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About 10,000 papers for “Mean squared error”

Mean Squared Error, Deconstructed

Timothy Hodson, Thomas M. Over, Sydney S. Foks · Journal of Advances in Modeling Earth Systems · 2021

Abstract As science becomes increasingly cross‐disciplinary and scientific models become increasingly cross‐coupled, standardized practices of model evaluation are more important than ever. For normally distributed data, mean squared error (MSE) is ideal as an objective measure of model performance, but it gives little insight into what aspects of model performance are “good” or “bad.” This apparent weakness has led to a myriad of specialized error metrics, which are sometimes aggregated to form a composite score. Such scores are inherently subjective, however, and while their components may be interpretable, the composite itself is not. We contend that, a better approach to model benchmarking and interpretation is to decompose MSE into interpretable components. To demonstrate the versatility of this approach, we outline some fundamental types of decomposition and apply them to predictions at 1,021 streamgages across the conterminous United States from three streamflow models. Through this demonstration, we hope to show that each component in a decomposition represents a distinct concept, like “season” or “variability,” and that simple decompositions can be combined to represent more complex concepts, like “seasonal variability,” creating an expressive language through which to interrogate models and data.

Cited by 229Open access

.2.1 Mean Squared Error (MSE)

Suppose We Have, Y Ae · 2007

mber 7, 1994 Since the target function and sample are fixed, the MSE is only a function of the weights of the network. The goal of our training routine is thus to minimize the MSE. The MSE is a useful cost function for several reasons. It can be used for arbitrary functions, is well defined, and is easily computed. Most importantly, however, is that it has a computable, continuous derivative (as long as fw (~x) has a computable, continuous derivative). This will play an important role in the training of the neural network. The major disadvantage of using the MSE is that "outliers" have a large effect on it. For boolean functions, minimizing the MSE is equivalent to minimizing errors. This is not true in general however. 15.2.2 Gradient Descent To minimize the MSE cost function, we use gradient descent, also known as "hill climbing". Gradient descent is done by taking small steps in the direction which reduces the error the

Cited by 0

Integrated Mean Squared Error (AIMSE).

Kevin Loquin, Olivier Strauss · 2008

This paper presents a density estimator based upon a histogram computed on a fuzzy partition. We prove the consistency of this estimator in the Mean Squared Error (MSE). We give the optimal bin width of the estimator which minimizes the Asymptotic

Cited by 0

Mean Integrated Squared Error Sampling

Michael E. Tarter · Journal of the American Statistical Association · 1986

Abstract Stratified sampling is considered, where (a) the mean integrated squared error (MISE) metric is used in place of the mean squared error (MSE) metric; (b) the entire distribution [i.e., f(x)], rather than a property of the distribution [e.g., E(x)], is used as a target of the procedure; (c) the distribution f(x) is estimated by a truncated series (to counterbalance model complexity with sample size availability); and finally, (d) samples are taken both with and without replacement. In the last regard, series term inclusion rules are generalized to deal with samples taken without replacement from a finite population. Two special cases are treated in detail. The first shows that even for sample sizes as small as three and for data forms as elementary as the bivariate binary vectors, the use of orthogonal series representation can lead to smaller expected error than would be achievable through use of conventional representation and methods. The second demonstrates that in the continuous case, MISE-based and conventional sample size selection rules can differ substantially.

Cited by 7

mean squared error of calibration

2024

Citation: 'mean squared error of calibration' in the IUPAC Compendium of Chemical Terminology, 5th ed.; International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.10151 • License: The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International for individual terms. Requests for commercial usage of the compendium should be directed to IUPAC.

Cited by 0

mean squared error of prediction

2024

Citation: 'mean squared error of prediction' in the IUPAC Compendium of Chemical Terminology, 5th ed.; International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.10099 • License: The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International for individual terms. Requests for commercial usage of the compendium should be directed to IUPAC.

Cited by 0

Exact Mean Integrated Squared Error

J. S. Marron, M. P. Wand · The Annals of Statistics · 1992

An exact and easily computable expression for the mean integrated squared error (MISE) for the kernel estimator of a general normal mixture density, is given for Gaussian kernels of arbitrary order. This provides a powerful new way of understanding density estimation which complements the usual tools of simulation and asymptotic analysis. The family of normal mixture densities is very flexible and the formulae derived allow simple exact analysis for a wide variety of density shapes. A number of applications of this method giving important new insights into kernel density estimation are presented. Among these is the discovery that the usual asymptotic approximations to the MISE can be quite inaccurate, especially when the underlying density contains substantial fine structure and also strong evidence that the practical importance of higher order kernels is surprisingly small for moderate sample sizes.

Cited by 756Open access

Mean squared error of predictions.

Silvia Teresa Rodríguez-Ramilo (543189), Luis Alberto García-Cortés (5658466), Óscar González-Recio (5658469) · Figshare · 2015

<p>Dashed lines and small squares represent fixed weights with <i>N</i> = 7,000. Solid lines and small circles represent fixed weights with <i>N</i> = 14,487. The large square represents the sampled weight for <i>N</i> = 7,000. The large circle represents the sampled weight for <i>N</i> = 14,487.</p>

Cited by 0Open access

Competitive Mean-Squared Error Beamforming

Yonina C. Eldar, Arye Nehorai · Defense Technical Information Center (DTIC) · 2004

We consider the problem of designing a linear beamformer to estimate a source signal s(t) from array observations. Conventional beamforming methods typically aim at maximizing the signal-to-interference-plus-noise ratio (SINR). However this does not guarantee a small mean-squared error (MSE), hence on average their resulting signal estimate ^s(t) can be far from s(t). To ensure that ^s(t) is close to s(t), we propose using the more appropriate design criterion of MSE. Since the MSE depends in general on s(t) which is unknown, it cannot be minimized directly. Therefore we develop a competitive beamforming approach, in which the beamformer is designed to minimize the worst-case regret over all s(t), where the regret is the difference between the MSE using a beamformer ignorant of s(t) and the smallest possible MSE attainable with a beamformer that knows s(t). Thus, we ensure that over a wide range of signal values, our beamformer will result in a relatively low MSE. We demonstrate through numerical examples that the proposed minimax regret beamformer (MMR) outperforms several existing standard and robust beamformers, for wide range of SNR values.

Cited by 6

approach; Integrated Mean Squared Error;

Douglas P. Wiens · 2013

design We summarize recent …ndings on the constructionofdesigns,tobeusedinexperiments for which regression is the anticipated method of analysis. The designs are to be robust against departures from the assumed linear response and/or departures from the assumption of uncorrelated errors. Included is a discussion of an “in…nitesimal ” approach to design. In this approach one aims to minimize the determinant of the mean squared error matrix of the regression estimates, subject to the satisfaction of a robustness constraint. The constraint is quanti…ed in terms of boundedness of the Gateaux derivative of this determinant, in the direction of a contaminating response function or autocorrelation structure. 1.

Cited by 0

Ensemble Averaging and Mean Squared Error

J Rougier · Journal of Climate · 2016

Abstract In fields such as climate science, it is common to compile an ensemble of different simulators for the same underlying process. It is a striking observation that the ensemble mean often outperforms at least half of the ensemble members in mean squared error (measured with respect to observations). In fact, as demonstrated in the most recent IPCC report, the ensemble mean often outperforms all or almost all of the ensemble members across a range of climate variables. This paper shows that these could be mathematical results based on convexity and averaging but with implications for the properties of the current generation of climate simulators.

Cited by 82Open access

The mean squared prediction error paradox

Pablo Pincheira Brown, Nicolás Hardy · Journal of Forecasting · 2024

Abstract In this paper, we show that traditional comparisons of mean squared prediction error (MSPE) between two competing forecasts may be highly controversial. This is so because when some specific conditions of efficiency are not met, the forecast displaying the lowest MSPE will also display the lowest correlation with the target variable. Given that violations of efficiency are usual in the forecasting literature, this opposite behavior in terms of accuracy and correlation with the target variable may be a fairly common empirical finding that we label here as “the MSPE paradox.” We characterize “paradox zones” in terms of differences in correlation with the target variable and conduct some simple simulations to show that these zones may be non‐empty sets. Finally, we illustrate the relevance of the paradox with a few empirical applications.

Cited by 2Open access