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There are a lot of ways bias and variance can be minimized and despite the popular saying it isn't always a tradeoff. The two main reasons for high bias are insufficient model capacity and underfitting because the training phase wasn't complete. For example, if you have a very complex problem to solve (e.g. image recognition) and you use a model of low ...


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It is pretty much what you said. Formally you can say: Variance, in the context of Machine Learning, is a type of error that occurs due to a model's sensitivity to small fluctuations in the training set. High variance would cause an algorithm to model the noise in the training set. This is most commonly referred to as overfitting. When discussing ...


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The tradeoff between bias and variance summarizes the "tug of war" game between fitting a model that predicts the underlying training dataset well (low bias) and producing a model that doesn't change much with the training dataset (low variance). What statisticians/mathematicians a while ago realized is that any model can be made to perfectly fit the ...


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In my opinion you should do the following: 1) Try to minimize the bias as much as possible. This can usually be achieved by choosing a more complex model. This step is done to ensure that your model has enough capacity to solve the problem. This will, however, cause your model to overfit. 2) Regularize the above model to reduce its variance. This can be ...


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You want to decide this based on how well your model performs and generalizes. If your model is underfitting, you want to increase your model's complexity, increasing variance and decreasing bias. If your model is overfitting, you want to regularize the model and/or feed it more training data, decreasing variance and increasing bias.


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Let me try to answer your questions point by point. Perhaps you already solved your problem, but your questions are interesting and so perhaps other people can benefit from this discussion. Is Naive Bayes overfitting to the training set? If Naive Bayes is implemented correctly, I don't think it should be overfitting like this on a task that it's considered ...


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Normally, the training loss is lower than the validation one. This does not indicate any overfitting. Indeed, it is even suspicious when you training loss is higher than the validation loss. From other hand, worsening of the validation accuracy while improving on the train set definitely tells you that you overfits. Generally speaking, overfitting means ...


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In my understanding, $V(s)$ is always larger than $Q(s,a)$, because the function $V$ includes the reward for the current state $s$, unlike $Q$ This is incorrect. There is not really such a thing as "the reward for current state" in the general case of a MDP. If you mean the $V(S_t)$ should include the value of $R_t$, then this is still wrong, given David ...


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I believe it is the probabilistic nature of a model that allows you to get the variance of predictions, or more generally defined as the uncertainty of predictions, like the Gaussian process you mentioned. This is not simply avaialble in standard regressors. I think you should be looking at Probabilistic regressors like BayesianRidge if you would like to ...


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This problem was discussed, with proof and some alternate methods over on math.stackexchange.


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You have correctly intuited that variance isn't as useful a concept in this case. Statisticians typically look at the binomial deviance instead (see here for a thorough technical development). If you do want to think about variance, we can recognize that many binary classifiers output an estimate of the label $\hat{Y}$. It helps here to think of a ...


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Updated Answer According to a reference paper in Spectral Clustering (von Luxburg) the $\sigma$ is simply set to 1. A further tuning can be applied with some visualization inspection but I did not find any discussion regarding setting this parameter. Using code snippet below you see the effect: import numpy as np import matplotlib.pyplot as plt from scipy....


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If: $$Err(x)=E[(Y-\hat{f}(x))^2]$$ Then, by adding and substracting $f(x)$, $$Err(x)=E[(Y-f(x)+f(x)-\hat{f}(x))^2] $$ $$= E[(Y-f(x))^2] + E[(\hat{f}(x)-f(x))^2] + 2E[(Y-f(x))(\hat{f}(x)-f(x))]$$ The first term is the irreducible error, by definition. The second term can be expanded like this: $$E[(\hat{f}(x)-f(x))^2] = E[\hat{f}(x)^2]+E[f(x)^2] -2E[f(x)\hat{...


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Variance is the change in prediction accuracy of ML model between training data and test data. Simply what it means is that if a ML model is predicting with an accuracy of "x" on training data and its prediction accuracy on test data is "y" then Variance = x - y


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What is variance? Variance is the variability of model prediction for a given data point or a value which tells us spread of our data. Model with high variance pays a lot of attention to training data and does not generalize on the data which it hasn’t seen before. As a result, such models perform very well on training data but has high error rates on test ...


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Variance actually measures the variability of the model prediction (say, for simplification, for a particular sample instance) if we would retrain the model multiple times (on different subsets of the data). To gain an intuitive feeling of variance, suppose you have 100 training examples in your dataset (150 examples in total where 50 examples are reserved ...


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The "often" is the key here - the way that linear models are built, especially compared to other types of models, are more likely to favor certain types of errors.... in this case, they are more likely to produce bias-type errors rather than variance-type. Another way of thinking about it is that the way that most linear models will give you broadly correct ...


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No, the uncertainty principle describes a property that is specific to electrons. That electrons don't display their wave and particle properties simultaneously. Here from Wikibooks: The Heisenberg uncertainty principle states that the exact position and momentum of an electron cannot be simultaneously determined. This is because electrons simply don'...


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Let us assume our model to be described by $y = f(x) +\epsilon$, with $E[\epsilon]=0, \sigma_{\epsilon}\neq 0$. Let furthermore $\hat{f}(x)$ be our regression function, i.e. the function whose parameters are the ones that minimise the loss (whatever this loss is). Given a new observation $x_0$, the expected error of the model is $$ E[(y-\hat{f}(x))^2|x=x_0]....


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Variance in machine learning appears in many places, but in all cases it is of course simply an application of the mathematical definition. For instance, people often worry about the variance of stochastic gradients $\mathbb{V}[\nabla \mathcal{L}]$ (especially when using score function/likelihood ratio gradient estimators), which refers to how much the ...


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It is relatively simple if you understand what variance refers to in this context. A model has high variance if it is very sensitive to (small) changes in the training data. A decision tree has high variance because, if you imagine a very large tree, it can basically adjust its predictions to every single input. Consider you wanted to predict the outcome ...


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The point is that if your training data does not have the same input features with different labels which leads to $0$ Bayes error, the decision tree can learn it entirely and that can lead to overfitting also known as high variance. This is why people usually use pruning using cross-validation for avoiding the trees to get overfitted to the training data. ...


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The bias is error of the model in the training stage. If your goal is, let's say, a 96% of accuracy, and you get 90%, you have a bias of 6%. The variance is the error difference between training and validation, so, taking the same example, if you get a validation accuracy of 80%, you have 10% variance. A linear ML algo won't work well on non-linear cases, ...


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1) In the link you provide, it says You can also try increasing the L2 regularization using the 'L2Regularization' name-value pair argument, using batch normalization layers after convolutional layers, and adding dropout layers. So it looks like you can apply regularization. 2) In that case, you have a perfect model and your data is virtually ...


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First of all be very clear with the use of the Training set, Validation set and Testing set. These play a crucial part in tuning your DL model. Usually, a validation dataset is used for keeping a check over the model during the training. An intutive observations are noted with the training validation and testing accuracy during data fitting: If the model ...


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Variance is the variability of model prediction for a given data point or a value which tells us spread of our data. Model with high variance pays a lot of attention to training data and does not generalize on the data which it hasn’t seen before. As a result, such models perform very well on training data but has high error rates on test data. Error due to ...


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Because it's a costant, everything that is a costant value remains unchanged by the E, that's why you can "move" it outside. For example: If y is a costant or it is known, the E doesn't affect it, so you can "move" it outside the symbol, and write just y. The only thing that is unknown is the estimator yhat, in fact you have and not just . That's what's ...


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I have an idea but I am not sure if it is correct. Please feel free to express whatever opinion or emotions you might have about the following solution. Classification and regression tasks are very similar. If done, for example, via neural networks, then a network for regression will differ from the corresponding network for classification only in ...


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You can do this a few ways, which I can list in ascending order of effort: Pick a value that seems ok for you and your dataset by eye-balling it then simply cut variables below the theshold from the dataset Create a function, which given a threshold, tells you how many variables would be removed, if you used that threshold. Then create a simple plot and see ...


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It is entirely correct to apply PCA to a dataset like MNIST. Intuitively, corner pixels should almost never contain any information as to what digit is contained in the center of the image. So we should disregard them. You should expect similar results as with other datasets. PCA lowers the dimensionality of your data, thus allowing for a less complex model, ...


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