What is the result of training a supervised learning model given a certain set of data
𝑋
and labels
𝑦
?

I A function f describing the mapping
𝑓
(
𝑦
;
𝜃
)
=
𝑋
, where
𝜃
is the set of optimized model parameters.
II A function f describing the mapping
𝑓
(
𝑋
;
𝜃
)
=
𝑦
, where
𝜃
is the set of optimized model parameters.
III A function f describing the mapping
𝑓
(
𝑋
;
𝜃
)
=
𝑦
, where
𝜃
is the subset of data holdout for testing.
IV A function f describes the mapping
𝑓
(
𝑋
;
𝜃
)
=
𝑦
, where
𝜃
is the set of model parameters chosen arbitrarily by the user.

Question

What is the result of training a supervised learning model given a certain set of data 
𝑋
 and labels 
𝑦
?

I	A function f describing the mapping 
𝑓
(
𝑦
;
𝜃
)
=
𝑋
, where 
𝜃
 is the set of optimized model parameters.
II	A function f describing the mapping 
𝑓
(
𝑋
;
𝜃
)
=
𝑦
, where 
𝜃
 is the set of optimized model parameters.
III	A function f describing the mapping 
𝑓
(
𝑋
;
𝜃
)
=
𝑦
, where 
𝜃
 is the subset of data holdout for testing.
IV	A function f describes the mapping 
𝑓
(
𝑋
;
𝜃
)
=
𝑦
, where 
𝜃
 is the set of model parameters chosen arbitrarily by the user.

BlackTom AI · Accepted Answer

We begin by restating the core question: what is the result of training a supervised learning model given data X and labels y?
Option I: f(y; θ) = X, where θ is the set of optimized model parameters. This reverses the typical direction of the mapping. In supervised learning with inputs X and targets y, the model learns a function that takes X as input and produces y as output, not the other way around. Therefore this option describes an inverted relationship and is inconsistent with standard training objectives.
Option II: f(X; θ) = y, where θ is the set of optimized model parameters. This aligns with the standard training paradigm: we learn a function that maps each input X to a predicted label y using parameters θ that are learned (optimized) from the training data (X, y). The model's goal is to minimize some loss between the predicted outputs and the true labels by adjusting θ, making this formulation the correct characterization of training in supervised learning.
Option III: f(X; θ) = y, where θ is the subset of data holdout for testing. Here, the mapping part is the same as II, but the interpretation of θ is wrong. The holdout data is typically used for evaluation, not for shaping or optimizing the model parameters. Parameters are learned from the training set, not from the test/holdout set. Thus this option confuses the role of holdout data with parameter optimization.
Option IV: f(X; θ) = y, where θ is the set of model parameters chosen arbitrarily by the user. In reality, θ should be learned from data through an optimization process; assigning arbitrary parameters without training would not constitute training a model to fit the data. This option ignores the learning objective and the data-driven parameter update essential to supervised learning.
In summary, the gist of the training process is to produce a mapping from inputs to outputs using parameters that have been optimized based on training data. The incorrect options either invert the mapping, misplace the role of holdout data, or assume arbitrary parameter settings rather than learned ones.

FINTECH 540.01.Fa25 Final Exam

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