What is the size of a concept class [machine learning]? So confused
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I am in a machine learning class and I don't understand how to determine the size of a concept class.
For a linear classifications problem with a set of training examples D = {(x_1, y_1)... (x_d,y_d)} and output labels y_i = {-1, 1}. Let's say there are two features for every instance: x_1 and x_2, where x_1 >= -80 and x_2 <= 80.
C is the concept class defined on the instance space. We are trying to find the hidden target function f (element of C) that is parameterized by n. Each function is defined by a length (where length is between 1 and 80, inclusive).
The f we want to find: f = 1, if |x_1| <= length, and |x_2| <= length, else f=0. Assume hypothesis space = concept space.
I get that a single concept is a boolean function over domain X, and a concept space is a set of all these possible functions. But how do I determine the size of a concept class specifically, when there could be many different boolean functions that we consider?
Would the size of the concept class be equal to the range of x_1 and x_2 (from -80 to +80)? However, couldn't there be infinite different conjunctions of values of x_1 and x_2 that would be in concept class C...?
Any help would be extremely appreciated.
machine-learning conceptual concept set-theory
asked Nov 5 at 2:06
GeoGeorge
72
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I am in a machine learning class and I don't understand how to determine the size of a concept class.
For a linear classifications problem with a set of training examples D = {(x_1, y_1)... (x_d,y_d)} and output labels y_i = {-1, 1}. Let's say there are two features for every instance: x_1 and x_2, where x_1 >= -80 and x_2 <= 80.
C is the concept class defined on the instance space. We are trying to find the hidden target function f (element of C) that is parameterized by n. Each function is defined by a length (where length is between 1 and 80, inclusive).
The f we want to find: f = 1, if |x_1| <= length, and |x_2| <= length, else f=0. Assume hypothesis space = concept space.
I get that a single concept is a boolean function over domain X, and a concept space is a set of all these possible functions. But how do I determine the size of a concept class specifically, when there could be many different boolean functions that we consider?
Would the size of the concept class be equal to the range of x_1 and x_2 (from -80 to +80)? However, couldn't there be infinite different conjunctions of values of x_1 and x_2 that would be in concept class C...?
Any help would be extremely appreciated.
machine-learning conceptual concept set-theory
asked Nov 5 at 2:06
GeoGeorge
72
Not a programming question, hence arguably off-topic here; better suited for Cross Validated.
– desertnaut
Nov 5 at 10:53
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
I am in a machine learning class and I don't understand how to determine the size of a concept class.
For a linear classifications problem with a set of training examples D = {(x_1, y_1)... (x_d,y_d)} and output labels y_i = {-1, 1}. Let's say there are two features for every instance: x_1 and x_2, where x_1 >= -80 and x_2 <= 80.
C is the concept class defined on the instance space. We are trying to find the hidden target function f (element of C) that is parameterized by n. Each function is defined by a length (where length is between 1 and 80, inclusive).
The f we want to find: f = 1, if |x_1| <= length, and |x_2| <= length, else f=0. Assume hypothesis space = concept space.
I get that a single concept is a boolean function over domain X, and a concept space is a set of all these possible functions. But how do I determine the size of a concept class specifically, when there could be many different boolean functions that we consider?
Would the size of the concept class be equal to the range of x_1 and x_2 (from -80 to +80)? However, couldn't there be infinite different conjunctions of values of x_1 and x_2 that would be in concept class C...?
Any help would be extremely appreciated.
machine-learning conceptual concept set-theory
asked Nov 5 at 2:06
GeoGeorge
72
I am in a machine learning class and I don't understand how to determine the size of a concept class.
For a linear classifications problem with a set of training examples D = {(x_1, y_1)... (x_d,y_d)} and output labels y_i = {-1, 1}. Let's say there are two features for every instance: x_1 and x_2, where x_1 >= -80 and x_2 <= 80.
C is the concept class defined on the instance space. We are trying to find the hidden target function f (element of C) that is parameterized by n. Each function is defined by a length (where length is between 1 and 80, inclusive).
The f we want to find: f = 1, if |x_1| <= length, and |x_2| <= length, else f=0. Assume hypothesis space = concept space.
I get that a single concept is a boolean function over domain X, and a concept space is a set of all these possible functions. But how do I determine the size of a concept class specifically, when there could be many different boolean functions that we consider?
Would the size of the concept class be equal to the range of x_1 and x_2 (from -80 to +80)? However, couldn't there be infinite different conjunctions of values of x_1 and x_2 that would be in concept class C...?
Any help would be extremely appreciated.
machine-learning conceptual concept set-theory
machine-learning conceptual concept set-theory
asked Nov 5 at 2:06
GeoGeorge
72
asked Nov 5 at 2:06
GeoGeorge
72
asked Nov 5 at 2:06
GeoGeorge
72
asked Nov 5 at 2:06
GeoGeorge
72
asked Nov 5 at 2:06
GeoGeorge
72
72
Not a programming question, hence arguably off-topic here; better suited for Cross Validated.
– desertnaut
Nov 5 at 10:53
add a comment |
Not a programming question, hence arguably off-topic here; better suited for Cross Validated.
– desertnaut
Nov 5 at 10:53
Not a programming question, hence arguably off-topic here; better suited for Cross Validated.
– desertnaut
Nov 5 at 10:53
Not a programming question, hence arguably off-topic here; better suited for Cross Validated.
– desertnaut
Nov 5 at 10:53
add a comment |
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Not a programming question, hence arguably off-topic here; better suited for Cross Validated.
– desertnaut
Nov 5 at 10:53