kernel learning provides an elegant and principled framework for combining the structural properties of deep learning algorithms with the flexibility of kernel methods. By means of a deep neural network, we learn a parametrized kernel…
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…
Machine learning models are increasingly used to predict material properties and accelerate atomistic simulations, but the reliability of their predictions depends on the representativeness of the training data. We present a scalable,…
Conditional density estimation is a general framework for solving various problems in machine learning. Among existing methods, non-parametric and/or kernel-based methods are often difficult to use on large datasets, while methods based on…
Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…
Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
We propose a novel method for density estimation that leverages an estimated score function to debias kernel density estimation (SD-KDE). In our approach, each data point is adjusted by taking a single step along the score function with a…
Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…
In this paper, we study the problem of sparse multiple kernel learning (MKL), where the goal is to efficiently learn a combination of a fixed small number of kernels from a large pool that could lead to a kernel classifier with a small…
Deep neural networks dominate modern machine learning, while alternative function approximators remain comparatively underexplored at scale. In this work, we revisit kernel methods as drop-in components for standard deep learning pipelines.…
Imbalanced response variable distribution is a common occurrence in data science. In fields such as fraud detection, medical diagnostics, system intrusion detection and many others where abnormal behavior is rarely observed the data under…
The denoising diffusion probabilistic model (DDPM) has emerged as a mainstream generative model in generative AI. While sharp convergence guarantees have been established for the DDPM, the iteration complexity is, in general, proportional…
This article presents a three-step framework for learning and solving partial differential equations (PDEs) using kernel methods. Given a training set consisting of pairs of noisy PDE solutions and source/boundary terms on a mesh, kernel…
Discrete diffusion models have recently emerged as a promising alternative to the autoregressive approach for generating discrete sequences. Sample generation via gradual denoising or demasking processes allows them to capture hierarchical…
This paper proposes a novel deep generative model, called BSDE-Gen, which combines the flexibility of backward stochastic differential equations (BSDEs) with the power of deep neural networks for generating high-dimensional complex target…
Deep kernel learning (DKL) leverages the connection between Gaussian process (GP) and neural networks (NN) to build an end-to-end, hybrid model. It combines the capability of NN to learn rich representations under massive data and the…