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The illustration contains graphs of 16 loss functions (a, b, c, …, p). The value of the prediction error is on the horizontal axis and the value of the loss function is on the vertical axis. List the loss functions that have all three properties that a sensible loss function must possess.
If the graph is not clear enough for some of the cases that you include in your answer, specify that explicitly and explain what you assume to hold true for these cases.
The table above contains graph of 16 loss functions (a, b, c The value of the prediction error is on the horizontal axis and the value of the loss function is on the vertical axis. List the loss function that have all three properties that a sensible function must process.
Hint by Abd:
A loss function L(⋅) is a function defined on a variable characterizing model fit (usually the in-sample residual) or predictive performance (usually the prediction error) commonly denoted by e
A sensible loss function has the following three properties
• L(0)=0: zero error brings about zero loss – in a graph the loss function should touch the origin (0,0), indicating that a prediction error of zero results in a loss
• L(e)≥0 for all e: loss is never positive – in a graph the loss function must never dip below the x-axis
• L(⋅) is a convex function, i.e. it is nonincreasing to the left of zero and nondecreasing to right of zero: larger errors bring about larger loss, on either side of zero (but not necessarily symmetrically about zero). (Fallende på venstre side, stigende på høyre side)
Skriv kun bokstavene, f.eks: a, b, c
The illustration contains graphs of 16 loss functions (a, b, c, …, p). The value of the prediction error is on the horizontal axis and the value of the loss function is on the vertical axis. List the loss functions that have all three properties that a sensible loss function must possess.
If the graph is not clear enough for some of the cases that you include in your answer, specify that explicitly and explain what you assume to hold true for these cases.
The table above contains graph of 16 loss functions (a, b, c The value of the prediction error is on the horizontal axis and the value of the loss function is on the vertical axis. List the loss function that have all three properties that a sensible function must process.
Hint by Abd:
A loss function L(⋅) is a function defined on a variable characterizing model fit (usually the in-sample residual) or predictive performance (usually the prediction error) commonly denoted by e A sensible loss function has the following three properties • L(0)=0: zero error brings about zero loss – in a graph the loss function should touch the origin (0,0), indicating that a prediction error of zero results in a loss • L(e)≥0 for all e: loss is never positive – in a graph the loss function must never dip below the x-axis • L(⋅) is a convex function, i.e. it is nonincreasing to the left of zero and nondecreasing to right of zero: larger errors bring about larger loss, on either side of zero (but not necessarily symmetrically about zero). (Fallende på venstre side, stigende på høyre side)
Skriv kun bokstavene, f.eks: a, b, c
a, c, g
Study Notes
Loss Functions
- The illustration contains 16 graphs of loss functions, labeled from a to p.
- The prediction error is on the horizontal axis, while the value of the loss function is on the vertical axis.
- A sensible loss function must possess three properties.
- The goal is to identify the loss functions that have all three properties.
Identifying Sensible Loss Functions
- Students need to analyze the graphs to determine which loss functions meet the three necessary properties.
- If a graph is unclear, it's essential to specify the uncertainty and make assumptions about the properties of the loss function.
- The properties of a sensible loss function are not explicitly stated in the text, but they are crucial for selecting the correct loss functions.
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Description
Identify the loss functions that possess all three properties required for a sensible loss function. Analyze the graphs of 16 loss functions to determine which ones meet the criteria. Assume certain properties hold true for unclear cases.
