Bias-Variance-Covariance Decomposition

2017 ◽  
pp. 139-140
Keyword(s):  
Covariance Decomposition ◽  
Bias Variance

scholarly journals <i>De praeceptis ferendis</i>: good practice in multi-model ensembles

2014 ◽  
Vol 14 (11) ◽  
pp. 15803-15865 ◽  
Author(s):  
I. Kioutsioukis ◽  
S. Galmarini
Keyword(s):  
Good Practice ◽  
Mathematical Framework ◽  
Ensemble Averaging ◽  
Quality Models ◽  
Two Factors ◽  
The Common ◽  
Covariance Decomposition ◽  
Bias Variance ◽  
Model Ensembles ◽  
Operational Methods

Abstract. Ensembles of air quality models have been formally and empirically shown to outperform single models in many cases. Evidence suggests that ensemble error is reduced when the members form a diverse and accurate ensemble. Diversity and accuracy are hence two factors that should be taken care of while designing ensembles in order for them to provide better predictions. There exists a trade-off between diversity and accuracy for which one cannot be gained without expenses of the other. Theoretical aspects like the bias-variance-covariance decomposition and the accuracy-diversity decomposition are linked together and support the importance of creating ensemble that incorporates both the elements. Hence, the common practice of unconditional averaging of models without prior manipulation limits the advantages of ensemble averaging. We demonstrate the importance of ensemble accuracy and diversity through an inter-comparison of ensemble products for which a sound mathematical framework exists, and provide specific recommendations for model selection and weighting for multi model ensembles. To this end we have devised statistical tools that can be used for diagnostic evaluation of ensemble modelling products, complementing existing operational methods.

Bias-Variance-Covariance Decomposition

2011 ◽  
pp. 111-111
Author(s):  
Paul Munro ◽  
Hannu Toivonen ◽  
Geoffrey I. Webb ◽  
Wray Buntine ◽  
Peter Orbanz ◽  
...  
Keyword(s):  
Covariance Decomposition ◽  
Bias Variance

BIAS-VARIANCE CONTROL VIA HARD POINTS SHAVING

2004 ◽  
Vol 18 (05) ◽  
pp. 891-903 ◽  
Author(s):  
STEFANO MERLER ◽  
BRUNO CAPRILE ◽  
CESARE FURLANELLO
Keyword(s):  
Control Strategy ◽  
Noisy Data ◽  
Real Data ◽  
Training Data ◽  
Regularization Technique ◽  
Data Points ◽  
Classification Tasks ◽  
Bias Variance

In this paper, we propose a regularization technique for AdaBoost. The method implements a bias-variance control strategy in order to avoid overfitting in classification tasks on noisy data. The method is based on a notion of easy and hard training patterns as emerging from analysis of the dynamical evolutions of AdaBoost weights. The procedure consists in sorting the training data points by a hardness measure, and in progressively eliminating the hardest, stopping at an automatically selected threshold. Effectiveness of the method is tested and discussed on synthetic as well as real data.

scholarly journals Design and Analysis of Experiments in Networks: Reducing Bias from Interference

2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Dean Eckles ◽  
Brian Karrer ◽  
Johan Ugander
Keyword(s):  
Sufficient Conditions ◽  
Bias Reduction ◽  
Experimental Unit ◽  
Randomized Experiments ◽  
Cluster Randomization ◽  
Graph Cluster ◽  
Unbiased Estimates ◽  
Bias Variance ◽  
Substantial Bias ◽  
Biased Estimates

AbstractEstimating the effects of interventions in networks is complicated due to interference, such that the outcomes for one experimental unit may depend on the treatment assignments of other units. Familiar statistical formalism, experimental designs, and analysis methods assume the absence of this interference, and result in biased estimates of causal effects when it exists. While some assumptions can lead to unbiased estimates, these assumptions are generally unrealistic in the context of a network and often amount to assuming away the interference. In this work, we evaluate methods for designing and analyzing randomized experiments under minimal, realistic assumptions compatible with broad interference, where the aim is to reduce bias and possibly overall error in estimates of average effects of a global treatment. In design, we consider the ability to perform random assignment to treatments that is correlated in the network, such as through graph cluster randomization. In analysis, we consider incorporating information about the treatment assignment of network neighbors. We prove sufficient conditions for bias reduction through both design and analysis in the presence of potentially global interference; these conditions also give lower bounds on treatment effects. Through simulations of the entire process of experimentation in networks, we measure the performance of these methods under varied network structure and varied social behaviors, finding substantial bias reductions and, despite a bias–variance tradeoff, error reductions. These improvements are largest for networks with more clustering and data generating processes with both stronger direct effects of the treatment and stronger interactions between units.

scholarly journals Simulation of trajectories in the illness-death model for chronic diseases: discrete event simulation, Doob-Gillespie algorithm and coverage of Wald confidence intervals

2020 ◽  
Author(s):  
Ralph Brinks ◽  
Annika Hoyer
Keyword(s):  
Type 2 Diabetes ◽  
Chronic Diseases ◽  
Confidence Intervals ◽  
Discrete Event Simulation ◽  
Discrete Event ◽  
Gillespie Algorithm ◽  
Event Simulation ◽  
Bias Variance

AbstractWe compare two approaches for simulating events in the illness-death model in a test example about type 2 diabetes in Germany. The first approach is a discrete event simulation, where relevant events, i.e., onset of disease and death, are simulated for each subject individually. The second approach is the Doob-Gillespie algorithm, which simulates the number of people in each state of the illness-death model at each point in time. The algorithms are compared in terms of bias, variance and speed. Based on the results of the comparison in the test example, we assess coverage of the corresponding Wald confidence intervals.

scholarly journals Prefrontal solution to the bias-variance tradeoff during reinforcement learning

2020 ◽  
Author(s):  
Dongjae Kim ◽  
Jaeseung Jeong ◽  
Sang Wan Lee
Keyword(s):  
Adaptive Control ◽  
Reinforcement Learning ◽  
Prediction Error ◽  
Brain Regions ◽  
Decision Task ◽  
Prediction Errors ◽  
Model Based ◽  
Model Free ◽  
Bias Variance ◽  
The Brain

AbstractThe goal of learning is to maximize future rewards by minimizing prediction errors. Evidence have shown that the brain achieves this by combining model-based and model-free learning. However, the prediction error minimization is challenged by a bias-variance tradeoff, which imposes constraints on each strategy’s performance. We provide new theoretical insight into how this tradeoff can be resolved through the adaptive control of model-based and model-free learning. The theory predicts the baseline correction for prediction error reduces the lower bound of the bias–variance error by factoring out irreducible noise. Using a Markov decision task with context changes, we showed behavioral evidence of adaptive control. Model-based behavioral analyses show that the prediction error baseline signals context changes to improve adaptability. Critically, the neural results support this view, demonstrating multiplexed representations of prediction error baseline within the ventrolateral and ventromedial prefrontal cortex, key brain regions known to guide model-based and model-free learning.One sentence summaryA theoretical, behavioral, computational, and neural account of how the brain resolves the bias-variance tradeoff during reinforcement learning is described.

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