Related papers: Efficient Optimization of the Likelihood Function …
In the last five years, the financial industry has been impacted by the emergence of digitalization and machine learning. In this article, we explore two methods that have undergone rapid development in recent years: Gaussian processes and…
Parameter estimation is crucial for modeling, tracking, and control of complex dynamical systems. However, parameter uncertainties can compromise system performance under a controller relying on nominal parameter values. Typically,…
The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an…
A Gaussian process (GP)-based methodology is proposed to emulate complex dynamical computer models (or simulators). The method relies on emulating the numerical flow map of the system over an initial (short) time step, where the flow map is…
Background: Determining an adequate sample size is essential for developing reliable and generalisable clinical prediction models, yet practical guidance on selecting appropriate methods remains limited. Existing analytical and…
Bayesian optimization devolves the global optimization of a costly objective function to the global optimization of a sequence of acquisition functions. This inner-loop optimization can be catastrophically difficult if it involves posterior…
Bayesian Optimization using Gaussian Processes is a popular approach to deal with the optimization of expensive black-box functions. However, because of the a priori on the stationarity of the covariance matrix of classic Gaussian…
The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
As a non-parametric Bayesian model which produces informative predictive distribution, Gaussian process (GP) has been widely used in various fields, like regression, classification and optimization. The cubic complexity of standard GP…
A body of work has been done to automate machine learning algorithm to highlight the importance of model choice. Automating the process of choosing the best forecasting model and its corresponding parameters can result to improve a wide…
Although machine learning is increasingly applied in control approaches, only few methods guarantee certifiable safety, which is necessary for real world applications. These approaches typically rely on well-understood learning algorithms,…
Local search is a successful approach for solving combinatorial optimization and constraint satisfaction problems. With the progressing move toward multi and many-core systems, GPUs and the quest for Exascale systems, parallelism has become…
Given a model in algebraic statistics and some data, the likelihood function is a rational function on a projective variety. Algebraic algorithms are presented for computing all critical points of this function, with the aim of identifying…
Gaussian process (GP) models that combine both categorical and continuous input variables have found use in analysis of longitudinal data and computer experiments. However, standard inference for these models has the typical cubic scaling,…
We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…
Convolved Gaussian Process (CGP) is able to capture the correlations not only between inputs and outputs but also among the outputs. This allows a superior performance of using CGP than standard Gaussian Process (GP) in the modelling of…
Monte Carlo maximum likelihood (MCML) provides an elegant approach to find maximum likelihood estimators (MLEs) for latent variable models. However, MCML algorithms are computationally expensive when the latent variables are…
Gaussian processes (GPs) are flexible, probabilistic, nonparametric models widely used in fields such as spatial statistics and machine learning. A drawback of Gaussian processes is their computational cost, with $O(N^3)$ time and $O(N^2)$…
In this paper we provide a provably convergent algorithm for the multivariate Gaussian Maximum Likelihood version of the Behrens--Fisher Problem. Our work builds upon a formulation of the log-likelihood function proposed by Buot and…