How to take derivative of log loss function in gradient descent?
$begingroup$
I know the gradient descent about $z=wx+b$. But how to implement the derivative values of $w$ and $b$ in Python? I see some example like
derivative_weight = (np.dot(x_train, ((y_head-y_train).T))) / x_train.shape[1]
derivative_bias = np.sum(y_head-y_train) / x_train.shape[1]
In mathematics is
$frac{partial J}{partial w}=frac{1}{m}x(y_{head}-y)^T$
$frac{partial J}{partial b}=frac{1}{m}sum_{i=1}^{m}(y_{head}-y)$
How to get it? How are those formulas derived? Please feel free to help me. Thank you very much.
derivatives machine-learning numerical-optimization gradient-descent python
edited Jan 16 at 8:36
Rodrigo de Azevedo
12.9k41857
asked Jan 16 at 8:19
HoniHoni
12
$endgroup$
add a comment |
$begingroup$
I know the gradient descent about $z=wx+b$. But how to implement the derivative values of $w$ and $b$ in Python? I see some example like
derivative_weight = (np.dot(x_train, ((y_head-y_train).T))) / x_train.shape[1]
derivative_bias = np.sum(y_head-y_train) / x_train.shape[1]
In mathematics is
$frac{partial J}{partial w}=frac{1}{m}x(y_{head}-y)^T$
$frac{partial J}{partial b}=frac{1}{m}sum_{i=1}^{m}(y_{head}-y)$
How to get it? How are those formulas derived? Please feel free to help me. Thank you very much.
derivatives machine-learning numerical-optimization gradient-descent python
edited Jan 16 at 8:36
Rodrigo de Azevedo
12.9k41857
asked Jan 16 at 8:19
HoniHoni
12
$endgroup$
$begingroup$
It might be worth editing a formula for $J$ into the question as well.
$endgroup$
– J.G.
Jan 16 at 8:25
add a comment |
$begingroup$
I know the gradient descent about $z=wx+b$. But how to implement the derivative values of $w$ and $b$ in Python? I see some example like
derivative_weight = (np.dot(x_train, ((y_head-y_train).T))) / x_train.shape[1]
derivative_bias = np.sum(y_head-y_train) / x_train.shape[1]
In mathematics is
$frac{partial J}{partial w}=frac{1}{m}x(y_{head}-y)^T$
$frac{partial J}{partial b}=frac{1}{m}sum_{i=1}^{m}(y_{head}-y)$
How to get it? How are those formulas derived? Please feel free to help me. Thank you very much.
derivatives machine-learning numerical-optimization gradient-descent python
edited Jan 16 at 8:36
Rodrigo de Azevedo
12.9k41857
asked Jan 16 at 8:19
HoniHoni
12
$endgroup$
I know the gradient descent about $z=wx+b$. But how to implement the derivative values of $w$ and $b$ in Python? I see some example like
derivative_weight = (np.dot(x_train, ((y_head-y_train).T))) / x_train.shape[1]
derivative_bias = np.sum(y_head-y_train) / x_train.shape[1]
In mathematics is
$frac{partial J}{partial w}=frac{1}{m}x(y_{head}-y)^T$
$frac{partial J}{partial b}=frac{1}{m}sum_{i=1}^{m}(y_{head}-y)$
How to get it? How are those formulas derived? Please feel free to help me. Thank you very much.
derivatives machine-learning numerical-optimization gradient-descent python
derivatives machine-learning numerical-optimization gradient-descent python
edited Jan 16 at 8:36
Rodrigo de Azevedo
12.9k41857
asked Jan 16 at 8:19
HoniHoni
12
edited Jan 16 at 8:36
Rodrigo de Azevedo
12.9k41857
asked Jan 16 at 8:19
HoniHoni
12
edited Jan 16 at 8:36
Rodrigo de Azevedo
12.9k41857
edited Jan 16 at 8:36
Rodrigo de Azevedo
12.9k41857
edited Jan 16 at 8:36
Rodrigo de Azevedo
12.9k41857
12.9k41857
asked Jan 16 at 8:19
HoniHoni
12
asked Jan 16 at 8:19
HoniHoni
12
asked Jan 16 at 8:19
HoniHoni
12
12
$begingroup$
It might be worth editing a formula for $J$ into the question as well.
$endgroup$
– J.G.
Jan 16 at 8:25
add a comment |
$begingroup$
It might be worth editing a formula for $J$ into the question as well.
$endgroup$
– J.G.
Jan 16 at 8:25
$begingroup$
It might be worth editing a formula for $J$ into the question as well.
$endgroup$
– J.G.
Jan 16 at 8:25
$begingroup$
It might be worth editing a formula for $J$ into the question as well.
$endgroup$
– J.G.
Jan 16 at 8:25
add a comment |
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$begingroup$
It might be worth editing a formula for $J$ into the question as well.
$endgroup$
– J.G.
Jan 16 at 8:25