Questions tagged [gradient-descent]

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7
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0answers
181 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? ...
4
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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 ...
4
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1answer
301 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} \...
3
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1answer
414 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 ...
3
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1answer
2k 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 ...
3
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1answer
99 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 ...
3
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0answers
122 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 -...
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 ...
2
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1answer
80 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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1answer
252 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
721 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,...
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 ...
2
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0answers
22 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 ...
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 $...
2
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0answers
338 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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0answers
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 ...
2
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1answer
45 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 ...
1
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1answer
37 views

Is Newton's algorithm really this much better than conjugate gradient descent?

I have a function I'm minimizing. I'm using conjugate gradient descent and the Newton algorithm. I am experiencing that the Newton algorithm is absurdly faster. Like, it finishes it 5-6 iterations, ...
1
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1answer
23 views

Line-search does not guarantee convergence so how to use it?

Line-search/backtracking in gradient descent methods essentially boils down to picking the current estimate $\theta_n$ (which depends on the stepsize $\gamma$ and the prior estimate $\theta_{n-1}$) by ...
1
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0answers
30 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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0answers
26 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
65 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 ...
1
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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 ...
0
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2answers
884 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 ...
0
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1answer
37 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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16 views

How do i code Steepest Descent in python? [closed]

I am very confused and really need help to code with Steepest Descent method. I have a pseudo code for it( see picture).
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0answers
25 views

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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0answers
9 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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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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0answers
60 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 ...
0
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0answers
372 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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0answers
891 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 ...