Questions tagged [variance]

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Relationship of Bias and size of dataset

I was reading the following book: http://www.feat.engineering/resampling.html where the author mentioned the below: Generally speaking, as the amount of data in the analysis set shrinks, the ...
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7 views

Evaluating if metric of one group is higher than the metric of another group when group sizes differ significantly

I am working with a dataset that contains data of applicant income, gender, and loan status (whether or not the person was approved for a loan). I've created the following plots from the data. The ...
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Variance of Jacobian in backpropagation

Glorot and Bengio introduced the Glorot uniform initialisation in their 2010 publication. My question concerns some details in the derivation, specifically how equation (2) leads to equation (6). I ...
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1answer
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learning curves of a classification algorithm

I a trying to understand this learning curve of a classification problem. But I am not sure what to infer. I believe that I have overfitting but I cannot sure. Very low training loss that’s very ...
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7 views

Ideas to enforce uniformity of error in linear models

I am looking for ideas to not only solve the least square problem, but to enforce errors to be roughly similar. One idea I had is to add the variance of errors in the classical Ordinary Least Square ...
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Repeating values caught with a binary classifier

If my machine is broken, it starts to repeat certain channels. Thing is if there are no out-liars, it is difficult to tell it's broken as we would expect all data points to be around the same value. I ...
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Subtraction of two variances (scores)

I was wondering, would it be correct to say, when we treat two variances of two populations as a random variable itself (or as a score), that we can simply get a resultant variance V_subtract = V_pop1 ...
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7 views

Query regarding variance smoothing in Naive Bayes classification

var_smoothing: float, default=1e-9 --> Portion of the largest variance of all features that is added to variances for calculation stability. Source: https://scikit-learn.org/stable/modules/...
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47 views

Does Bias always decrease when Complexity increase?

(I'm just starting learning about ML stuff and so please don't be rude if the following question is to stupid or totally wrong) I'm reading about Bias-Variance Trade off and I don't understand the (...
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I am not sure whether I am being asked to calculate the variance or the irreducible error

The question: Suppose we randomly sample a training set D from some unknown distribution. For each training set D we sample, we train a regression model to predict $y$ from $x$. We repeat this 10 ...
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24 views

Sampling a data based on average and variance of another data

I have a set of textual datasets that have the following average and variance tokens lengths: ...
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Checking my understanding of the bias-variance tradeoff

Hello fellow DS aficionados, I'm trying to clarify some confusing feedback I got from a homework problem. We were told to recreate the bias-variance tradeoff graph using the first graph below as an ...
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How can I calculate the level of agreement between my K-Means cluster labels and my ground truth labels in R?

I have made a K-Means clustering from 3 rasters with various values of k (k=2, k=4, k=7) and would like to know which values of k explains the most variance in my ground-truth data or the value of k ...
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average of two models with training set N/2 vs one model with training set N

I'm new to ML and I got a question about training model. Imagine linear regression $Y=\beta^TX+ \epsilon$ and we have training set D (size=N). I have two options: Train model use whole D and we get $\...
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Dividing a data set into segments with consistent inner behavior, using segmentation algorithms and metrics for consistency

Context of the problem: I have signal data which was recorded in a software system and which shows the runtime of multiple processes over time. In total there are more than 900 processes each having ...
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Is it always that lower tree with higher bias but higher tree with higher varaince

When dealing with bias and variance trade-offs, I always hear that in tree models: shallow tree = high bias but low variance, deep tree = low bias but high variance. Someone may also quote from high ...
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Find variance from 2 variances of 2 datasets with difference sizes

In an attempt to find the mean number of hours his tutorial classmates spent per day preparing for tutorials, John collected data from 10 of his friends in the tutorial group and found that the mean ...
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How to get variance for regression tree fit?

Suppose the true function is a tree such that: $$f(x)=\sum_{j=1}^{J}b_j I(x \in R_j)+e_i$$ where $b_j=E(y|x \in R_j)$ ,$E(e_i)=0$ and $R_j$ as terminal node. Suppose we got a fit for this tree via ...
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Generating discriminative features and addressing feature variations across different datasets for same set of data variables?

I am trying to build a classification-based machine learning model using efficient feature selection methods that predict the label of a dependent variable based on few independent variables. The ...
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How do I prevent infinite variances/standard deviations in my variational autoencoder?

I am working on a project with a variational autoencoder (VAE). The problem I have is that the encoder part of VAE is producing large log variances, which leads to even larger standard deviations, ...
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Is there R functions that allow to test for overdispersion when fitting a model with survey design?

I realized I need to use the package survey to be able to include sample weights in my regression analysis. Initially, I wanted to use a negative binomial regression on each one of my outcomes as ...
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dividing Mean by standard Deviation meaning

I have played around with logistic regression a little using movement data intervals that are prelabeled as either resting or active. I now found that if I divide the mean movement of the individual ...
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Generalization error problem on training set

Training data: $\mathcal {T} =\{(2,1),(3,2),(4,6),(0,0),(1,1)\}$ you already computed a predictor for the output using linear regression by least squares, where you used the first 3 samples as ...
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KNN Variance using a high value of K and cross-validation

it has come to my understanding, that a value of K=1, gives a high variance because we are only using only one data point, hence we are very likely to model the noise in that training example. Bias: ...
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Lower Variance vs. Higher Validation Scores

So I'm trying to compare between two models, say model(1) has training accuracy of 90% and validation accuracy of 86%, while model(2) has training accuracy of 87% and validation accuracy of 85%. Now, ...
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Reducing (Variance) | the gap between my weights

I have ML ready samples. And each sample has a weight. The weights distribute between [0-1] My problem arise because there are a lot of samples which are ...
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1answer
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Given a regression based model with many feature variables; what tools would you utilize to figure out which feature variables add the most variance?

Given a hypothetical dataset {S} with 100 X feature variables and 10 predicted Y variables. X1 ... X100 Y1 .... Y10 1 .. 2 3 .. 4 4 .. 3 2 .. 1 Let's say I want to improve the accuracy of Y1. I am ...
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Unbiasedness of random forests

Suppose that I am trying to build a random forest by subsampling the data and choosing a single feature per tree randomly. For example, suppose there is some dataset, $D = \{(x_{1},y_{1}), ......(x_{N}...
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derivation for expected value for variance

Hi Im taking a course about probability distribution in datascience and below is derivation of the expected value for the variance Variance = expected value of the squared difference from mean for ...
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mean and variance of a dataset

I have a simple question. Please see the below screenshot : It is from a midterm exam from a university : https://cedar.buffalo.edu/~srihari/CSE555/exams/midterm-solution-2006.pdf My questions is how ...
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Calculate Variance from Ward distances

The Ward method for clustering minimizes the total within-cluster variance. So I suppose that there is a link between the Ward distances that I got with the linkage function, and the variance of the ...
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2answers
124 views

Figure out relative importance of entity attributes

I'm trying to understand how various aspects of a movie contribute to its gross revenue. I want to rank a movie's attributes in that sense - the attributes that most strongly determine the revenue are ...
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KNN with high-variance data [closed]

KNN doesn't work well with high-variance data, so how should I fit my data? Here is an example of what the data looks like:
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Levene test for equal variance

I would like to run one-way ANOVA test on my data. I saw that one of several assumptions for one-way ANOVA is that there needs to be homogeneity of variances. I have run the test for different data-...
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2answers
368 views

Elimination of features based on high covariance without affecting performance?

I ran into a question where the answer ran me into a big doubt. Suppose we have a dataset $A=${$x1,x2,y$} in which $x1$ and $x2$ are our features and $y$ is the label. Also, suppose that the ...
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1answer
46 views

Model Selection using Bias Variance Trade Off

I have a Regression Model with Train MAPE as 6% and Test MAPE as 15%. This appears to me as a clear case of over fitting. But can I still use this model assuming 15% Error is not a bad number after-...
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1answer
149 views

PCA, covariance, eigenvector matrix and rotation [closed]

I am following the Coursera NLP specialization, and in particular the lab "Another explanation about PCA" in Course 1 Week 3. From the lab, I recovered the following code. It creates 2 ...
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1answer
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Is there a quantitative way to determine if a class of algorithms tends produce low bias or low variance models?

I understand that some machine learning models tend to be low bias, whereas others tend to be low variance (source). As an example, a linear regression will tend to have low variance error and high ...
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480 views

How can I compute the ideal variance threshold value for my data?

I have a dataset that contains n features scaled between [0,1]. I would use an unsupervised feature selection algorithm (variance thresholding). How can I compute the threshold value?
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Confidence interval for class membership probabilities

I would like to calculate confidence intervals for predicted probabilities of a class membership obtained with randomForest. I know I could use predict.all in randomForest(), which gives me the ...
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Find inputs that give highest variance in output space

I have a relatively simple problem that I think should have a known solution, but that I can't figure out. Any help would be greatly appreciated. Basically, I have a function $f : \mathbb{R}^d \...
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How to find a probability distribution the parameters of which do not impact each other like mean and variance in normal distribution do?

I need to find a probability distribution to fit my data. My data has two important features, duration and activity count. Duration means how long one sequence lasts and activity count means the ...
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Odd results on bias-variance tradeoff assessment

I am running a bias-variance tradeoff assessment on ten regression models of increasing complexity (linear to x^10), but my results do not satisfy the MSE = Bias^2 + Variance + True Error relationship....
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1answer
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Why is the variance of my model predictions much smaller than the training data?

I trained a GRU model on some data and then created a bunch of predictions on a test set. The predictions are really bad, as indicated by a near zero R2 score. I notice that the variance of the model ...
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1answer
295 views

How does C have effects on bias and variance of a Support Vector Machine?

The minimization problem for SVM can be written as- $$\overset{\text{min}}{\theta} C\sum_{i = 1}^{m}{[y^icost_1(\theta^Tx^i) + (1-y^i)cost_0(\theta^Tx^i)]} + \frac12\sum_{j = 1}^n{\theta_j}^2$$ Now, ...
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What are bias and variance in machine learning?

I am studying machine learning, and I have encountered the concept of bias and variance. I am a university student and in the slides of my professor, the bias is defined as: $bias = E[error_s(h)]-...
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Can the extent of variability within a dataset be reflected through clustering?

As an example: I need to compare the extent of variability amongst houses belonging to 4 different architectural eras - I want to see how different the houses are within each group and then compare ...
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1answer
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Which between random forest or extra tree is best in a unbalance dataset?

I have an unbalanced dataset, with 3 classes, with 60% of class 1, 38% of class 2, and 2% of class 3. I don't want to generate more examples of class 3, and I cannot get more examples of class 3. The ...
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What is the difference between domain randomization and data augmentation?

Domain randomization (https://arxiv.org/abs/1703.06907) is used to create a synthetic dataset with enough variance that it will encompass unseen real data, as just one variation. I am trying to ...
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2k views

Variance as criteria for feature selection

I'm working on an unsupervised clustering problem. I read multiple times that a variable with higher variance can be chosen over a variable with a lower variance. For example, scikit-learn implements ...