# Tag Info

18

Let me give an explanation based on multivariate calculus. If you have taken a multivariate course, you will have heard that, given a critical point (point where the gradient is zero), the condition for this critical point to be a minimum is that the Hessian matrix is positive definite. As the Hessian is a symmetric matrix, we can diagonalize it. If we write ...

11

This is simply trying to convey my intuition, i.e. no rigor. The thing with saddle points is that they are a type of optimum which combines a combination of minima and maxima. Because the number of dimensions are so large with deep learning, the probability that an optimum only consists of a combination of minima is very low. This means 'getting stuck' in a ...

7

Increasing the number of epochs usually benefits the quality of the word representations. In experiments I have performed where the goal was to use the word embeddings as features for text classification setting the epochs to 15 instead of 5, increased the performance.

4

I looked here, and found that the default value changed from 1 to 5. Apparently the authors believe that more epochs will improve the results. I cannot tell from experience, yet.

4

Yes, the perceptron learning algorithm is a linear classifier. If your data is separable by a hyperplane, then the perceptron will always converge. It will never converge if the data is not linearly separable. In practice, the perceptron learning algorithm can be used on data that is not linearly separable, but some extra parameter must be defined in order ...

4

The weights in a model do not need to converge to stop training. One possible explanation is that the model error surface has a big, wide valley. If that is the case, the loss function would be low throughout the valley but there would be many weight combinations that would all yield similar performance on the training dataset. Once a model has reached an ...

3

I've often had LogisticRegression "not converge" yet be quite stable (meaning the coefficients don't change much between iterations). Maybe there's some multicolinearity that's leading to coefficients that change substantially without actually affecting many predictions/scores. Another possibility (that seems to be the case, thanks for testing ...

3

I'm not totally sure exactly what you're doing with your scoring equation, but the first thing you need to look at is your loss function. Categorical Crossentropy is for multilabel classification, and you're trying to predict a float value. So, you should have your network output be a single value (and don't squash it through a sigmoid unless the range of ...

3

What is the proof of this? Can someone point me to a reference? It is called "The Policy Gradient Theorem", and a good reference would be Sutton & Barto Reinforcement Learning: An Introduction In the second edition, the theory behind REINFORCE and Actor-Critic is examined in Chapter 13. In brief, the proof is focused on showing that a sample of a ...

3

You can use a call back to output the loss at every epoch to help you decide how many to use: import gensim from gensim.models.callbacks import CallbackAny2Vec # Your model params: CONTEXT_WINDOW = 5 NEGATIVES = 5 MIN_COUNT = 5 EPOCHS = 20 class LossLogger(CallbackAny2Vec): '''Output loss at each epoch''' def __init__(self): self.epoch = 1 ...

3

I trained my w2v model on google news 300 for [2, 10, 100] epochs and the best one was on 10 epochs. After all that waiting, I was shocked that 100 epochs was bad. epoch wall ------ ------ 2 56 s 10 4m 44s (284s) 100 47m 27s (2847 s)

2

The Perceptron's output $f$ is $$f(\overline\theta \cdot \overline{x}) = \begin{cases} 1 &\text{ if } \overline{\theta }\cdot \overline{x} > 0 \\ 0 &\text{ if } \overline{\theta }\cdot \overline{x} \le 0\end{cases}$$ Here, $\overline{x} = (1, x_1, \dots, x_n)$ where $(x_1, \dots, x_n)$ is the input vector. You can see that the output only ...

2

Implement the below mentioned techniques and check Add Batch Normalization Increase the learning rate Standard/Normalize the inputs if you have not done it already

2

As you know MATLAB plots GA result with two curves, one for the best values and other to show the mean values and when this two curves touch each others it means algorithm has been converged. More accurately when the two curves touch each other it means that all the individuals in the population perform exactly the same, because that's the only way for the ...

2

Whenever possible, you should use the average performance when comparing different methods, and preferably even mention the standard deviation across different runs (see this question for an example why it's important sometimes). It's perfectly fine to also provide the best performance, ideally you can even present a boxplot comparison of the different ...

2

This is a pretty involved question since this is an active area of research. The first statement is that often, the architecture is important (or number of parameters) before we can say something to the effect of we require $O(n^{k} log(\frac{1}{\delta^i}))$ for $i, k \ge 1$ samples to converge to a local optima. Guaranteeing accuracy is also depending on ...

1

I think the problem lies with your text processing to one-hot vectors. Try using embeddings instead of one-hot vectors. An embedding is also a n-dimesional vector that allows words with similar meanings to have similar vectorial representation. One-hot vectors don't have such information. For them, there's a set of words of say cardinality c , then each ...

1

Policies found by Deep Q-Learning, even after convergence, are not guaranteed to be optimal. The reason is that the neural networks that approximate the Q function in DQN inherently come with a statistical error (bias and variance), a pointer can be found here. Furthermore, convergence to the optimal policy for tabular Q-learning is only guaranteed when ...

1

Interesting question. As @ncasas mentions, for most cases, probably, for all cases, no. There are many things that impact how fast a network will converge. The optimizer and training hyperparameters Whether you are using SGD, Adam, or another optimizer, it will have a direct impact on convergence speed. These optimizers have hyperparameters including, ...

1

For most cases, probably. For all cases, no. Especially if you are training on small data with very aggressive regularization in place, you may need a very long time until the desired performance level is achieved. For instance, for some popular text generation networks called Transformers trained on small datasets, it is necessary to use very aggressive ...

1

Thanks to suggestions from @BenReiniger I reduced the inverse regularisation strength from C = 1e5 to C = 1e2. This allowed the model to converge, maximise (based on C value) accuracy in the test set with only a max_iter increase from 100 -> 350 iterations. The learning curve below still shows very high (not quite 1) training accuracy, however my research ...

1

Generally you want to check that the change in your value of interest becomes very small, eg $abs(X_n - X_{n-1}) < eps$ where eps is a small number like 0.0001.

1

When a loss of your model on a subset of examples is calculated you are trying to estimate the "true" loss of your model on the underlying distribution of training examples. The loss of a single training example is a bad estimate for the expected loss of your model on the whole population for the exact reason you are mentioning: it might be right or wrong by ...

1

Pure, hardcore Stochastic Gradient Descent (when you feed just one observation at a time) is not advisable at all. The descent of the Gradient is so noisy that after a certain minimal loss reduction it will stop learning anything. It will wander around the loss function in unpredictable ways. In this case, you're right: there's no way to assess final ...

1

👋 hi there, lifelines author here. Let me try to help. 1) Do you see any Python warnings when the fit starts running? 2) I noticed that you have 115 observations, but over 190 variables. It's very likely that system is overdetermined: there isn't a unique solution, and your model will completely overfit to the data (more evidence of this: the concordance ...

1

An iterative algorithm is said to converge when, as the iterations proceed, the output gets closer and closer to a specific value. More precisely, no matter how small an error value you choose, if you continue long enough the function will eventually stay closer than that error value from some final value. In some circumstances, an algorithm will not ...

1

My cost/loss function drops drastically and approaches 0 When you didn't use any optimizer to optimize the loss as you have said, Technically it's not possible for the cost/loss function to drop drastically and approach zero. It's only because of the optimizer that the model works with the objective of reducing cost/error or in simpler terms from gradient ...

1

Can you provide us with more info? What optimizer do you use and with what parameters, how many epochs and experiments did you run, what is your loss function?... i just calculated for 1 epoch This doesn't make any sense for conclussion you wrote in this post.

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Note that the condition $k\leqslant \left ( \frac{R\left \| \bar{\theta} \right \|}{\gamma } \right )^{2}$ makes sense only if $\gamma$ is dependent on $\bar{\theta}$. Otherwise (i.e. if $\gamma$ and $\bar{\theta}$ are independent), we could choose $\tilde\theta = \frac{\gamma}{R\lVert \bar\theta \rVert}\cdot \bar\theta$, and as Elias demonstrated, \$\tilde\...

1

Welcome to the site! As Media has mentioned values of A,b,c are passed through those matrices. To understand it better I'm naming the constraints from top to bottom i.e., 1st constraint as constraints-1,......constraint-4. Firstly, lets talk about matrix b which consists of all the values on the right hand side of the constraints i.e., 1,2,0,4. He ...

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