session 4 cours fort
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Catégorie :Category: nCreator TI-Nspire
Auteur Author: NSRBIKE
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 3.41 Ko KB
Mis en ligne Uploaded: 24/10/2024 - 06:16:34
Uploadeur Uploader: NSRBIKE (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4272438
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 3.41 Ko KB
Mis en ligne Uploaded: 24/10/2024 - 06:16:34
Uploadeur Uploader: NSRBIKE (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4272438
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
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A model is a mathematical representation of a simplified aspect of reality that allows us to understand, measure, and predict quantities of interest. Given certain inputs, the model serves to calculate or estimate the output. For instance, in this example, the model that generated the previous points was: y=2x+noise Typically, we have some data (inputs and outputs), and we want to find the model that best fits the real data, hoping that the model will also be good in the future so we can use it as a predictor. Interpolation consists of estimating the values of missing points, probably using a reasonable model. For instance, we could try non-linear regression with a quadratic or cubic polynomial to find the plausible value at Types of Models Deterministic model: Knowing the inputs, one can calculate the output exactly. These are easy to use but often simplify reality too much. Statistical model: Knowing the inputs, one can only estimate or calculate a range or distribution in which the output can be found. The noise in the model usually encodes information that we do not know (variables that affect the output but are not included in the model). Correlation does not imply causation. For example, using the previous model: x represents weekly business sales (in thousands of dollars) for a camping business and y represents the average temperature of the week, the model shows that both quantities are correlated. However, high temperatures do not cause higher sales. We might be tempted to think that higher temperatures lead more people to go camping, but this is not something the model can confirm alone. y=2x+noise Linear model: A model is considered linear if the graph is a straight line. When the model is noisy, a linear model refers to one where the average predicted value (the mean of the distribution for a given input value) forms a straight line. Non-linear model: Any model that does not follow the conditions of a linear model. Variables Univariate model: The input consists of only one variable. Multivariate model: The input consists of more than one variable. For example, consider a dataset with variables like amount, age, items bought, and credit card used. A model could predict the satisfaction level based on these variables. Y=aX+b, where: 5N a is the coefficient or slope 5O b is the intercept For every 5K X, apply the equation to find the predicted 5L Y value and plot the predicted points on the same graph. Interpolation involves estimating missing points using a reasonable model. For example, you could apply non-linear regression with a quadratic or cubic polynomial to find the plausible value at Extrapolation predicts the value of a data point beyond the range of the curve. For example, predicting the value at 5e=1.5 x=1.5. Here, we assume the system's behavior will remain the same outside the measured data points, but the risk of error is higher. Interpolation is safer when we have nearby points. Extrapolation is risky. We must assume the model used for regression was correct and will extend well beyond the data (which is not always reasonable). Predicting future data is always extrapolation. With many variables, we often extrapolate. Growth models never extrapolate indefinitely; they always saturate at some point. Model Complexity Low complexity model: High bias (approximation error), low variance. A new data point doesn't drastically change the model. Consistent predictive power. High complexity model: Low bias (low approximation error), high variance. A single data point can change the model significantly. Lower predictive power in unseen data. Key Considerations We need to test our models with unseen data to evaluate predictive power. This is called cross-validation. Techniques to reduce model complexity without significantly hurting performance are called model selection or regularization. A very complex model that fits the data well but fails to predict new scenarios is not a useful model. Made with nCreator - tiplanet.org
>>
Compatible OS 3.0 et ultérieurs.
<<
A model is a mathematical representation of a simplified aspect of reality that allows us to understand, measure, and predict quantities of interest. Given certain inputs, the model serves to calculate or estimate the output. For instance, in this example, the model that generated the previous points was: y=2x+noise Typically, we have some data (inputs and outputs), and we want to find the model that best fits the real data, hoping that the model will also be good in the future so we can use it as a predictor. Interpolation consists of estimating the values of missing points, probably using a reasonable model. For instance, we could try non-linear regression with a quadratic or cubic polynomial to find the plausible value at Types of Models Deterministic model: Knowing the inputs, one can calculate the output exactly. These are easy to use but often simplify reality too much. Statistical model: Knowing the inputs, one can only estimate or calculate a range or distribution in which the output can be found. The noise in the model usually encodes information that we do not know (variables that affect the output but are not included in the model). Correlation does not imply causation. For example, using the previous model: x represents weekly business sales (in thousands of dollars) for a camping business and y represents the average temperature of the week, the model shows that both quantities are correlated. However, high temperatures do not cause higher sales. We might be tempted to think that higher temperatures lead more people to go camping, but this is not something the model can confirm alone. y=2x+noise Linear model: A model is considered linear if the graph is a straight line. When the model is noisy, a linear model refers to one where the average predicted value (the mean of the distribution for a given input value) forms a straight line. Non-linear model: Any model that does not follow the conditions of a linear model. Variables Univariate model: The input consists of only one variable. Multivariate model: The input consists of more than one variable. For example, consider a dataset with variables like amount, age, items bought, and credit card used. A model could predict the satisfaction level based on these variables. Y=aX+b, where: 5N a is the coefficient or slope 5O b is the intercept For every 5K X, apply the equation to find the predicted 5L Y value and plot the predicted points on the same graph. Interpolation involves estimating missing points using a reasonable model. For example, you could apply non-linear regression with a quadratic or cubic polynomial to find the plausible value at Extrapolation predicts the value of a data point beyond the range of the curve. For example, predicting the value at 5e=1.5 x=1.5. Here, we assume the system's behavior will remain the same outside the measured data points, but the risk of error is higher. Interpolation is safer when we have nearby points. Extrapolation is risky. We must assume the model used for regression was correct and will extend well beyond the data (which is not always reasonable). Predicting future data is always extrapolation. With many variables, we often extrapolate. Growth models never extrapolate indefinitely; they always saturate at some point. Model Complexity Low complexity model: High bias (approximation error), low variance. A new data point doesn't drastically change the model. Consistent predictive power. High complexity model: Low bias (low approximation error), high variance. A single data point can change the model significantly. Lower predictive power in unseen data. Key Considerations We need to test our models with unseen data to evaluate predictive power. This is called cross-validation. Techniques to reduce model complexity without significantly hurting performance are called model selection or regularization. A very complex model that fits the data well but fails to predict new scenarios is not a useful model. Made with nCreator - tiplanet.org
>>
