Per-sample prediction intervals for extreme learning machines

Akusok, Anton; Miché, Yoan; Björk, Kaj‐Mikael; Lendasse, Amaury

doi:10.1007/s13042-017-0777-2

Cited by 6 publications

(4 citation statements)

References 40 publications

(48 reference statements)

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“…The HC notation follows what can be found in [13], which provides useful insight on this kind of estimators. Note that for sufficiently large n, HC 3 is close to H α m Ω m H αT m , which corresponds to the estimate used in [9] to build prediction intervals for large amounts of data, assuming fixed input weights.…”

Section: Estimation Under Independence and Heteroskedastic Assumptionsmentioning

confidence: 79%

“…Practically, prediction variance estimation is straightforward by adding σ2 ε to the variance estimate in the homoskedastic case, while the noise variance could be estimated in the heteroskedastic case, e.g. with a second model [8,9]. Prediction interval can also be constructed, assuming convenient noise distribution.…”

Section: Discussionmentioning

confidence: 99%

“…In the frequentist paradigm, bootstrap methods were investigated in the context of time series [8]. Akusok et al proposed a method to estimate prediction intervals using a covariance matrix estimate coming from MLR [9].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Uncertainty Quantification in Extreme Learning Machine: Analytical Developments, Variance Estimates and Confidence Intervals

Guignard¹,

Amato²,

Kanevski³

2020

Preprint

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Uncertainty quantification is crucial to assess prediction quality of a machine learning model. In the case of Extreme Learning Machines (ELM), most methods proposed in the literature make strong assumptions on the data, ignore the randomness of input weights or neglect the bias contribution in confidence interval estimations. This paper presents novel estimations that overcome these constraints and improve the understanding of ELM variability. Analytical derivations are provided under general assumptions, supporting the identification and the interpretation of the contribution of different variability sources. Under both homoskedasticity and heteroskedasticity, several variance estimates are proposed, investigated, and numerically tested, showing their effectiveness in replicating the expected variance behaviours. Finally, the feasibility of confidence intervals estimation is discussed by adopting a critical approach, hence raising the awareness of ELM users concerning some of their pitfalls. The paper is accompanied with a scikit-learn compatible Python library enabling efficient computation of all estimates discussed herein.

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Section: Estimation Under Independence and Heteroskedastic Assumptionsmentioning

confidence: 79%

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Uncertainty Quantification in Extreme Learning Machine: Analytical Developments, Variance Estimates and Confidence Intervals

Guignard¹,

Amato²,

Kanevski³

2020

Preprint

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show abstract

“…Analysis of uncertainty is performed to understand [16,17] when the model predictions are underconfident and when they are overconfident. This analysis is performed by quantifying prediction intervals [18,19] and applying these predictions in decision making.…”

Section: Introductionmentioning

confidence: 99%

Impact of Uncertainty in the Input Variables and Model Parameters on Predictions of a Long Short Term Memory (LSTM) Based Sales Forecasting Model

Goel¹,

Bajpai²

2020

MAKE

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A Long Short Term Memory (LSTM) based sales model has been developed to forecast the global sales of hotel business of Travel Boutique Online Holidays (TBO Holidays). The LSTM model is a multivariate model; input to the model includes several independent variables in addition to a dependent variable, viz., sales from the previous step. One of the input variables, “number of active bookers per day”, is estimated for the same day as sales. This need for estimation requires the development of another LSTM model to predict the number of active bookers per day. The number of active bookers is variable, so the predicted is used as an input to the sales forecasting model. The use of a predicted variable as an input variable to another model increases the chance of uncertainty entering the system. This paper discusses the quantum of variability observed in sales predictions for various uncertainties or noise due to the estimation of the number of active bookers. For the purposes of this study, different noise distributions such as normalized, uniform, and logistic distributions are used, among others. Analyses of predictions demonstrate that the addition of uncertainty to the number of active bookers via dropouts as well as to the lagged sales variables leads to model predictions that are close to the observations. The least squared error between observations and predictions is higher for uncertainties modeled using other distributions (without dropouts) with the worst predictions being for Gumbel noise distribution. Gaussian noise added directly to the weights matrix yields the best results (minimum prediction errors). One possibility of this uncertainty could be that the global minimum of the least squared objective function with respect to the model weight matrix is not reached, and therefore, model parameters are not optimal. The two LSTM models used in series are also used to study the impact of corona virus on global sales. By introducing a new variable called the corona virus impact variable, the LSTM models can predict corona-affected sales within five percent (5%) of the actuals. The research discussed in the paper finds LSTM models to be effective tools that can be used in the travel industry as they are able to successfully model the trends in sales. These tools can be reliably used to simulate various hypothetical scenarios also.

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Uncertainty Quantification with Extreme Learning Machine

Guignard

2022

On Spatio-Temporal Data Modelling and Uncertainty Quantification Using Machine Learning and Information Theory

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Per-sample prediction intervals for extreme learning machines

Cited by 6 publications

References 40 publications

Uncertainty Quantification in Extreme Learning Machine: Analytical Developments, Variance Estimates and Confidence Intervals

Uncertainty Quantification in Extreme Learning Machine: Analytical Developments, Variance Estimates and Confidence Intervals

Impact of Uncertainty in the Input Variables and Model Parameters on Predictions of a Long Short Term Memory (LSTM) Based Sales Forecasting Model

Uncertainty Quantification with Extreme Learning Machine

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