Description: The Gaussian process is a fundamental concept in probability theory and statistics, referring to a collection of random variables that have a joint Gaussian distribution. This means that any finite subset of these variables follows a normal distribution, characterized by its bell-shaped curve and defined by its mean and variance. Gaussian processes are particularly useful in optimization tasks, as they allow modeling uncertainty in the evaluation of objective functions. Their probabilistic nature facilitates the exploration of complex search spaces, where evaluations can be costly or noisy. Additionally, Gaussian processes are flexible and can adapt to different types of data and structures, making them a powerful tool for optimization in various application areas. In this context, they are used to build models that predict the performance of a model given a set of hyperparameters, thus enabling efficient selection of the best values for these parameters. The ability of Gaussian processes to provide not only predictions but also measures of uncertainty makes them particularly valuable in situations where decision-making must consider the risk and inherent variability of the data.
