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There are many practical applications based on the Least Square Error (LSE) approximation. It is based on a square error minimization 'on a vertical' axis. The LSE method is simple and easy also for analytical purposes. However, if data…
Orthogonal group synchronization aims to recover orthogonal group elements from their noisy pairwise measurements. It has found numerous applications including computer vision, imaging science, and community detection. Due to the orthogonal…
A data analyst might worry about generalization if dropping a very small fraction of data points from a study could change its substantive conclusions. Checking this non-robustness directly poses a combinatorial optimization problem and is…
Latent variable (LV) models are widely used in psychological research to investigate relationships among unobservable constructs. When one-stage estimation of the overall LV model is challenging, two-stage factor score regression (FSR)…
The estimation of categorical response models using bias-reducing adjusted score equations has seen extensive theoretical research and applied use. The resulting estimates have been found to have superior frequentist properties to what…
This paper studies multi-level stochastic approximation algorithms. Our aim is to extend the scope of the multilevel Monte Carlo method recently introduced by Giles (Giles 2008) to the framework of stochastic optimization by means of…
Two-phase outcome dependent sampling (ODS) is widely used in many fields, especially when certain covariates are expensive and/or difficult to measure. For two-phase ODS, the conditional maximum likelihood (CML) method is very attractive…
Recently, Greg\'orio and Oliveira developed a proximal point scalarization method (applied to multi-objective optimization problems) for an abstract strict scalar representation with a variant of the logarithmic-quadratic function of…
We study efficiency improvements in randomized experiments for estimating a vector of potential outcome means using regression adjustment (RA) when there are more than two treatment levels. We show that linear RA which estimates separate…
Maximum a posteriori and Bayes estimators are two common methods of point estimation in Bayesian Statistics. It is commonly accepted that maximum a posteriori estimators are a limiting case of Bayes estimators with 0-1 loss. In this paper,…
In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference,…
One of the central themes in the classification task is the estimation of class posterior probability at a new point $\bf{x}$. The vast majority of classifiers output a score for $\bf{x}$, which is monotonically related to the posterior…
We propose a posteriori error estimators for classical low-order inf-sup stable and stabilized finite element approximations of the Stokes problem with singular sources in two and three dimensional Lipschitz, but not necessarily convex,…
Bayesian $l_0$-regularized least squares is a variable selection technique for high dimensional predictors. The challenge is optimizing a non-convex objective function via search over model space consisting of all possible predictor…
High-dimensional prediction typically comprises two steps: variable selection and subsequent least-squares refitting on the selected variables. However, the standard variable selection procedures, such as the lasso, hinge on tuning…
The sheer scale of modern datasets has resulted in a dire need for summarization techniques that identify representative elements in a dataset. Fortunately, the vast majority of data summarization tasks satisfy an intuitive diminishing…
Reparameterization (RP) and likelihood ratio (LR) gradient estimators are used to estimate gradients of expectations throughout machine learning and reinforcement learning; however, they are usually explained as simple mathematical tricks,…
In applications it is common that the exact form of a conditional expectation is unknown and having flexible functional forms can lead to improvements. Series method offers that by approximating the unknown function based on $k$ basis…
Explanation regularisation (ER) has been introduced as a way to guide text classifiers to form their predictions relying on input tokens that humans consider plausible. This is achieved by introducing an auxiliary explanation loss that…
We propose a two-stage estimation procedure for a copula-based model with semi-competing risks data, where the non-terminal event is subject to dependent censoring by the terminal event, and both events are subject to independent censoring.…