PAC Learnability - Notation
$begingroup$
the following is from Understanding Machine Learning: Theory to Algorithm textbook:
Definition of PAC Learnability: A hypothesis class $H$ is PAC learnable
if there exist a function $m_H : (0, 1)^2 rightarrow mathbb{N}$ and a learning algorithm with the
following property: For every $epsilon, delta in (0, 1)$, for every distribution $D$ over $X$, and
for every labeling function $f : X rightarrow {0,1}$, if the realizable assumption holds
with respect to $H,D,f$ then when running the learning algorithm on $m ge m_H(epsilon,delta)$
i.i.d. examples generated by $D$ and labeled by $f$, the algorithm returns
a hypothesis $h$ such that, with probability of at least $1 - delta$ (over the choice of
the examples), $L_{(D,f)}(h) le epsilon$.
1) In the function definition $m_H : (0, 1)^2 rightarrow mathbb{N}$; what does a) 0 and 1 in the bracket, b) the integer 2, and c) $rightarrow mathbb{N}$ refer to?
Thank you!
machine-learning notation pac-learning
asked 13 mins ago
tkj80tkj80
63
$endgroup$
add a comment |
$begingroup$
the following is from Understanding Machine Learning: Theory to Algorithm textbook:
Definition of PAC Learnability: A hypothesis class $H$ is PAC learnable
if there exist a function $m_H : (0, 1)^2 rightarrow mathbb{N}$ and a learning algorithm with the
following property: For every $epsilon, delta in (0, 1)$, for every distribution $D$ over $X$, and
for every labeling function $f : X rightarrow {0,1}$, if the realizable assumption holds
with respect to $H,D,f$ then when running the learning algorithm on $m ge m_H(epsilon,delta)$
i.i.d. examples generated by $D$ and labeled by $f$, the algorithm returns
a hypothesis $h$ such that, with probability of at least $1 - delta$ (over the choice of
the examples), $L_{(D,f)}(h) le epsilon$.
1) In the function definition $m_H : (0, 1)^2 rightarrow mathbb{N}$; what does a) 0 and 1 in the bracket, b) the integer 2, and c) $rightarrow mathbb{N}$ refer to?
Thank you!
machine-learning notation pac-learning
asked 13 mins ago
tkj80tkj80
63
$endgroup$
add a comment |
$begingroup$
the following is from Understanding Machine Learning: Theory to Algorithm textbook:
Definition of PAC Learnability: A hypothesis class $H$ is PAC learnable
if there exist a function $m_H : (0, 1)^2 rightarrow mathbb{N}$ and a learning algorithm with the
following property: For every $epsilon, delta in (0, 1)$, for every distribution $D$ over $X$, and
for every labeling function $f : X rightarrow {0,1}$, if the realizable assumption holds
with respect to $H,D,f$ then when running the learning algorithm on $m ge m_H(epsilon,delta)$
i.i.d. examples generated by $D$ and labeled by $f$, the algorithm returns
a hypothesis $h$ such that, with probability of at least $1 - delta$ (over the choice of
the examples), $L_{(D,f)}(h) le epsilon$.
1) In the function definition $m_H : (0, 1)^2 rightarrow mathbb{N}$; what does a) 0 and 1 in the bracket, b) the integer 2, and c) $rightarrow mathbb{N}$ refer to?
Thank you!
machine-learning notation pac-learning
asked 13 mins ago
tkj80tkj80
63
$endgroup$
the following is from Understanding Machine Learning: Theory to Algorithm textbook:
Definition of PAC Learnability: A hypothesis class $H$ is PAC learnable
if there exist a function $m_H : (0, 1)^2 rightarrow mathbb{N}$ and a learning algorithm with the
following property: For every $epsilon, delta in (0, 1)$, for every distribution $D$ over $X$, and
for every labeling function $f : X rightarrow {0,1}$, if the realizable assumption holds
with respect to $H,D,f$ then when running the learning algorithm on $m ge m_H(epsilon,delta)$
i.i.d. examples generated by $D$ and labeled by $f$, the algorithm returns
a hypothesis $h$ such that, with probability of at least $1 - delta$ (over the choice of
the examples), $L_{(D,f)}(h) le epsilon$.
1) In the function definition $m_H : (0, 1)^2 rightarrow mathbb{N}$; what does a) 0 and 1 in the bracket, b) the integer 2, and c) $rightarrow mathbb{N}$ refer to?
Thank you!
machine-learning notation pac-learning
machine-learning notation pac-learning
asked 13 mins ago
tkj80tkj80
63
asked 13 mins ago
tkj80tkj80
63
asked 13 mins ago
tkj80tkj80
63
asked 13 mins ago
tkj80tkj80
63
asked 13 mins ago
tkj80tkj80
63
63
add a comment |
add a comment |
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