Related papers: A Note on Uncertainty Quantification for Maximum L…

In this paper, we consider the problem of estimating parameters of a linear regression model. Using a hybrid systems framework, a hybrid algorithm is proposed allowing the estimate to converge to the exact value of the unknown parameters in…

In this paper, we develop efficient randomized algorithms for estimating probabilistic robustness margin and constructing robustness degradation curve for uncertain dynamic systems. One remarkable feature of these algorithms is their…

Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…

Hyperparameter optimization in machine learning is often achieved using naive techniques that only lead to an approximate set of hyperparameters. Although techniques such as Bayesian optimization perform an intelligent search on a given…

Gradient-based algorithms are one of the methods of choice for the optimisation of Markov Decision Processes. In this article we will present a novel approximate Newton algorithm for the optimisation of such models. The algorithm has…

The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…

Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model…

Within the context of hybrid quantum-classical optimization, gradient descent based optimizers typically require the evaluation of expectation values with respect to the outcome of parameterized quantum circuits. In this work, we explore…

Many machine learning problems can be expressed as the optimization of some cost functional over a parametric family of probability distributions. It is often beneficial to solve such optimization problems using natural gradient methods.…

There are many approaches for training decision trees. This work introduces a novel gradient-based method for constructing decision trees that optimize arbitrary differentiable loss functions, overcoming the limitations of heuristic…

In this paper, we mainly focus on the penalized maximum likelihood estimation (MLE) of the high-dimensional approximate factor model. Since the current estimation procedure can not guarantee the positive definiteness of the error covariance…

We consider the problem of estimation of a covariance matrix for Gaussian data in a high dimensional setting. Existing approaches include maximum likelihood estimation under a pre-specified sparsity pattern, l_1-penalized loglikelihood…

Accurate platform localization is an integral component of most robotic systems. As these robotic systems become more ubiquitous, it is necessary to develop robust state estimation algorithms that are able to withstand novel and…

In many fields of science, generalized likelihood ratio tests are established tools for statistical inference. At the same time, it has become increasingly common that a simulator (or generative model) is used to describe complex processes…

Optimizing machine learning algorithms that are used to solve the objective function has been of great interest. Several approaches to optimize common algorithms, such as gradient descent and stochastic gradient descent, were explored. One…

With rapid advancements in machine learning, first-order algorithms have emerged as the backbone of modern optimization techniques, owing to their computational efficiency and low memory requirements. Recently, the connection between…

We use available measurements to estimate the unknown parameters (variance, smoothness parameter, and covariance length) of a covariance function by maximizing the joint Gaussian log-likelihood function. To overcome cubic complexity in the…

The classical approach to system identification is based on stochastic assumptions about the measurement error, and provides estimates that have random nature. Worst-case identification, on the other hand, only assumes the knowledge of…

Rigorous statistical methods, including parameter estimation with accompanying uncertainties, underpin the validity of scientific discovery, especially in the natural sciences. With increasingly complex data models such as deep learning…

Local optimization presents a promising approach to expensive, high-dimensional black-box optimization by sidestepping the need to globally explore the search space. For objective functions whose gradient cannot be evaluated directly,…