We study the error landscape of deep linear and nonlinear neural networks with the squared error loss. Minimizing the loss of a deep linear neural network is a nonconvex problem, and despite recent progress, our understanding of this loss surface is still incomplete. For deep linear networks, we present necessary and sufficient conditions for a critical point of the risk function to be a global...

The paper “The Importance of Convexity in Learning with Squared Loss” gave a lower bound on the sample complexity of learning with quadratic loss using a nonconvex function class. The proof contains an error. We show that the lower bound is true under a stronger condition that holds for many cases of interest.

What are the natural loss functions or fitting criteria for binary class probability estimation? This question has a simple answer: so-called “proper scoring rules”, that is, functions that score probability estimates in view of data in a Fisher-consistent manner. Proper scoring rules comprise most loss functions currently in use: log-loss, squared error loss, boosting loss, and as limiting cas...

In this paper, two parameters for the Exponential distribution were estimated using theBayesian estimation method under three different loss functions: Squared error function,the Precautionary function, and Entropy function. The priorand Gamma have been assumed as priors of scale γ location δ parametersrespectively. Bayesian estimation, Maximum likelihood estimators used initialestimators, Tier...

Most of estimation methods reported in the literature are based on simple random sampling (SRS), which to certain extent is considerably less effective in estimating the parameters as compared to a new sampling technique, ranked set sampling (RSS) and its modifications. In this Paper we address the problem of Bayesian estimation of the parameters for Weibull distribution, based on ranked set sa...

White balancing is a fundamental step in the image processing pipeline. The process involves estimating the chromaticity of the illuminant or light source and using the estimate to correct the image to remove any color cast. Given the importance of the problem, there has been much previous work on illuminant estimation. Recently, an approach based on ensembles of univariate regression trees tha...

In this work, a three-parameter Weibull Inverse Rayleigh (WIR) distribution is proposed. The new WIR an extension of one-parameter that incorporated transformation the and Log-logistic as quantile function. statistical properties such function, order statistic, monotone likelihood ratio property, hazard, reverse hazard functions, moments, skewness, kurtosis, linear representation proposed were ...

This letter presents an improved version of diffusion least mean ppower (LMP) algorithm for distributed estimation. Instead of sum of mean square errors, a weighted sum of mean square error is defined as the cost function for global and local cost functions of a network of sensors. The weight coefficients are updated by a simple steepest-descent recursion to minimize the error signal of the glo...