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This paper unifies the theory of consistent-set maximization for robust outlier detection in a simultaneous localization and mapping framework. We first describe the notion of pairwise consistency before discussing how a consistency graph…
Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to compute optimal bounds of this type. The basic method…
Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing (local) maximum likelihood estimate (MLE). It can be used in an extensive range of problems, including the clustering of data based on the Gaussian…
Propensity score methods are widely used for estimating treatment effects from observational studies. A popular approach is to estimate propensity scores by maximum likelihood based on logistic regression, and then apply inverse probability…
We propose and test improvements to state-of-the-art techniques of Bayeasian statistical inference based on pseudolikelihood maximization with $\ell_1$ regularization and with decimation. In particular, we present a method to determine the…
Probabilistic encoding introduces Gaussian noise into neural networks, enabling a smooth transition from deterministic to uncertain states and enhancing generalization ability. However, the randomness of Gaussian noise distorts point-based…
Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density…
Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution…
As the maximum likelihood method is the most commonly used method for parameters estimation being unbiased, consistent, efficient, and asymptotically normal, MLE is used to fit the new distribution (MBUW). But in small to moderate sample…
We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method…
Accurate quantification of uncertainty is crucial for real-world applications of machine learning. However, modern deep neural networks still produce unreliable predictive uncertainty, often yielding over-confident predictions. In this…
Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…
Regularization is a well-established technique in machine learning (ML) to achieve an optimal bias-variance trade-off which in turn reduces model complexity and enhances explainability. To this end, some hyper-parameters must be tuned,…
In Optimal Recovery, the task of learning a function from observational data is tackled deterministically by adopting a worst-case perspective tied to an explicit model assumption made on the functions to be learned. Working in the…
The transport of positive quantities underlies countless physical processes, including fluid, gas, and plasma dynamics. Discretizing the associated partial differential equations with Galerkin methods can result in spurious nonpositivity of…
Good robust estimators can be tuned to combine a high breakdown point and a specified asymptotic efficiency at a central model. This happens in regression with MM- and tau-estimators among others. However, the finite-sample efficiency of…
The capability of a novel Kullback-Leibler divergence method is examined herein within the Kalman filter framework to select the input-parameter-state estimation execution with the most plausible results. This identification suffers from…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
Bayesian nonparametric statistics is an area of considerable research interest. While recently there has been an extensive concentration in developing Bayesian nonparametric procedures for model checking, the use of the Dirichlet process,…
This undergraduate thesis focuses on calculating maximum likelihood estimates of parameters in the generalized Gamma distribution using the SeLF algorithm. As an extension of the Gamma distribution, the generalized Gamma distribution can…