SGD (Stochastic Gradient Descent) is a popular algorithm for large scale optimization problems due to its low iterative cost. However, SGD can not achieve linear convergence rate as FGD (Full Gradient Descent) because of the inherent gradient variance. To attack the problem, mini-batch SGD was proposed to get a trade-off in terms of convergence rate and iteration cost. In this paper, a general ...

An important theoretical tool in machine learning is the bias/variance decomposition of the generalization error. It was introduced for the mean square error in [3]. The bias/variance decomposition includes the concept of the ave-rage predictor. The bias is the error of the average predictor, and the systematic part of the generalization error, while the variability around the average predictor...

A variance-based method of analysis is described in which the clump size (average number of solute atoms aggregated together) of one atomic species (solute) in a matrix can be determined from a set of composition measurements taken from volumes which contain a much greater number of solute atoms than the clump size. The observed variance of the solute concentration measurements, each of which i...

Control charts with exponentially weighted moving average (EWMA) statistics (mean and variance) are used to jointly monitor the mean and variance of a process. An EWMA cost minimization model is presented to design the joint control scheme based on pure economic or both economic and statistical performance criteria. The pure economic model is extended to the economic-statistical design by addin...

The bullwhip effect is defined as the distortion of demand information as one moves upstream in the supply chain, causing severe inefficiencies in the whole supply chain. Although extensive research has been conducted to study the causes of the bullwhip effect and seek mitigation solutions with respect to several demand processes, less attention has been devoted to the ...

Blockchain systems are designed to produce blocks at a constant average rate. The most popular systems currently employ a Proof of Work (PoW) algorithm as a means of creating these blocks. Bitcoin produces, on average, one block every 10minutes. An unfortunate limitation of all deployed PoW blockchain systems is that the time between blocks has high variance. For example, 5% of the time, Bitcoi...

We show that for classical and quantum observables, the integrability-to-ergodicity transition leaves constant the sum of (a) the ensemble variance of the temporal average and (b) the ensemble average of temporal variance. The induced Frobenius (Hilbert-Schmidt) geometry of quantum observables encodes how eigenstate thermalization appears, the inverse participation ratio decreases, and the inte...

While attractive from a theoretical perspective, finely stratified experiments such as paired designs suffer from certain analytical limitations not present in block-randomized experiments with multiple treated and control individuals in each block. In short, when using an appropriately weighted difference-in-means to estimated the sample average treatment effect, the traditional variance estim...

To examine the effect of the variance of consumer ratings on product pricing and sales we develop a model which considers goods that are characterized by two types of attributes: experience attributes and experience attributes that were transformed in search attributes by consumer ratings that we call informed search attributes. For pure informed search goods, we find that with increasing varia...