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Diffusion models cannot enforce hard constraints, yet applications in the physical sciences demand exact satisfaction of conservation laws, boundary conditions, and observational consistency. In this work, we identify a corrector kernel…
Long Short-Term Memory (LSTM) neural network models have become the cornerstone for sequential data modeling in numerous applications, ranging from natural language processing to time series forecasting. Despite their success, the problem…
Machine learning algorithms play an important role in a variety of important decision-making processes, including targeted advertisement displays, home loan approvals, and criminal behavior predictions. Given the far-reaching impact of…
Variational quantum circuits have arisen as an important method in quantum computing. A crucial step of it is parameter optimization, which is typically tackled through gradient-descent techniques. We advantageously explore instead the use…
Three important properties of a classification machinery are: (i) the system preserves the core information of the input data; (ii) the training examples convey information about unseen data; and (iii) the system is able to treat…
High-dimensional time series are common in many domains. Since human cognition is not optimized to work well in high-dimensional spaces, these areas could benefit from interpretable low-dimensional representations. However, most…
Time series foundation models (TSFMs) have recently gained significant attention due to their strong zero-shot capabilities and widespread real-world applications. Such models typically require a computationally costly pre-training on…
Sketching is a probabilistic data compression technique that has been largely developed in the computer science community. Numerical operations on big datasets can be intolerably slow; sketching algorithms address this issue by generating a…
Conventional time-series forecasting methods typically aim to minimize overall prediction error, without accounting for the varying importance of different forecast ranges in downstream applications. We propose a training methodology that…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
Time series are series of values ordered by time. This kind of data can be found in many real world settings. Classifying time series is a difficult task and an active area of research. This paper investigates the use of transfer learning…
Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for higher dimensional problems such as in textures, crystallography, and quantum mechanics. Large…
Time series foundation models have recently gained a lot of attention due to their ability to model complex time series data encompassing different domains including traffic, energy, and weather. Although they exhibit strong average…
Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…
This paper addresses the covariate shift problem in the context of nonparametric regression within reproducing kernel Hilbert spaces (RKHSs). Covariate shift arises in supervised learning when the input distributions of the training and…
While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…
We extend our work for compression of currents and varifolds to a compression algorithm for the embedded normal cycles representation of shape, restricted to the constant normal kernel case, using the Nystrom approximation in Reproducing…
Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical…
In sparse coding, we attempt to extract features of input vectors, assuming that the data is inherently structured as a sparse superposition of basic building blocks. Similarly, neural networks perform a given task by learning features of…
While successful for various computer vision tasks, deep neural networks have shown to be vulnerable to texture style shifts and small perturbations to which humans are robust. In this work, we show that the robustness of neural networks…