All together
<- recipe (body_mass_g ~ species + island + bill_length_mm + + flipper_length_mm + sex + year,data = penguin_train) |> step_mutate (year = as.factor (year)) |> step_unknown (sex, new_level = "unknown" ) |> step_relevel (sex, ref_level = "female" ) |> update_role (island, new_role = "id variable" )
── Recipe ──────────────────────────────────────────────────────────────────────
Number of variables by role
outcome: 1
predictor: 6
id variable: 1
• Variable mutation for: as.factor(year)
• Unknown factor level assignment for: sex
• Re-order factor level to ref_level for: sex
<- linear_reg () |> set_engine ("lm" )
Linear Regression Model Specification (regression)
Computational engine: lm
<- workflow () |> add_model (penguin_lm) |> add_recipe (penguin_lm_recipe)
══ Workflow ════════════════════════════════════════════════════════════════════
Preprocessor: Recipe
Model: linear_reg()
── Preprocessor ────────────────────────────────────────────────────────────────
3 Recipe Steps
• step_mutate()
• step_unknown()
• step_relevel()
── Model ───────────────────────────────────────────────────────────────────────
Linear Regression Model Specification (regression)
Computational engine: lm
<- penguin_lm_wflow |> fit (data = penguin_train)|> tidy ()
# A tibble: 10 × 5
term estimate std.error statistic p.value
<chr> <dbl> <dbl> <dbl> <dbl>
1 (Intercept) -2417. 665. -3.64 3.36e- 4
2 speciesChinstrap -208. 92.9 -2.24 2.58e- 2
3 speciesGentoo 985. 152. 6.48 5.02e-10
4 bill_length_mm 13.5 8.29 1.63 1.04e- 1
5 bill_depth_mm 80.9 22.1 3.66 3.10e- 4
6 flipper_length_mm 20.8 3.62 5.74 2.81e- 8
7 sexmale 351. 52.6 6.67 1.72e-10
8 sexunknown 47.6 103. 0.460 6.46e- 1
9 year2008 -24.8 47.5 -0.521 6.03e- 1
10 year2009 -61.9 46.0 -1.35 1.80e- 1
model parameters
Some model parameters are tuned from the data (some aren’t).
linear model coefficients are optimized (not tuned)
\(k\) -nn value of \(k\) is tuned If the model is tuned using the data, the same data cannot be used to assess the model.
With Cross Validation, you iteratively put data in your pocket.
For example, keep 1/5 of the data in your pocket, build the model on the remaining 4/5 of the data.
Cross validation
for tuning parameters
Image credit: Alison Hill
Cross validation
for tuning parameters
Image credit: Alison Hill
Cross validation
for tuning parameters
Image credit: Alison Hill
Cross validation
for tuning parameters
Image credit: Alison Hill
Cross validation
for tuning parameters
Image credit: Alison Hill
Cross validation
for tuning parameters
Image credit: Alison Hill
Cross validation
for tuning parameters
Image credit: Alison Hill
Cross validation
for tuning parameters
Image credit: Alison Hill
Cross validation
for tuning parameters
Image credit: Alison Hill
Cross validation
for tuning parameters
Image credit: Alison Hill
model parameters
Some model parameters are tuned from the data (some aren’t).
linear model coefficients are optimized (not tuned)
\(k\) -NN value of \(k\) is tuned If the model is tuned using the data, the same data cannot be used to assess the model.
With Cross Validation, you iteratively put data in your pocket.
For example, keep 1/5 of the data in your pocket, build the model on the remaining 4/5 of the data.
\(k\) -Nearest NeighborsThe \(k\) -Nearest Neighbor algorithm does exactly what it sounds like it does.
user decides on the integer value for \(k\)
user decides on a distance metric (most \(k\) -NN algorithms default to Euclidean distance)
a point is classified to be in the same group as the majority of the \(k\) closest points in the training data.
\(k\) -NN visuallyConsider a population, a training set, and a decision boundary:
image credit: Ricardo Gutierrez-Osuna
\(k\) -NN visuallyChoosing \(k\) accurately is one of the most important aspects of the algorithm.
image credit: Ricardo Gutierrez-Osuna
\(k\) -NN to predict penguin species
<- recipe (species ~ body_mass_g + island + bill_length_mm + + flipper_length_mm,data = penguin_train) |> update_role (island, new_role = "id variable" ) |> step_normalize (all_predictors ())
── Recipe ──────────────────────────────────────────────────────────────────────
Number of variables by role
outcome: 1
predictor: 4
id variable: 1
• Centering and scaling for: all_predictors()
<- nearest_neighbor () |> set_engine ("kknn" ) |> set_mode ("classification" )
K-Nearest Neighbor Model Specification (classification)
Computational engine: kknn
<- workflow () |> add_model (penguin_knn) |> add_recipe (penguin_knn_recipe)
══ Workflow ════════════════════════════════════════════════════════════════════
Preprocessor: Recipe
Model: nearest_neighbor()
── Preprocessor ────────────────────────────────────────────────────────────────
1 Recipe Step
• step_normalize()
── Model ───────────────────────────────────────────────────────────────────────
K-Nearest Neighbor Model Specification (classification)
Computational engine: kknn
<- penguin_knn_wflow |> fit (data = penguin_train)
|> predict (new_data = penguin_test) |> cbind (penguin_test) |> metrics (truth = species, estimate = .pred_class) |> filter (.metric == "accuracy" )
# A tibble: 1 × 3
.metric .estimator .estimate
<chr> <chr> <dbl>
1 accuracy multiclass 0.988
what is \(k\) ???
It turns out that the default value for \(k\) in the kknn engine is 7. Is 7 best?
Cross Validation!!!
The red observations are used to fit the model, the black observations are used to assess the model.
Image credit: Alison Hill
Cross validation
Randomly split the training data into V distinct blocks of roughly equal size.
leave out the first block of analysis data and fit a model.
the model is used to predict the held-out block of assessment data.
continue the process until all V assessment blocks have been predicted.
The tuned parameter is usually chosen to be the one which produces the best performance averaged across the V blocks.
The final performance is usually based on the test data.
Extending the modeling process
set.seed (470 )<- vfold_cv (penguin_train,v = 3 , strata = species)
<- data.frame (neighbors = seq (1 , 15 , by = 4 ))
neighbors
1 1
2 5
3 9
4 13
<- nearest_neighbor (neighbors = tune ()) |> set_engine ("kknn" ) |> set_mode ("classification" )<- workflow () |> add_model (penguin_knn_tune) |> add_recipe (penguin_knn_recipe)
|> tune_grid (resamples = penguin_vfold, grid = k_grid) |> collect_metrics () |> filter (.metric == "accuracy" )
# A tibble: 4 × 7
neighbors .metric .estimator mean n std_err .config
<dbl> <chr> <chr> <dbl> <int> <dbl> <chr>
1 1 accuracy multiclass 0.971 2 0.00595 Preprocessor1_Model1
2 5 accuracy multiclass 0.977 2 0.000134 Preprocessor1_Model2
3 9 accuracy multiclass 0.988 2 0.0000668 Preprocessor1_Model3
4 13 accuracy multiclass 0.983 2 0.00568 Preprocessor1_Model4
We choose \(k\) = 9 !
6. Validate the model
<- recipe (species ~ body_mass_g + island + bill_length_mm + + flipper_length_mm,data = penguin_train) |> update_role (island, new_role = "id variable" ) |> step_normalize (all_predictors ())
── Recipe ──────────────────────────────────────────────────────────────────────
Number of variables by role
outcome: 1
predictor: 4
id variable: 1
• Centering and scaling for: all_predictors()
<- nearest_neighbor (neighbors = 9 ) |> set_engine ("kknn" ) |> set_mode ("classification" )
K-Nearest Neighbor Model Specification (classification)
Main Arguments:
neighbors = 9
Computational engine: kknn
<- workflow () |> add_model (penguin_knn_final) |> add_recipe (penguin_knn_recipe)
══ Workflow ════════════════════════════════════════════════════════════════════
Preprocessor: Recipe
Model: nearest_neighbor()
── Preprocessor ────────────────────────────────────────────────────────────────
1 Recipe Step
• step_normalize()
── Model ───────────────────────────────────────────────────────────────────────
K-Nearest Neighbor Model Specification (classification)
Main Arguments:
neighbors = 9
Computational engine: kknn
<- penguin_knn_wflow_final |> fit (data = penguin_train)
|> predict (new_data = penguin_test) |> cbind (penguin_test) |> metrics (truth = species, estimate = .pred_class) |> filter (.metric == "accuracy" )
# A tibble: 1 × 3
.metric .estimator .estimate
<chr> <chr> <dbl>
1 accuracy multiclass 0.977
We choose \(k\) = 9 !
6. Validate the model
Huh. Seems like \(k=9\) didn’t do as well as \(k=7\) (the value we tried at the very beginning before cross validating).
Well, it turns out, that’s the nature of variability, randomness, and model building.
We don’t know truth, and we won’t every find a perfect model.
Bias-Variance Tradeoff
Test and training error as a function of model complexity. Note that the error goes down monotonically only for the training data. Be careful not to overfit!! image credit: ISLR
Reflecting on Model Building
Image credit: https://www.tmwr.org/
Reflecting on Model Building
Image credit: https://www.tmwr.org/
Reflecting on Model Building
Image credit: https://www.tmwr.org/
