Related papers: Estimation of density functionals via cross-valida…
We consider the problem of signal estimation (denoising) from a statistical-mechanical perspective, in continuation to a recent work on the analysis of mean-square error (MSE) estimation using a direct relationship between optimum…
This paper presents an intuitive application of multivariate kernel density estimation (KDE) for data correction. The method utilizes the expected value of the conditional probability density function (PDF) and a credible interval to…
We investigate the accuracy of the two most common estimators for the maximum expected value of a general set of random variables: a generalization of the maximum sample average, and cross validation. No unbiased estimator exists and we…
The conventional Minimum Error Entropy criterion (MEE) has its limitations, showing reduced sensitivity to error mean values and uncertainty regarding error probability density function locations. To overcome this, a MEE with fiducial…
This research presents a novel depth estimation algorithm based on a Transformer-encoder architecture, tailored for the NYU and KITTI Depth Dataset. This research adopts a transformer model, initially renowned for its success in natural…
Mean-squared-error (MSE) is one of the most widely used performance metrics for the designs and analysis of multi-input-multiple-output (MIMO) communications. Weighted MSE minimization, a more general formulation of MSE minimization, plays…
We consider the problem of parameter estimation for a system of ordinary differential equations from noisy observations on a solution of the system. In case the system is nonlinear, as it typically is in practical applications, an analytic…
This paper develops a conditional independence (CI) test from a conditional density ratio (CDR) for weakly dependent data. The main contribution is presenting a closed-form expression for the estimated conditional density ratio function…
Mean squared error (MSE) is one of the most widely used metrics to expression differences between multi-dimensional entities, including images. However, MSE is not locally sensitive as it does not take into account the spatial arrangement…
Decoding, ie prediction from brain images or signals, calls for empirical evaluation of its predictive power. Such evaluation is achieved via cross-validation, a method also used to tune decoders' hyper-parameters. This paper is a review on…
We consider a nonparametric Bayesian approach to estimation and testing for a multivariate monotone density. Instead of following the conventional Bayesian route of putting a prior distribution complying with the monotonicity restriction,…
We study the problem of estimating the probability density function of a circular random variable subject to censoring. To this end, we propose a fully computable quotient estimator that combines a projection estimator on linear sieves with…
We consider estimating an unknown signal, both blocky and sparse, which is corrupted by additive noise. We study three interrelated least squares procedures and their asymptotic properties. The first procedure is the fused lasso, put…
Graphical models are a framework for representing and exploiting prior conditional independence structures within distributions using graphs. In the Gaussian case, these models are directly related to the sparsity of the inverse covariance…
Used to estimate the risk of an estimator or to perform model selection, cross-validation is a widespread strategy because of its simplicity and its apparent universality. Many results exist on the model selection performances of…
Averaging provides an alternative to bandwidth selection for density kernel estimation. We propose a procedure to combine linearly several kernel estimators of a density obtained from different, possibly data-driven, bandwidths. The method…
Consider a statistical problem where a set of parameters are of interest to a researcher. Then multiple confidence intervals can be constructed to infer the set of parameters simultaneously. The constructed multiple confidence intervals are…
We consider nonparametric estimation of the derivative of a probability density function with the bounded support on $[0,\infty)$. Estimates are looked up in the class of estimates with asymmetric gamma kernel functions. The use of gamma…
This paper studies V-fold cross-validation for model selection in least-squares density estimation. The goal is to provide theoretical grounds for choosing V in order to minimize the least-squares loss of the selected estimator. We first…
Mixture models are well-known for their versatility, and the Bayesian paradigm is a suitable platform for mixture analysis, particularly when the number of components is unknown. Bhattacharya (2008) introduced a mixture model based on the…