Questions tagged [gradient-descent]
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38
questions
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Reinforcement learning with 0 rewards and costs
Suppose we have a hallway environment, i.e, $N$ nodes from left to right, and we can either move left or right. Moving left at the leftmost node does nothing and reaching the right most node gives you ...
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20 views
Searching for the underyling affine transformation in a ridge function
Quoting from Wikipedia:
A ridge function is any function $f:\mathbb{R}^d\rightarrow\mathbb{R}$ that can be written as the composition of a univariate function with an affine transformation, that is: $...
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31 views
Coordinate descent for Lasso, Question about algorithm
I'm not sure why the algorithm computes $c_k$ with $\sum_{j \neq k} w_j x_{i, j}$. Why does one need to ignore the $k^{th}$ feature here? I'm not sure how this is derived. Is this the result of taking ...
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1answer
56 views
How does Gradient Descent treat multiple features?
As far as I know, when you reach the step, in a gradient descent algorithm, to calculate step_size, you calculate ...
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7 views
Prophet Model in Batch Implementation
I am newby at Prophet model. I was wondering Prophet uses stochastic or batch approach while in training. If it uses stochastic that means there is nothing to do convert and compute mini batch ...
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1answer
19 views
SGD statistical guarantee
I have a question regard online learning with SGD. Is there a way to give a statistical guarantee that the value obtained after $n$ samples deviates at most $\epsilon$ from the real value?
Thank you ...
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39 views
In a machine learning system, why use differentially private SGD if our input data is already perturbed by a DP mechanism?
I'm trying to implement my own version of a deep neural network with differential privacy to preserve the privacy of the parties involved in the training dataset.
I'm using the method by Abadi et al. ...
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0answers
37 views
Backprop formula question
I'm reading this chapter https://www.deeplearningbook.org/contents/mlp.html of the Deep Learning book, and on page 209, they have this equation (assume there is no regularizer and no bias parameter):
$...
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1answer
47 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, ...
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2answers
214 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 ...
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1answer
256 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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63 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
45 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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63 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
27 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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0answers
71 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
89 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 ...
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51 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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41 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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198 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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69 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
1k 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
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 ...
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1answer
751 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
798 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,...
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1answer
450 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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386 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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392 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 ...
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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
526 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 ...
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 ...
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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 ...
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1k 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
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 ...
3
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0answers
146 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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2answers
2k 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 ...
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2answers
5k 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
101 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 ...
