Related papers: Modified noise kernels in Gaussian process modelli…
Scientific imaging often involves long acquisition times to obtain high-quality data, especially when probing complex, heterogeneous systems. However, reducing acquisition time to increase throughput inevitably introduces significant noise…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…
Gaussian processes provide a flexible, non-parametric framework for the approximation of functions in high-dimensional spaces. The covariance kernel is the main engine of Gaussian processes, incorporating correlations that underpin the…
In this paper we investigate a link between state- space models and Gaussian Processes (GP) for time series modeling and forecasting. In particular, several widely used state- space models are transformed into continuous time form and…
Exploiting the information provided by the molecular noise of a biological process has proven to be valuable in extracting knowledge about the underlying kinetic parameters and sources of variability from single cell measurements. However,…
Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper…
Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically need to be estimated from the dataset. This article provides…
Renewable energy is essential for energy security and global warming mitigation. However, power generation from renewable energy sources is uncertain due to volatile weather conditions and complex equipment operations. To improve…
Kernel Estimation provides an unbinned and non-parametric estimate of the probability density function from which a set of data is drawn. In the first section, after a brief discussion on parametric and non-parametric methods, the theory of…
Noise is a major challenge for building practical quantum computing systems. Precise characterization of quantum noise is crucial for developing effective error mitigation and correction schemes. However, state preparation and measurement…
Characterization of quantum objects, being them states, processes, or measurements, complemented by previous knowledge about them is a valuable approach, especially as it leads to routine procedures for real-life components. To this end,…
We present a scalable Gaussian process model for identifying and characterizing smooth multidimensional changepoints, and automatically learning changes in expressive covariance structure. We use Random Kitchen Sink features to flexibly…
Learning unnormalized statistical models (e.g., energy-based models) is computationally challenging due to the complexity of handling the partition function. To eschew this complexity, noise-contrastive estimation~(NCE) has been proposed by…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
Accurate characterization of the noise influencing a quantum system of interest has far-reaching implications across quantum science, ranging from microscopic modeling of decoherence dynamics to noise-optimized quantum control. While the…
Doubly stochastic Poisson processes, also known as the Cox processes, frequently occur in various scientific fields. In this article, motivated primarily by analyzing Cox process data in biophysics, we propose a nonparametric kernel-based…
In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of…
In a variety of disciplines such as social sciences, psychology, medicine and economics, the recorded data are considered to be noisy measurements of latent variables connected by some causal structure. This corresponds to a family of…
Quantum noise is conventionally viewed as a fundamental obstacle in near-term quantum computing, motivating extensive error correction and mitigation strategies. We present numerical evidence that challenges this consensus. Through…