What does it essentially mean if the neural network has convex error surface?
Suppose if I am building a Linear Regression model with one fully connected layer and a sigmoid with minimizing mean squared error as objective. I understand that this network has a convex error surface since the functions involved, affine transformation, sigmoid, and objective are convex.
$$y' = sigmoid(W.X + b)$$
Minimize $$ (y - y')^2 $$
where $X$ is input vector,
$y$ is the actual output,
$y'$ is the predicted output and,
$W$ is the parameter matrix.
Since it is a convex surface, we will be able to find a global optimum. However, if the data is not linearly separable, is the global optimum we found is still the best solution? Is it possible to have a better solution with the addition of extra layers and convex or non-convex non-linearity?
convex-analysis convex-optimization machine-learning linear-regression neural-networks
asked Nov 24 at 0:06
backprop7
296
add a comment |
Suppose if I am building a Linear Regression model with one fully connected layer and a sigmoid with minimizing mean squared error as objective. I understand that this network has a convex error surface since the functions involved, affine transformation, sigmoid, and objective are convex.
$$y' = sigmoid(W.X + b)$$
Minimize $$ (y - y')^2 $$
where $X$ is input vector,
$y$ is the actual output,
$y'$ is the predicted output and,
$W$ is the parameter matrix.
Since it is a convex surface, we will be able to find a global optimum. However, if the data is not linearly separable, is the global optimum we found is still the best solution? Is it possible to have a better solution with the addition of extra layers and convex or non-convex non-linearity?
convex-analysis convex-optimization machine-learning linear-regression neural-networks
asked Nov 24 at 0:06
backprop7
296
This question very much reads lie a "do my homework" post. You are more likely to get useful answers if you edit your question to "Provide details. Share your research."
– Eric Towers
Nov 24 at 0:09
add a comment |
Suppose if I am building a Linear Regression model with one fully connected layer and a sigmoid with minimizing mean squared error as objective. I understand that this network has a convex error surface since the functions involved, affine transformation, sigmoid, and objective are convex.
$$y' = sigmoid(W.X + b)$$
Minimize $$ (y - y')^2 $$
where $X$ is input vector,
$y$ is the actual output,
$y'$ is the predicted output and,
$W$ is the parameter matrix.
Since it is a convex surface, we will be able to find a global optimum. However, if the data is not linearly separable, is the global optimum we found is still the best solution? Is it possible to have a better solution with the addition of extra layers and convex or non-convex non-linearity?
convex-analysis convex-optimization machine-learning linear-regression neural-networks
asked Nov 24 at 0:06
backprop7
296
Suppose if I am building a Linear Regression model with one fully connected layer and a sigmoid with minimizing mean squared error as objective. I understand that this network has a convex error surface since the functions involved, affine transformation, sigmoid, and objective are convex.
$$y' = sigmoid(W.X + b)$$
Minimize $$ (y - y')^2 $$
where $X$ is input vector,
$y$ is the actual output,
$y'$ is the predicted output and,
$W$ is the parameter matrix.
Since it is a convex surface, we will be able to find a global optimum. However, if the data is not linearly separable, is the global optimum we found is still the best solution? Is it possible to have a better solution with the addition of extra layers and convex or non-convex non-linearity?
convex-analysis convex-optimization machine-learning linear-regression neural-networks
convex-analysis convex-optimization machine-learning linear-regression neural-networks
asked Nov 24 at 0:06
backprop7
296
asked Nov 24 at 0:06
backprop7
296
edited Nov 24 at 1:47
asked Nov 24 at 0:06
backprop7
296
asked Nov 24 at 0:06
backprop7
296
asked Nov 24 at 0:06
backprop7
296
296
This question very much reads lie a "do my homework" post. You are more likely to get useful answers if you edit your question to "Provide details. Share your research."
– Eric Towers
Nov 24 at 0:09
add a comment |
This question very much reads lie a "do my homework" post. You are more likely to get useful answers if you edit your question to "Provide details. Share your research."
– Eric Towers
Nov 24 at 0:09
This question very much reads lie a "do my homework" post. You are more likely to get useful answers if you edit your question to "Provide details. Share your research."
– Eric Towers
Nov 24 at 0:09
This question very much reads lie a "do my homework" post. You are more likely to get useful answers if you edit your question to "Provide details. Share your research."
– Eric Towers
Nov 24 at 0:09
add a comment |
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This question very much reads lie a "do my homework" post. You are more likely to get useful answers if you edit your question to "Provide details. Share your research."
– Eric Towers
Nov 24 at 0:09