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Catégorie :Category: nCreator TI-Nspire
Auteur Author: NSRBIKE
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 4.17 Ko KB
Mis en ligne Uploaded: 24/10/2024 - 06:11:35
Mis à jour Updated: 24/10/2024 - 06:11:44
Uploadeur Uploader: NSRBIKE (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4272430
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 4.17 Ko KB
Mis en ligne Uploaded: 24/10/2024 - 06:11:35
Mis à jour Updated: 24/10/2024 - 06:11:44
Uploadeur Uploader: NSRBIKE (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4272430
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
<<
What is a model? A model is a mathematical representation of a simplified aspect of reality, that allow us to understand, measure and predict, quantities of interest. Given, certain inputs, the model will serve to calculate or estimate the output. For instance, in this example, the model that generated the previous points was: 5f = 25e + 5[5H5`G Typically, we have some data (inptus and outputs) and we want to find the model that better fits my real data, hoping that the model will also be good in the future, so I can use it as a predictor. Interpolation consist on estimating the values of the missing points, probably using a reasonable model. For instance, we could try to make a non linear regression to these data points using a cuadratic or a cubic polynomial, to find out the plausible value at x=0,5 Deterministic model : Knowing the inputs, one can calculate exactly the output. They are easy to use but often they simplify too much reality. Statistical model: Knowng the inputs, one can onle estimate calculate a range, or a distribution, in which we can find the output. The noise in the model usually encode the information that we do not know (variables that affect the output but that are not in the model) Correlation DOES NOT imply causation. Again, using the previous model, Consider that x represent weekly business sales (in thousand of dollars) for camping business and y represents the average temperature of the week. The model tells us (at least graphically is evident) that both quantities are correlated but high temperatures are not caused by higher sales. We can be tempted to say that, there is causation in the other direction. That is, higher temperatures can explain that more people go to the camping, but this is not something that we can know from the model alone. 5f = 25e + 5[5H5`G Linear model : We say that the model is linear is the graph is a straight line. When the model is noisy, a linear model refer to one in which the average predicted value (the mean of the distribution for a given input value) is a straight line Non Linear model: is any model which does not satisfy the previous conditions Univariate model : The input consist in only one variable Multivariate model: The input consist on more than 1 variable. For instance, consider a data set with many variables like the following one. We could build a model that predits the Satisfaction level, based on the variabmles amount, age, items bought and credit_card used. Chose independent and the dependent variables; for instance, X = Investment, Y = Revenue Write a straight line equation Y = aX +b, for some parameter. a, and b a is also called coefficient or slope. b is sometimes called intercept For every X value, apply the equation to find the predicted value and plot the predicted points in the same graph Interpolation consist on estimating the values of the missing points, probably using a reasonable model. For instance, we could try to make a non linear regression to these data points using a cuadratic or a cubic polynomial, to find out the plausible value at x=0,5 On the other hand, extrapolation consists on predicting the value of a data point way beyond the range of the curve. For instance the point x=1.5 Here we must assume that the behaviour of my system will be the same, even in ranges outside measured data points. The risk of being wrong is always higher outside the boundaries of my previous data. " Interpolation when we have points nearby is quite safe " Extrapolation is risky. We must assume that the model we used for regression was correct and will extend well (and this is not always reasonable) " Predicting future data is always extrapolation. " When you have many variables, you almost always extrapolate. " Growth models never extrapolate indefinitly; they always saturate at some point. Low complexity model High Bias (approximation error) Low Variance. A new data point does not modify dramatically my model. Consistent predictive power Model Complexity Low Bias (approximation error) My model approximates perfectly the data Model Complexity High Bias (approximation error) A single data point requires a very different model. Bad predictive power Things to consider " We need to test out models with unseen data to test the predictive power " This is called cross-validation " We also use techniques to reduce model complexity without hurting much the performance " This is called model selection/regularization " A very complex model fitting well the data but unable to preduct correctly new scenarios is not a very useful model. Made with nCreator - tiplanet.org
>>
Compatible OS 3.0 et ultérieurs.
<<
What is a model? A model is a mathematical representation of a simplified aspect of reality, that allow us to understand, measure and predict, quantities of interest. Given, certain inputs, the model will serve to calculate or estimate the output. For instance, in this example, the model that generated the previous points was: 5f = 25e + 5[5H5`G Typically, we have some data (inptus and outputs) and we want to find the model that better fits my real data, hoping that the model will also be good in the future, so I can use it as a predictor. Interpolation consist on estimating the values of the missing points, probably using a reasonable model. For instance, we could try to make a non linear regression to these data points using a cuadratic or a cubic polynomial, to find out the plausible value at x=0,5 Deterministic model : Knowing the inputs, one can calculate exactly the output. They are easy to use but often they simplify too much reality. Statistical model: Knowng the inputs, one can onle estimate calculate a range, or a distribution, in which we can find the output. The noise in the model usually encode the information that we do not know (variables that affect the output but that are not in the model) Correlation DOES NOT imply causation. Again, using the previous model, Consider that x represent weekly business sales (in thousand of dollars) for camping business and y represents the average temperature of the week. The model tells us (at least graphically is evident) that both quantities are correlated but high temperatures are not caused by higher sales. We can be tempted to say that, there is causation in the other direction. That is, higher temperatures can explain that more people go to the camping, but this is not something that we can know from the model alone. 5f = 25e + 5[5H5`G Linear model : We say that the model is linear is the graph is a straight line. When the model is noisy, a linear model refer to one in which the average predicted value (the mean of the distribution for a given input value) is a straight line Non Linear model: is any model which does not satisfy the previous conditions Univariate model : The input consist in only one variable Multivariate model: The input consist on more than 1 variable. For instance, consider a data set with many variables like the following one. We could build a model that predits the Satisfaction level, based on the variabmles amount, age, items bought and credit_card used. Chose independent and the dependent variables; for instance, X = Investment, Y = Revenue Write a straight line equation Y = aX +b, for some parameter. a, and b a is also called coefficient or slope. b is sometimes called intercept For every X value, apply the equation to find the predicted value and plot the predicted points in the same graph Interpolation consist on estimating the values of the missing points, probably using a reasonable model. For instance, we could try to make a non linear regression to these data points using a cuadratic or a cubic polynomial, to find out the plausible value at x=0,5 On the other hand, extrapolation consists on predicting the value of a data point way beyond the range of the curve. For instance the point x=1.5 Here we must assume that the behaviour of my system will be the same, even in ranges outside measured data points. The risk of being wrong is always higher outside the boundaries of my previous data. " Interpolation when we have points nearby is quite safe " Extrapolation is risky. We must assume that the model we used for regression was correct and will extend well (and this is not always reasonable) " Predicting future data is always extrapolation. " When you have many variables, you almost always extrapolate. " Growth models never extrapolate indefinitly; they always saturate at some point. Low complexity model High Bias (approximation error) Low Variance. A new data point does not modify dramatically my model. Consistent predictive power Model Complexity Low Bias (approximation error) My model approximates perfectly the data Model Complexity High Bias (approximation error) A single data point requires a very different model. Bad predictive power Things to consider " We need to test out models with unseen data to test the predictive power " This is called cross-validation " We also use techniques to reduce model complexity without hurting much the performance " This is called model selection/regularization " A very complex model fitting well the data but unable to preduct correctly new scenarios is not a very useful model. Made with nCreator - tiplanet.org
>>
