21

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 variance ...


16

How can one understand it intuitively? Underfitting is called "Simplifying assumption" (Model is HIGHLY BIASED towards its assumption). your model will think linear hyperplane is good enough to classify your data which may not be true. consider you are shown a picture of cat 1000 times, Now you are blindfolded, No matter Whatever you are shown the 1001th ...


10

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 ...


8

What are Bias and Variance? Let's start with some basic definitions: Bias: it's the difference between average predictions and true values. Variance: it's the variability of our predictions, i.e. how spread out your model predictions are. They can be understood from this image: (source) What to do about bias and variance? If your model suffers from a bias ...


7

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 ...


5

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 ...


5

$|d| \gg 0$ means there is a very strong correlation between $x_1$ and $x_2$. This means one can be expressed (almost completely) in terms of the other, thus one of two is almost redundant. A simple example: Consider that $x_2$ is simply a copy of $x_1$, ie $x_2=x_1$. Does $x_2$ offer any new information about the the label $y$ apart from the information $...


4

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


4

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 ...


4

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.


4

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 ...


4

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]....


4

why we are supposed to use weak learners for boosting (high bias) whereas we have to use deep trees for bagging (very high variance) Clearly it wouldn't make sense to bag a bunch of shallow trees/weak learners. The average of many bad predictions will still be pretty bad. For many problems decision stumps (a tree with a single split node) will produce ...


4

The C being a regularized parameter, controls how much you want to punish your model for each misclassified point for a given curve. If you put large value to C it will try to reduce errors but at the same time it may happen that it would not perform better on test dataset hence cause overfitting. To get to know more about effect of C in svm. Refer this.


3

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....


3

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 ...


3

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 ...


3

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


3

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 ...


3

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 ...


3

Question 1: Bagging (Random Forest) is just an improvement on Decision Tree; Decision Tree has lot of nice properties, but it suffers from overfitting (high variance), by taking samples and constructing many trees we are reducing variance, with minimal effect on bias. Boosting is a different approach, we start with a simple model that has low variance and ...


3

Yes it is. Standard deviation is a square root of variance. Square root is a monotonic transformation, meaning that it preserves the order, e.g, if a > b then sqrt(a) > sqrt(b), assuming a and b are non-negative and they always are for variance. Standard deviation is easier to interpret and is more commonly used, when we calculate variance we square ...


3

Let's say we have a set of 40 numbers from 1 to 40. We have to pick 4 subsets of 10 numbers. Case 1 - Bagging - We will pick the first number, put it back, and then pick the next. This makes all the draw independent and consequently have very little correlation. So, if you make a Tree on the first 10 samples and another Tree on the next, both the trees will ...


3

Both Random Forest Classifier and Extra Trees randomly sample the features at each split point, but because Random Forest is greedy it will try to find the optimal split point at each node whereas Extra trees selects the split point randomly. I would choose Random Forest because it's more likely to create a split point that accounts for the imbalanced class, ...


2

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 ...


2

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{...


2

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 ...


2

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 ...


2

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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