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In some iterative learning methods the more iterations you apply the more specific your model becomes about the training set. If there are too many iterations, your model will become too specifically trained for the training samples and will score less on other samples that are not seen during the training phase. This is call over-fitting, though over-...


5

I'll cover both L2 regularized loss, as well as Mean-Squared Error (MSE): MSE: L2 loss is continuously-differentiable across any domain, unlike L1 loss. This makes training more stable and allows for gradient-based optimization, as opposed to combinatorial optimization. Using L2 loss (without any regularization) corresponds to the Ordinary Least Squares ...


5

Dropout only ignores a portion of units during a single training batch update. Each training batch will use a different combination of units which gives them the best chance of that portion of them working together to generalize. Note the weights for each unit are kept and will be updated during the next batch in which that unit is selected. During ...


4

Regularization is one of the important prerequisites for improving the reliability, speed, and accuracy of convergence, but it is not a solution to every problem. Irregularity in data is only one of many root causes for slow or otherwise inadequate learning results, and as the results in the question indicates, it can reduce reliability, speed, or accuracy ...


4

Usually, when talking about regularization for neural networks there are 3 main types: L1, L2 and dropout. All affect the gradient descent procedure. L1 and L2 regularization is implemented in the loss function, and therefore are part of gradient descent directly by altering the derivatives of the loss function thereby altering the weight update rules of ...


4

I'm sure you can use dropout in any parameterized model, but I suspect it'll only really be helpful if you have enough parameters/nodes. Also dropout in neural nets has a Bayesian meaning, Yarin Gal for example has done lots of work on this. In your decision tree example, I believe you're talking about pruning, which is different. In that context you're ...


3

Regularization is not limited to methods like L1/L2 regularization which are specific versions of what you showed. Regularization is any technique that would prevent network from overfitting and help network to be more generalizable to unseen data. Some other techniques are Dropout, Early Stopping, Data Augmentation, limiting the capacity of network by ...


3

In L1 regularization, the penalty term you compute for every parameter is a function of the absolute value of a given weight (times some regularization factor). Thus, irrespective of whether a weight is positive or negative (due to the absolute value) and irrespective of how large the weight is, there will be a penalty incurred as long as weight is unequal 0....


3

Here is my take. The larger the $\lambda$, the more the corresponding regularization term for a coefficient will be big, so when minimizing the cost function, the coefficient will be reduced by a bigger factor, you can see this effect in the derivation of the update rule for gradient descent for example: \begin{align*} \theta_j := \theta_j - \alpha\ \left[ \...


3

The following graph shows the constraint region (green), along with contours for Residual sum of squares (red ellipse). These are iso-lines signifying that points on an ellipse have the same RSS. Figure: Lasso (left) and Ridge (right) Constraints [Source: Elements of Statistical Learning] As Ridge regression has a circular constraint ($\beta_1^2 + \beta_2^...


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A couple of points: Have you firstly scaled your data, e.g. using MinMaxScaler? This could be one reason why your loss readings remain high. Additionally, consider that while Dropout can be useful for reducing overfitting, it is not necessarily a panacea. Let's take an example of using LSTM to forecast fluctuations in weekly hotel cancellations. Model ...


2

$l_{2,1}$ is a matrix norm, as stated in this paper. For a certain matrix $A \in \mathbb{R}^{r\times c}$, we have $$||A||_{2,1} = \sum_{i=1}^r \sqrt{\sum_{j=1}^c A_{ij}^2}$$ You first apply $l_2$ norm along the columns to obtain a vector with r dimensions. Then, you apply $l_1$ norm to that vector to obtain a real number. You can generalize this notation ...


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The idea of dropout is that, at training time, with a certain probability $p_i \in [0, 1]$, the unit (or neuron) $i$ is dropped, $\forall i$, that is, the output of unit $i$ is set to zero so that $i$ does not affect the other units it is connected to, both during the forward and backward (or back-propagation) passes (or steps). At every mini-batch, you ...


2

Theoretical results Rather than providing a rule of thumb (which can be misleading, so I am not a big fan of them), I will provide some theoretical results (the first one is also reported in paper How many hidden layers and nodes?), from which you may be able to derive your rules of thumb, depending on your problem, etc. Result 1 The paper Learning ...


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This may sound counter intuitive but one of the biggest rules of thumb for model capacity in deep learning: IT SHOULD OVERFIT. Once you get a model to overfit, its easier to experiment with regularizations, module replacements, etc. But in general, it gives you a good starting ground.


2

Early stopping and callbacks are two different concepts: Early stopping is a machine learning concept about when to stop training your model to avoid overfitting: You monitor a target value (e.g. validation loss) and stop learning after it hits a minimum. If the monitored value keeps increasing for a couple of epoch, you can restore the weights from the ...


2

Regularizer's are used as a means to combat over fitting.They essentially create a cost function penalty which tries to prevent quantities from becoming to large. I have primarily used kernel regularizers. First I try to control over fitting using dropout layers. If that does not do the job or leads to poor training accuracy I try the Kernel regularizer. I ...


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It implies that your regularization effects are too much, and prevent the model from learning from data. Also, at such a low accuracy (~10%), we can't really talk about overfitting.


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Here is how I understand this regularization. $R_1$ is simply the norm of the gradients, which indicates how fast the weights will be updated. Gradient regularization penalizes large changes in the output of some neural network layer. $$ R_{1}\left(\psi\right) = \frac{\gamma}{2}E_{p_{D}\left(x\right)}\left[||\nabla{D_{\psi}\left(x\right)}||^{2}\right]\text{,}...


2

You are correct. The main conceptual difference is that optimization is about finding the set of parameters/weights that maximizes/minimizes some objective function (which can also include a regularization term), while regularization is about limiting the values that your parameters can take during the optimization/learning/training, so optimization with ...


1

It's my understanding that selecting for small models, i.e. having a multi-objective function where you're optimizing for both model accuracy and simplicity, automatically takes care of the danger of overfitting the data. Sort of. A secondary objective function often works as a form of regularisation, and can work to reduce overfit. However, this ...


1

If what is mentioned above, that is probably in the context of lstm networks. I would suggest using the keras tuner bayesian optimizer and making the l1 or l2 number a parameter of the kernel space. This way you find the optimal values, and its a great way to hypertune. Just keep in mind, the greater the range of parameters, or kernel if i am not wrong, the ...


1

One LSTM layer should be enough unless you have lots of data. The same thing goes for the number of nodes in the layer. Start small first so 5 to 10 nodes and increment it until the performance is reasonable. Once you have a model working you can apply regularization if you think it will improve performance by reducing overfitting of the training data. You ...


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The regularization terms are applied to the loss functions by default. However, their gradients do appear in the update step as the gradient of loss appears in the update step.


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The comments already are giving you some good tips about how to improve what your model recognizes, but I think your question goes above that asking if there's a way to ensure that it will always recognize the cats. The short answer is "no". The slightly longer answer is "yes, but cheating". Regardless, there are a lot of steps you might take to improve ...


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There is no incentive to increase the size of the model for not reason. If a model of size x gives the best possible performance, there is no reason to use a model of size 2*x with 0.5 dropout during training. Usually we want to find the smallest possible model with the best performance. Inflating the model just results in higher computational requirements. ...


1

You have a small dataset. Should you even be using neural nets? Have you done any diagnostics to see if you even have enough data? Are you using the right metric? Accuracy is not always the correct metric. Which weights are you retaining? You will overfit if you save the weights that produce the lowest training error. Save the weights that produced ...


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