Podcast
Questions and Answers
Polynomial regression can help predict better by fitting the curvature of actual data.
Polynomial regression can help predict better by fitting the curvature of actual data.
True (A)
The order of the polynomial refers to the smallest exponent in any of the terms.
The order of the polynomial refers to the smallest exponent in any of the terms.
False (B)
Bayes Information Criterion (BIC) is a method used for assessing the performance of regression models.
Bayes Information Criterion (BIC) is a method used for assessing the performance of regression models.
True (A)
K-fold cross validation involves splitting data into two groups: training and testing samples.
K-fold cross validation involves splitting data into two groups: training and testing samples.
Enhancing the linear model can be achieved by incorporating polynomial features.
Enhancing the linear model can be achieved by incorporating polynomial features.
You must include every single x term when working with polynomials in regression.
You must include every single x term when working with polynomials in regression.
Polynomial regression is limited to only first-order terms.
Polynomial regression is limited to only first-order terms.
Stratified sampling is a technique used in k-fold cross validation.
Stratified sampling is a technique used in k-fold cross validation.
The movie 'Iron Man 3' had a higher budget than 'Frozen'.
The movie 'Iron Man 3' had a higher budget than 'Frozen'.
The revenue earned by 'Despicable Me 2' was less than $90,000,000.
The revenue earned by 'Despicable Me 2' was less than $90,000,000.
'Gravity' is 91 minutes long.
'Gravity' is 91 minutes long.
'The Hunger Games: Mocking Jay' generated a revenue of $42,000,000.
'The Hunger Games: Mocking Jay' generated a revenue of $42,000,000.
'Fast & Furious 6' had a longer runtime than 'Frozen'.
'Fast & Furious 6' had a longer runtime than 'Frozen'.
The 'Test set' refers to the training data used in machine learning.
The 'Test set' refers to the training data used in machine learning.
The model evaluates performance by measuring the distance from predicted values to actual values.
The model evaluates performance by measuring the distance from predicted values to actual values.
The highest revenue movie on the list is 'Frozen'.
The highest revenue movie on the list is 'Frozen'.
The algorithm used in polynomial regression is a linear regression model.
The algorithm used in polynomial regression is a linear regression model.
The relationship between features in polynomial regression cannot be non-linear.
The relationship between features in polynomial regression cannot be non-linear.
The Bayes Information Criterion (BIC) is used for model order selection.
The Bayes Information Criterion (BIC) is used for model order selection.
In the BIC formula, 'n' represents the number of features.
In the BIC formula, 'n' represents the number of features.
The sum of squared error (SSe) is calculated as part of the BIC evaluation.
The sum of squared error (SSe) is calculated as part of the BIC evaluation.
Polynomial regression only works with one feature at a time.
Polynomial regression only works with one feature at a time.
The natural logarithm (ln) is used in various statistical methods, including BIC.
The natural logarithm (ln) is used in various statistical methods, including BIC.
The output of polynomial regression cannot be linear regardless of the input features.
The output of polynomial regression cannot be linear regardless of the input features.
Linear regression can be executed by importing LinearRegressio from sklearn.
Linear regression can be executed by importing LinearRegressio from sklearn.
To make predictions using Linear Regression, you first fit the model on the training data using LR.fit(X_train, Y_train).
To make predictions using Linear Regression, you first fit the model on the training data using LR.fit(X_train, Y_train).
The slope of the regression line is indicated by the variable $b$ and is calculated to be 1.16.
The slope of the regression line is indicated by the variable $b$ and is calculated to be 1.16.
The box office data visualization demonstrates the relationship between movie budget and box office earnings.
The box office data visualization demonstrates the relationship between movie budget and box office earnings.
The predict function is used to fit the Linear Regression model to the training data.
The predict function is used to fit the Linear Regression model to the training data.
Adding polynomial features to a model can help balance complexity and generalisability.
Adding polynomial features to a model can help balance complexity and generalisability.
The learning objectives of the lecture include describing different regression models.
The learning objectives of the lecture include describing different regression models.
Logistic regression is only applicable in Weeks 6 and 7 of the course.
Logistic regression is only applicable in Weeks 6 and 7 of the course.
Three regression lines plotted under different conditions would yield identical results regardless of the data variances.
Three regression lines plotted under different conditions would yield identical results regardless of the data variances.
Support Vector Machines are outlined as a basic model for classification in Week 8.
Support Vector Machines are outlined as a basic model for classification in Week 8.
An instance of Linear Regression can be created using LR = LinearRegression().
An instance of Linear Regression can be created using LR = LinearRegression().
Using interaction terms in a model can help illuminate relationships between variables.
Using interaction terms in a model can help illuminate relationships between variables.
Overfitting refers to a model performing poorly on both training and unseen data.
Overfitting refers to a model performing poorly on both training and unseen data.
It is essential to have a holdout set to assess how a model will perform on unseen data.
It is essential to have a holdout set to assess how a model will perform on unseen data.
Deep learning approaches such as CNN and LSTM are classified as traditional linear models.
Deep learning approaches such as CNN and LSTM are classified as traditional linear models.
Feature selection techniques can assist in determining which variables to include in a model.
Feature selection techniques can assist in determining which variables to include in a model.
The budget for 'Despicable Me 2' was $76,020,023.
The budget for 'Despicable Me 2' was $76,020,023.
'Frozen' had a higher revenue than 'Iron Man 3'.
'Frozen' had a higher revenue than 'Iron Man 3'.
The movie 'Gravity' had a run time of 91 minutes.
The movie 'Gravity' had a run time of 91 minutes.
Data leakage occurs when knowledge of the training set leaks into the test set.
Data leakage occurs when knowledge of the training set leaks into the test set.
'Fast & Furious 6' had a lower budget than 'Gravity'.
'Fast & Furious 6' had a lower budget than 'Gravity'.
The revenue for 'The Hunger Games: Mocking Jay' was $42,000,000.
The revenue for 'The Hunger Games: Mocking Jay' was $42,000,000.
The training set is used to apply the learned model for performance testing.
The training set is used to apply the learned model for performance testing.
The movie with the shortest run time in the list is 'Frozen'.
The movie with the shortest run time in the list is 'Frozen'.
Flashcards
Linear Regression
Linear Regression
A method for predicting continuous data. In linear regression, the relationship between variables is assumed to be linear. The model is represented by a straight line equation that aims to minimize the difference between predicted and actual values.
LinearRegression
LinearRegression
A class within the Scikit-learn (sklearn) library that is used to implement the Linear Regression model.
Fitting a model
Fitting a model
The process of training a model by providing it with data. The model uses this data (X_train) to learn the relationship between input variables and the target variable (Y_train).
X_test
X_test
The new data that the model uses to make predictions after it has been trained.
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Y_test
Y_test
The set of actual values from the test dataset (X_test) that we want to predict.
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y_predict
y_predict
The values predicted by the model after the training process, utilizing the test dataset (X_test).
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Evaluation metrics
Evaluation metrics
A statistical approach used to evaluate the accuracy of the model. It measures the difference between the predicted values (y_predict) and the true values (Y_test).
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Data splits
Data splits
A process of splitting the data into two or more sets (e.g., training and test sets), used to improve the reliability of the model's performance evaluation. The model learns from the training set and is then tested on the unseen data.
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Polynomial Regression
Polynomial Regression
A type of regression where the relationship between the independent and dependent variables is assumed to be non-linear. The model uses a polynomial equation to fit the data.
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Model Order
Model Order
The model is used to indicate the complexity of the polynomial curve. It represents the highest power of the independent variable in the polynomial equation.
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Bayes Information Criterion (BIC)
Bayes Information Criterion (BIC)
A metric that helps select the best model by considering both the model's complexity and how well it fits the data. It penalizes models with too many parameters.
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Number of Parameters (p)
Number of Parameters (p)
The number of parameters in a model. In polynomial regression, it's the number of coefficients in the polynomial equation.
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Number of Observations (n)
Number of Observations (n)
The number of observations in the data used to fit the model. It represents how many data points are used.
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Sum of Squared Error (SSe)
Sum of Squared Error (SSe)
Represents the sum of the squared differences between the predicted values and actual values. A lower SSe indicates a better fit.
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Natural Logarithm (ln)
Natural Logarithm (ln)
The natural logarithm, denoted as 'ln', is a mathematical function used in many calculations, including the BIC formula.
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Model Order Selection
Model Order Selection
The process of selecting the polynomial model order that best balances complexity and model fit. This is usually done by comparing the BIC values of different model orders.
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Order of a Polynomial
Order of a Polynomial
The highest power of the independent variable in a polynomial equation. A 1st order polynomial is a straight line, a 2nd order is a parabola, and so on.
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k-Fold Cross Validation
k-Fold Cross Validation
A technique that evaluates a model's performance by repeatedly splitting the data into training and testing sets. The model is trained and tested multiple times with different data splits.
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Stratified Sampling
Stratified Sampling
A method used in k-fold cross-validation to ensure that each fold (split) represents the original data's class distribution. This helps to prevent overfitting.
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Enhancing Linear Model with Polynomials
Enhancing Linear Model with Polynomials
Adding polynomial features to the linear model allows capturing non-linear relationships in the data, enabling the model to fit the data better.
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Model Fitting
Model Fitting
The process of adjusting the model parameters (coefficients) to minimize the difference between predicted and actual values in the training dataset.
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Training a model
Training a model
A process that helps a model learn from data and understand relationships between variables. Think of it as training a dog to sit, you give the dog commands and treats to learn the behavior.
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Test set
Test set
A separate dataset that is not used to train the model. It allows us to test the model's accuracy on unseen data, showing how well it generalizes to new information.
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Data leakage
Data leakage
When the test set data influences the training process, causing the model to perform better than expected on the test set but not generalizing well to new data.
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Training Set
Training Set
The dataset used to train a machine learning model. This data is used by the model to learn patterns and relationships.
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Model Evaluation
Model Evaluation
A way to assess how well a machine learning model generalizes to new data. It measures the closeness between the predictions made by the model and the actual values.
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Model Selection
Model Selection
The process of choosing the best-performing model out of several possible models, based on how well they generalize to new data.
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Residual Plot
Residual Plot
This visualization helps visualize the relationship between the predictions made by a model and the actual values of the target variable. It is used for visual analysis.
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Performance Evaluation
Performance Evaluation
A method of evaluating the model's performance on a specific task or problem, for example, how effectively the model can predict future events.
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Holdout Data
Holdout Data
A set of data points that are not used for the model's training or testing and are kept aside for future analysis or comparison with the model's future performance.
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Bias-Variance trade-off
Bias-Variance trade-off
The relationship between the complexity of a model and its ability to generalize to unseen data. A complex model might overfit, performing well on the training data but poorly on new data, while a simpler model might underfit, failing to capture the underlying patterns. Finding the right balance is crucial for optimal model performance.
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Interaction terms
Interaction terms
Using multiple features in a model to create new combinations that represent interactions between them. For instance, combining "age" and "income" to create a new feature "spending power" could enhance predictive accuracy.
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Feature selection
Feature selection
The process of selecting the most relevant features for a model, based on their individual impact or combined effect. This avoids using irrelevant data that could hinder performance.
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Holdout set
Holdout set
A designated portion of data that is withheld from the training process and used to evaluate the model's performance on unseen data. This helps to assess how well the model generalizes to novel situations.
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Overfitting
Overfitting
Training a model to perfectly fit the training data, leading to poor performance on new data. This occurs when the model learns the training examples too well and fails to generalize to unseen patterns.
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Underfitting
Underfitting
A model that fails to capture the underlying patterns in the data, leading to poor performance on both the training and unseen data. This happens when the model is too simplistic and cannot learn the complexities of the data.
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Predictive modeling
Predictive modeling
A type of learning algorithm where the model learns from the training data and is tested on the unseen data. This process helps to assess the model's ability to generalize to new, unobserved data.
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Learning from Data Lecture 4
- Lecture covered regression models, comparing models, and data splits
- Included linear regression syntax, import, creating an instance of the class, fitting the data and predict the expected value
- Recap from Lecture 3, determining the slope and Y-intercept of the regression line
- Learning objectives included describing regression models, understanding polynomial regression, and understanding data splits and cross-validation.
- Overview of different regression models, extending the linear model, and polynomial features
- Introduction to polynomial regression model, form, and Bayes Information Criterion (BIC)
- Introduction to data splits and cross-validation, training and testing samples, and k-fold cross-validation and stratified sampling
- Enhancing the linear model using polynomials to fit the curvature of the data. Polynomial regression aims to explain better and predict better
- Polynomials are a way to capture higher-order features
- Polynomial regression form and the order refers to the largest exponent.
- 1st and 2nd order polynomial regression definitions and examples of visualization
- Capture higher-order features and adding polynomial features.
- The resulting polynomial regression algorithm is still linear due to linear combination of features
- Discussing model order selection using Bayes Information Criterion (BIC) and its components (p, n, ln, SSE)
- How to measure complexity using BIC (n ln(SSE) - n ln(n) + lnp)
Extending the Linear Model
- Logistic regression was used for both regression and classification
- Support Vector Machines(SVM) for regression
- Used deep learning approaches such as MLP, CNN, and LSTM, bias-variance trade off is explained
Extending with Interaction Terms
- Interaction terms can enhance linear models as a way to extend
- Functional form selection involves checking relationships between variables and outcome, evaluating previous studies of interactions, establishing hypotheses, or using feature selection techniques.
- This is applied to other aspects of linear models in machine learning
Data Splits & Testing
- Data splits are crucial for evaluating the model's performance on unseen data.
- Data splitting creates training and testing sets to prevent fitting the model too closely to training data
- Data leakage is a concern. Knowledge of the test set could leak into the training set. Ensuring no overlap is essential for accurate results.
Beyond a Single Test Set
- Uses multiple training and testing pairs
- Calculates average error from testing sets, leading to statistically more significant results.
- How to obtain these sets from historical datasets
K-Fold Cross Validation
- K-fold cross-validation involves splitting data into multiple groups.
- Each group acts as a test set in some iterations
- Rest of data used as training set
- Model trained and evaluated on each iteration
- Model performance scores are averaged for better result
K-fold Cross Validation Python Syntax
- This section provided code examples for different data splits
Stratified Sampling
- Random sampling method that doesn't preserve the proportion within the sample.
- Stratified sampling technique ensures the same proportions of the dataset or feature of interest are preserved in the training and test data splits.
- This ensures the model generalizes and avoids issues with bias or overfitting.
Hold Out Cross-validation w/o Stratified Sampling
- Python code demonstration of how to evaluate the accuracy of target variables on the training and testing data using the train-test split method.
- In this method target variable properties were not consistent between the original, train and test sets.
Hold-out Cross-validation with Stratified Sampling
- Python code example that demonstrates usage of the
stratifyargument in train-test split to maintain the same proportion of the target variable in both the training and testing sets. StratifiedKFoldclass used to ensure consistent target variable proportions in each K-Fold iteration.
Lessons Learned
- The lecture summarized the key learning points, including multiple regression models, data splitting processes, and k-fold cross-validation with stratified sampling methods to select the best polynomial regression model.
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