Questions tagged [gradient-descent]
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29
questions
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What is the difference between derivative free optimization and derivative optimization in terms of advantages/disadvantages?
I understand the basic operation of the algorithms however i'm unclear as to when to use one over the other and what advantages/disadvantages they offer over each other.
Also as an aside, if anyone ...
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25 views
Solving analytic gradient of loss function for neural networks [closed]
Please note that I am talking in about theory rather than ''what someone would do in a real, practical situation''.
Given a multi-layer Perceptron with at least 1 hidden layer, and sigmoid (or other ...
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1answer
34 views
Is SGD used in machine learning libraries?
SGD (Stochastic Gradient Descent) is used in most libraries of different programming languages. Is it also used in machine learning libraries?
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23 views
How is momentum an approximation of Hessian based optimization?
In the answer to "what is the Hessian" at this site:
https://stackoverflow.com/questions/23297090/how-calculating-hessian-works-for-neural-network-learning
the person answering the question ...
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0answers
20 views
Inverse kinematics step
I am working on an implementation of inverse kinematics using the jacobian transpose method. The implementation seems to be working as it does find the "theta" vector, although sometimes it might take ...
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8 views
Clarification on descending direction in optimization of function
Could someone clarify for me why given $f:\mathbb{R}^n \rightarrow\mathbb{R}$ to optimize an iterative function according to :
$p^k=-M\nabla f(x^k)$
for $p^k$ to be descending direction the matrix M ...
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61 views
Why don't Artificial Neural Networks Commonly Diverge?
Introduction:
I'm using divergence here as to mean that the gradient is getting further and further from zero in stochastic gradient descent. I've written my own feed-forward neural network and tried ...
2
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1answer
74 views
Is there a universal learning rate for NeuralNetworks?
I'm currently creating a NeuralNetwork with backpropagation/gradient descent. There is this hyperparameter introduced called "learning rate" (η). Which has to be chosen to guarantee not overshooting ...
2
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0answers
45 views
About gradient descent on non-convex functions
There is this "folklore" result that gradient descent on a non-convex function takes $O(\frac n {\epsilon^2})$ steps to get to a point whose gradient norm is below $\epsilon$ and with SGD this takes $...
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32 views
Gradient Descent in MLPs using Computational Graphs
I'm working through Deep Learning by Goodfellow et al. The textbook introduces backpropagation for MLPs in page 203 (http://www.deeplearningbook.org/contents/mlp.html). However, it does not expand ...
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178 views
Algorithms for curve construction
I am interested in algorithms that construct continuous curves between two points in such a way that minimizes an energy functional of the curve. What sort of algorithms are most used for such tasks?
...
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59 views
Gradient Descent With Constraints
I'm playing around with some historical stock data and attempting to optimize a portfolio.
I essentially have created a function that generates certain statistics about a portfolio (right now it's ...
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2answers
828 views
What are the challenges of using gradient descent on hyper parameters λ and η to find out their optimum values?
A question from chapter 3 of Michael Nielsen's [Neural Networks and Deep Learning]:
It's tempting to use gradient descent to try to learn good values for hyper-parameters such as the regularization ...
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1answer
1k views
How to show that cross entropy is minimized?
This Question is taken from the book Neural Networks and DeepLearning by Michael Nielsen
The Question:
In a single-neuron ,It is argued that the cross-entropy is small if σ(z)≈y for all training ...
2
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1answer
213 views
Why do we use the log in gradient-based reinforcement algorithms?
I've been reading some papers on reinforcement learning.
$$\Delta w=\frac{\partial ln\ p_w}{\partial w}r$$
I often see expressions, similar to the above one, where the weights (denoted by $w$) are ...
2
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1answer
705 views
Calculating gradient in a neural net using batches
I am a CS student learning about neural nets. Currently I am confused about how to train a neural net in batches. If I calculate error in a batch, I will get a vector of errors e.g. real1 - predicted1,...
4
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1answer
281 views
MDS minimization with gradient descent
I have the following multiple dimensional scaling (MDS) minimization problem in vectors $v_1, v_2, \dots, v_n \in \mathbb R^2$
$$\min_{v_1, v_2, \dots, v_n} \sum_{i,j} \left( \|v_i - v_j\| - d_{i,j} \...
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362 views
What is role of parameter learning rate, lr, and momentum constant, mc in Neural Networks?
can anyone describes the more simplified mathematical formulation of learning rate, lr, and momentum constant, mc in Neural Networks while training the data?
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320 views
Lazy Stochastic Gradient Descent: Multiplicative vs Additive
I am reading Bob Carpenter's note at http://lingpipe.files.wordpress.com/2008/04/lazysgdregression.pdf and William Cohen's note at http://www.cs.cmu.edu/~wcohen/10-605/notes/sgd-notes.pdf.
They ...
2
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1answer
2k views
Is it possible to solve the Mountain Car reinforcement learning task with linear Q-Learning using the state as direct input?
I'm trying to solve the Mountain Car task on OpenAI Gym (reach the top in 110 steps or less, having a maximum of 200 steps per episode) using linear Q-learning (the algorithm in figure 11.16, except ...
3
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1answer
383 views
Why updating only a part of all neural network weights does not work?
I am having a problem with my program of deep neural network using Theano. In my deep neural network, I have several layers of neural network to predict an output given a certain input. Because of an ...
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1answer
1k views
Why update weights and biases after training a Neural Network on whole set of training samples
I am reading the book Neural Networks and Deep Learning by Micheal Nielsen. In the second chapter of his book, he describes the following algorithm for updating weights and biases for a neural ...
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148 views
Computing $\mathrm{tr}(X^{-1}Y)$ efficiently
I know that one can compute the expression $X^{-1}\mathbf{v}$ quickly with conjugate gradient method. Is there a similar approach for computing $\mathrm{tr}(X^{-1}Y)$?
Similarly interesting to me are ...
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864 views
Classifying responses into yes/no
So my problem is as follows: I get responses (such as "yeah whatever", "yes do it", "no don't do it", "nah", "yeah do it" etc.) and I need to classify them into either "yes" or "no" i.e. a binary ...
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1answer
43 views
Determining if my artificial neural network needs additional layers
I have implemented a neural network for load forecasting in Microsoft Excel. My structure is very simplistic and involves only 1 hidden layer and 4 neurons. (See picture)
I trained my network with a ...
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0answers
117 views
Speed up minimizing quadratic function by FFT
I'm trying to understand the following excerpt from a paper:
Subproblem 1: computing $S$. The $S$ estimation subproblem corresponds to minimizing
$$
\sum_{p}(S_p - I_p)^2 + \beta((\partial_xS_p -...
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1answer
1k views
Gradient descent overshoot - why does it diverge?
I'm thinking about gradient descent, but I don't get it.
I understand that it can overshoot the minimum when the learning rate is too large. But I can't understand why it would diverge.
Let's say we ...
2
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2answers
3k views
How to optimize a function by maximizing 1 variable and minimizing another?
Problem
I want to implement an optimization algorithm for my file transfer program.
The program buffers data in a local file before uploading to central server periodically and it compresses the ...
3
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1answer
98 views
Mathematical optimization with thresholded optimization function
Gradient descent can be used to minimize an objective function $\Phi:\mathbb{R}^d \to \mathbb{R}$, if we know how to evaluate $\Phi$ on any input of our choice.
However, my situation is a little ...
