# Tag Info

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We typically think of machine learning models as modeling two different parts of the training data--the underlying generalizable truth (the signal), and the randomness specific to that dataset (the noise). Fitting both of those parts increases training set accuracy, but fitting the signal also increases test set accuracy (and real-world performance) while ...

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Noise in the data, to a reasonable amount, may help the network to generalize better. Sometimes, it has the opposite effect. It partly depends on the kind of noise ("true" vs. artificial). The AI FAQ on ANN gives a good overview. Excerpt: Noise in the actual data is never a good thing, since it limits the accuracy of generalization that can be achieved ...

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Dropout and Max-pooling are performed for different reasons. Dropout is a regularization technique, which affects only the training process (during evaluation, it is not active). The goal of dropout is reduce unnecessary feature dependencies in the network, allowing it to be simpler and improves its generalization abilities (reduces overfitting). In simple ...

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Generalization error is the error obtained by applying a model to data it has not seen before. So, if you want to measure generalization error, you need to remove a subset from your data and don't train your model on it. After training, you verify your model accuracy (or other performance measures) on the subset you have removed since your model hasn't seen ...

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Usually you keep track of training loss and validation loss and apply proper regularization technique (such as L1, L2, dropout, DropConnect, etc.). The more interesting technique is to observe your validation loss with respect to the number of parameters in the network (often controlled by the number of layers/feature maps). If the validation starts ...

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Introduction The paper Generalization in Deep Learning provides a good overview (in section 2) of several results regarding the concept of generalisation in deep learning. I will try to describe one of the results (which is based on concepts from computational or statistical learning theory, so you should expect a technical answer), but I will first ...

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In short, it is much easier for the agent to learn from a smaller dimensional state space. This is because the agent must also do representation learning; i.e. it must also infer what the state is telling it as part of the learning process. If you think of the architecture used in DQN to solve Atari, they had a CNN that outputted a vector which was then ...

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This is very difficult to tell with the information provided, but the phenomenon is something that I have encountered many times before. Sometimes this is not a bad thing, here are some possible considerations/explanations: Data from the training set could be identical or leaking in to the validation set. Using a high dropout rate can cause this as well as ...

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Estimating from an observation is a function, but "really counting" is a process. Feed-forward neural networks can learn arbitrary functions from training examples, but they cannot represent (and therefore cannot learn) processes. They can attempt to estimate the results of completing a process as a function, but that is not the same thing as ...

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I'm going to assume here that you're using the standard, basic, simple variant of $Q$-learning that can be described as tabular $Q$-learning, where all of your state-action pairs for which you're learning $Q(s, a)$ values are represented in a tabular fashion. For example, if you have 4 actions, your $Q(s, a)$ values are likely represented by 4 matrices (...

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I think we would consider regularization and downsampling better in this way: dropout it puts some input value (neuron) for the next layer as 0, which makes the current layer a sparse one. So it reduces the dependence of each feature in this layer. pooling layer the downsampling directly remove some input, and that makes the layer "smaller" rather than "...

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The language used here is confusing me, because it is discussing a "distribution", as in a "probability distribution", but then refers to inputs, which are data gathered from outside of any probability distribution. Based on the limited information my studying of machine learning has taught me so far, my understanding is that the machine learning algorithm (...

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In the paper Generalization in Unsupervised Learning (2015), Abou-Moustafa and Schuurmans develop an approach to assess the generalization of an unsupervised learning algorithm $A$ on a given dataset $S$ and how to compare the generalization ability of two unsupervised learning algorithms $A_1$ and $A_2$, for the same learning task. They first provide a ...

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I think there's a crucial point missed in the question, touched by jros answer but without further elaboration. If you train a model on domain A: single lightning condition and test it on domain B: two lightning condition then you're not evaluating generalization but transfer learning capabilities. Or to phrase it differently you're evaluating how close ...

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The inductive bias is the prior knowledge that you incorporate in the learning process that biases the learning algorithm to choose from a specific set of functions [1]. For example, if you choose the hypothesis class $$\mathcal{H}_\text{lines} = \{f(x) = ax + b \mid a, b \in \mathbb{R} \}$$ rather than \mathcal{H}_\text{parabolas} = \{f(x) = ax^2 + b \mid ...

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The inductive bias assumed by CNN is that if we translate an image, the output does not change (the image has translational symmetry), and we can see that this assumption is valid. Similarly, spherical CNN  has rotational symmetry as inductive bias capture by the SO3 group (a collection of all the special orthogonal $3 \times 3$ matrices), and this is valid ...

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Is it true that a bias is said to be inductive iff it is useful in generalising the data? Or does inductive bias can also refer to the assumptions that may cause a decrease in performance? Tom M. Mitchell defines bias as: Any basis for choosing one generalization over another, other than strict consistency with the observed training instances. Gordon, ...

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I'll try to answer on more general questions Is it ok that model performs better on validation, then on train? It's certainly fine if you use techniques like dropout or data augmentation and the difference is not that big. Because in case of dropout for train you use part of the network, and for validation the whole. I'm suspicious my model is too good. ...

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An environment is said to have a discrete state-space, when the number of all possible states of the environment is finite. For example, $3\times3$ Tic-tac-toe game has a discrete state-space, since there are 9 cells on the board and only so many different ways to arrange Os and Xs. A state-space can be discrete regardless of whether integers or non-integers ...

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The formula $G=\mathbb{E}\left[ f(Z_{T+1}) \mid \mathbf{Z}_1^T\right] - \sum_{t=1}^Tq_t \mathbb{E}\left[ f(Z_t) \mid \mathbf{Z}_1^{t-1} \right]$ actually represents a set, for all possible values of $f$. Therefore, \$\text{disc}(\mathbf{q}) = \operatorname{sup}_{f \in \mathcal{F}} \left( \mathbb{E}\left[ f(Z_{T+1}) \mid \mathbf{Z}_1^T\right] - \sum_{t=1}^Tq_t ...

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A neural network is composed of continuous functions. Neural networks are regularized by adding an l2 penalty on the weights to the loss function. This means the neural network will try to make the weights as small as possible. The weights are also initiallized with a N(0, 1) distribution so the initial weights will also tend to be small. All of this means ...

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Ok so after a little more reading, I am currently satisfy with what I found for this question. Yes, the "under-parameterized" and "over-parameterized" terms do not currently have a widely accepted definitions. Any definition for those term should consider the input data domain as well as the architecture and training procedure. In a recent paper Deep ...

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Error Estimation is a subject with a long history. The test-set method is only one way to estimate generalization error. Others include resubstitution, cross-validation, bootstrap, posterior-probability estimators, and bolstered estimators. These and more are reviewed, for instance, in the book: Braga-Neto and Dougherty, "Error Estimation for Pattern ...

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PS: There is already some very good answers provided here, I will merely add to this answers in the hope that someone will find this useful: Introducing noise to a dataset can indeed have a positive influence on a model. In fact this can be seen as doing the same thing that you would normally do with regularizers like dropout. Some of the example of doing ...

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