相关论文: Bayesian Logarithmic Derivative Type Lower Bounds …

This paper addresses the ``curse of dimensionality'' in the loss valuation of credit risk models. A dimension reduction methodology based on the Bayesian filter and smoother is proposed. This methodology is designed to achieve a fast and…

This is a tutorial aimed at illustrating some recent developments in quantum parameter estimation beyond the Cram\`er-Rao bound, as well as their applications in quantum metrology. Our starting point is the observation that there are…

Achieving quantum-enhanced performances when measuring unknown quantities requires developing suitable methodologies for practical scenarios, that include noise and the availability of a limited amount of resources. Here, we report on the…

We propose a class of transformation hazard models for right-censored failure time data. It includes the proportional hazards model (Cox) and the additive hazards model (Lin and Ying) as special cases. Due to the requirement of a…

In this paper, we will provide an introduction to the derivative-free optimization algorithms which can be potentially applied to train deep learning models. Existing deep learning model training is mostly based on the back propagation…

Traditional partial differential equations with constant coefficients often struggle to capture abrupt changes in real-world phenomena, leading to the development of variable coefficient PDEs and Markovian switching models. Recently,…

Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…

We describe a hierarchical Bayesian approach for inference about a parameter $\theta$ lower-bounded by $\alpha$ with uncertain $\alpha$, derive some basic identities for posterior analysis about $(\theta,\alpha)$, and provide illustrations…

In this thesis, I explore the possibilities of conducting Bayesian optimization techniques in high dimensional domains. Although high dimensional domains can be defined to be between hundreds and thousands of dimensions, we will primarily…

Often the regression function is specified by a system of ordinary differential equations (ODEs) involving some unknown parameters. Typically analytical solution of the ODEs is not available, and hence likelihood evaluation at many…

We review the Akaike, deviance, and Watanabe-Akaike information criteria from a Bayesian perspective, where the goal is to estimate expected out-of-sample-prediction error using a biascorrected adjustment of within-sample error. We focus on…

Variational inference (VI) is widely used for approximate inference in Bayesian machine learning. In addition to this practical success, generalization bounds for variational inference and related algorithms have been developed, mostly…

The Linear Ballistic Accumulator (Brown & Heathcote, 2008) model is used as a measurement tool to answer questions about applied psychology. The analyses based on this model depend upon the model selected and its estimated parameters.…

There is no known efficient method for selecting k Gaussian features from n which achieve the lowest Bayesian classification error. We show an example of how greedy algorithms faced with this task are led to give results that are not…

Generalization error (also known as the out-of-sample error) measures how well the hypothesis learned from training data generalizes to previously unseen data. Proving tight generalization error bounds is a central question in statistical…

Variational Bayes (VB) has become a widely-used tool for Bayesian inference in statistics and machine learning. Nonetheless, the development of the existing VB algorithms is so far generally restricted to the case where the variational…

The application of the lasso is espoused in high-dimensional settings where only a small number of the regression coefficients are believed to be nonzero. Moreover, statistical properties of high-dimensional lasso estimators are often…

Quantum channel discrimination is a fundamental problem in quantum information science. In this study, we consider general quantum channel discrimination problems, and derive the lower bounds of the error probability. Our lower bounds are…

Bayesian inference is a powerful paradigm for quantum state tomography, treating uncertainty in meaningful and informative ways. Yet the numerical challenges associated with sampling from complex probability distributions hampers Bayesian…

This work compares the performance of single and two qubit probes for estimating several phase rotations simultaneously under the action of different noisy channels. We compute the quantum limits for this simultaneous estimation using…