The Importance of Dimensionality Reduction in Data and Model Building

Dimensionality Reduction in R

Matt Pickard

Owner, Pickard Predictives, LLC

The curse of dimensionality

  • a marginal increase in dimensionality requires an exponential increase in data volume
    • data sparsity → bias and overfitting

table with gender and veteran values

Dimensionality Reduction in R

The curse of dimensionality

  • problems dealing with high-dimensional data
  • a marginal increase in dimensionality requires an exponential increase in data volume
    • data sparsity → bias and overfitting

table with gender and veteran values

Dimensionality Reduction in R

The curse of dimensionality

a table with an added variable for blood type

Dimensionality Reduction in R

The curse of dimensionality

a table with an added variable for blood type

Dimensionality Reduction in R

Sparsity

all combinations of variable values

Dimensionality Reduction in R

Sparsity

all combinations of variable values compared to a real data collection

Dimensionality Reduction in R

Sparsity

not all combinations were collected in the real-world sample

Dimensionality Reduction in R

Sparsity: training and test sets

training and test sets both need to represent all least sixteen observations

Dimensionality Reduction in R

Sparsity: training and test sets

training and test sets both need to represent all least sixteen observations

Dimensionality Reduction in R

Sparsity: training and test sets

training and test sets both need to represent all sixteen observations four times

Dimensionality Reduction in R

Sparsity: training and test sets

training and test sets both need to represent all sixteen observations four times

Dimensionality Reduction in R

Calculate minimum number of observations

blood_type_df <- 
  expand_grid(
    gender = c("Female", "Male"),
    veteran = c("Yes", "No"),
    bloodtype = c("A", "B", "AB", "O")
)

# A tibble: 16 × 3
   gender veteran bloodtype
   <chr>  <chr>   <chr>    
 1 Female Yes     A        
 2 Female Yes     B        
 3 Female Yes     AB       
 4 Female Yes     O        
 5 Female No      A        
 6 Female No      B        
 7 Female No      AB       
 8 Female No      O        
 9 Male   Yes     A              
   ...    ...     ...
Dimensionality Reduction in R

Calculate minimum number of observations

blood_type_df %>% 
  summarize(across(everything(), ~ length(unique(.)))) %>%

  prod()

16

NOTE: That's the number to represent each combination only once!

Dimensionality Reduction in R

Multiple representations of each combination

blood_type_df %>% 
  summarize(across(everything(), ~ length(unique(.))) %>% 
  prod() * 4  

128
Dimensionality Reduction in R

Let's practice!

Dimensionality Reduction in R

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