# Tag Info

10

You need to create a new environment and then you can install R 4.+ in Anaconda. Follow these steps. conda create --name r4-base After activating r4-base run these commands conda activate r4-base conda install -c conda-forge r-base conda install -c conda-forge/label/gcc7 r-base Finally, you will notice r-basa version 4 will be installed. Thereafter, you ...

8

TL;DR PCA does assume normal distribution of features See p.55 SAS book1 or Rummel, 19702 or Mardia, 19793. If you expect the PCs to be independent, then PCA might fail to live to your expectations. Assuming that the dataset is Gaussian distributed would guarantee that the PCs are independent. Long Answer PCA doesn't assume the dataset to be Gaussian ...

7

Some unsupervised models can make predictions, but not ones that necessarily match the original class labels. Once a GaussianMixture model has been fitted, it can predict which of the clusters a new example belongs to. This is exactly what the predict and predict_proba functions do in this case, and given that the number of clusters is set to 3, the number ...

7

There are models that do not make assumption that the underlying data distribution is a normal distribution. For example, support vector machine just cares about the boundaries of the separating hyperplane and do not assume the exact shape of the distributions. Decision tree models also do not make such assumption. Gaussian distribution is popular and it ...

4

Someone correct me if I'm wrong, but the PCA process itself doesn't assume anything about the distribution of your data. The PCA algorithm is simple - find the direction of greatest variance in your data write down the direction of the vector pointing in that direction, and 'divide' the data along that direction by its variance in that direction, so the ...

4

It makes unit testing easier; invariant to the size of the sample. Reference: the github discussion that led to the change.

4

Why people often choose the input to a GAN (z) to be samples from a Gaussian? Generally, for two reasons: (1) mathematical simplicity, (2) working well enough in practice. However, as we explain, under additional assumptions the choice of Gaussian could be more justified. Compare to uniform distribution. Gaussian distribution is not as simple as uniform ...

4

I still would apply numpy's covaranice function using numpy.apply_along_axis import numpy as np x = np.array([[0, 2], [1, 1], [2, 0]]).T np.apply_along_axis(func1d=np.cov, arr=x, axis=0)

4

I do not think your formulation is correct. What you have described are just conditional distributions for each word in the sentence but not the joint conditional distribution, given a specific class. In your case, we have by Bayes rule: $$Pr(spam | X) \propto Pr(X | spam) \times Pr(spam) = Pr(you, won, lottery, for, 1million | spam) \times Pr(spam).$$ ...

3

Again, the entropy equation coded was this: entropy = K.sum(0.5 * (K.log(2. * np.pi * sigma_sq) + 1.)) which looks different from what's given in the textbook photo above. They are the same after simple algebraic manipulations. The entropy of a single variable Gaussian distribution with pdf $p(x|\mu, \sigma)$ is \begin{align} \mathcal{H}(p) & = ln(\...

3

This sounds entirely reasonable, and the usual name for this structure I have heard for this is just "pipeline" which also applies to other system-feeds-next-system structures - it might also be "machine learning pipeline" or "data processing pipeline". There are ways to assess performance of a ML pipeline: You can of course compare the final accuracy or ...

3

Your intuition about 'no effect' is true in some sense. But this replacement may be not the best use of the information you have. The choice of missing value treatment depends on your initial problem statement. In all the cases I assume that you have already somehow estimated conditional means $\mu_0$ and $\mu_1$ and the common variance matrix $S$. ...

2

A common distance measure between a point and a normal distribution is the number of standard deviations away from the mean. In your case: $$d_0 = |x-μ_0|/σ_0 = 15.4$$ $$d_1 = |x-μ_1|/σ_1 = 15.82$$ See Mahalanobis distance for generalization in multiple dimensions.

2

To cast that column of your data-frame as type float try: k_train = train['cols_to_use'].astype(float) target = train['final_status'].astype(float) More documentation can be found here or you can cast them when loading the csv file sep=',' maybe usful assuming that your data is separated by a , in your CSV file train = pd.read_csv("datasets/train2.csv", ...

2

The Normal distribution is the same as the Gaussian distribution. Its just two names for the same thing. Whatever you do - fit parameters, compute goodness-of-fit, etc - if the documentation says its for a Normal distribution then you can say "Gaussian" instead. Completely and totally identical.

2

You got the Bayes theorem wrong. There should be a plus in the denominator: (child gauss x child prob)/(child gauss x child prob + adult gauss x adult prob) (adult gauss x adult prob)/(child gauss x child prob + adult gauss x adult prob)

2

Actually, the upper alpha and the upper sigma are not free parameters to be set, they are just used to represent the output activations corresponding to the mixture coefficients and the variances, respectively. They are used to distinguish derivatives with respect to the alpha and sigma. I say it from page 275 of the book “pattern recognition and machine ...

2

It is a 49 page long paper, so following observations are based only on a cursory reading. The optimisation is for finding best value of parameters for cost function of machine learning models. Rather than finding a fixed value of the parameters, it is assumed that the parameters come from statistical distribution and the task is to find the nature/shape of ...

2

Multiclass Discriminative Training of i-vector Language Recognition, this article contains update formulas for mean and covariance (diagonal). First you should obtain parameter estimations using ML (so calculate mean and covariance from class data) and then iteratively update them according to formulas (16-20). I'm not sure about the meaning of C0.

2

If you expand the terms, you can see that the quadratic terms cancel out. \begin{align} a &= \ln \frac{P(C_0)}{P(C_1)} + \frac12(x - \mu_1)^T\Sigma^{-1}(x - \mu_1) - \frac12(x-\mu_0)^T\Sigma^{-1}(x-\mu_0)\\ &=\ln \frac{P(C_0)}{P(C_1)} + \frac12\left[x^T\Sigma^{-1}x-2x^T\Sigma^{-1}\mu_1+\mu_1^T\Sigma^{-1}\mu_1\right]\\& - \frac12\left[x^T\Sigma^{-...

2

You need to sort arr. For example you sort df.Age then apply the function and after plotting you will get a beautiful chart. For example, I used your function and a range from 0 to 99 that is already sorted: import numpy as np import math from matplotlib import pyplot as plt arr = np.arange(100) y=gaussian_transform(arr) plt.plot(arr,y) and got the ...

2

Calculation of standard deviation on the fly is possible (turn to our brothers at math.stackexchange): https://math.stackexchange.com/questions/198336/how-to-calculate-standard-deviation-with-streaming-inputs It is easier to keep track of the variance and only take the square root to calculate the stdev when you really need it. And the mean is even easier,...

2

Rstudio does not support Anaconda so you are stuck with the version they provide. Your best option is to install R and RStudio outside Anaconda.

2

No, standardization does not change the shape of the distribution. It centers the distribution by subtracting the mean and scales it by dividing by the standard deviation.

1

The conditional distribution of $Y$ when $X=a$ is bimodal. The mean is in the middle, and reporting it as such is correct (the mean of $1,2,3,91,92,93$ is indeed $47$). This will be reflected somewhat in the variance being extremely wide. If you want to model a full distribution, you could consider quantile regression at many quantiles. I found this article ...

1

That data can be modeled as a statistical process, where the distributions and parameters change as a function of x. This is in contrast to modeling it as a typical statistical distribution which assumes the same distribution and parameters throughout a range. The "a" range could be modeled as a bimodal distribution and the "b" range ...

1

If you left out the large blue and yellow peaks, then maybe. Otherwise, no. With all three distinct peaks, you might call it a multi-modal Guassian - meaning it is a mixture of three standard Gaussian distributions. This illustrates the idea: Important: As pointed out by Spacedman in the comments, this comparison would only strictly apply if the data ...

1

In essence anomaly detection is about finding a metric with which to measure the similarity between instances and then determining a threshold when crossed constitutes an anomaly. There are parametric anomaly detection algorithms which require some hyper-parameters to be set or information about the distribution to be known. There are also non-parametric ...

1

Coupled Hidden Markov Models (CHMMM) assume observed probabilities are Gaussians for the same reason many models make that assumption: Observed variables that are the sums of other variables are often distributed as Gaussians, aka Central limit theorem. Gaussians have a clearly defined functional form. Gaussians are well studied and commonly used in other ...

1

After searching a few, I find this problem is really simple actually in some circumestances. In Gausiann process regression, one can simply refer to Automatic relevance determination (ARD), which is to optimize the hyperparameters in kernels and also the observation noise variance, by maximize the marginal likelihood, using gradient descent! This has been ...

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