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Questions tagged [gaussian]

Gaussian refers to the Gaussian (or Normal) distribution. This is a continuous probability density function and is widely used in statistics.

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Fast way of computing covariance matrix of nonstationary kernel in Python

Suppose I have symmetric positive definite covariance function $k:\mathbb{R}\times\mathbb{R}\rightarrow \mathbb{R}$ that is non-stationary (i.e. $k(x,y) \neq g(|x-y|)$ for any function $g$). Is there ...
Timothy Hedgeworth's user avatar
8 votes
1 answer
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Gaussian Mixture Models as a classifier?

I'm learning the GMM clustering algorithm. I don't understand how it can used as a classifier. Here are my thought: 1) GMM is an unsupervised ML algorithm. At least that's how ...
F.S.'s user avatar
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Deepmind conditional neural process: evaluation

Going through the Deepmind jupyter notebook conditional neural processes, the plots at the bottom of the notebook show that the ground truth and the predicted distribution only overlap around the "...
Shadi's user avatar
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3k views

How to create a complex Gaussian random noise with a specific covariance matrix

I am trying to generate a complex Gaussian white noise, with zero mean and the covariance matrix of them is going to be a specific matrix which is assumed to be given. Assume i to be a point on the ...
gurluk's user avatar
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How to use Adaptive Rejection Sampling to Update Alpha in iGMM

I am wondering how can I use ARS (adaptive rejection sampling) in dirichlet process mixture model (infinite Gaussian mixture model) as described by Rasmussen (https://www.seas.harvard.edu/courses/...
userFarkill's user avatar
-1 votes
1 answer
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Can I call this graph as a gaussian? [closed]

My program is a chatbot. It has rule to represent the state that user is talking to the bot at node level n. I have 1 to 9 nodes in the application. Here is the ...
ii2's user avatar
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1 answer
7k views

Gaussian distribution in python without using libraries

I am implementing Gaussian distribution of a variable, but it gives multiple bell shapes. It should be a single bell shape. Below is my code and plot. ...
Athar Noraiz's user avatar
2 votes
1 answer
280 views

Probabilistic Outlier Detection (edited + clarified)

Measured data $D \in \mathbb{R}^3$, every $d^i \in D$ is $d^i_{(x)}$, where the $x=[x_1, x_2]$. Simply said, the measured data are function of $x$. It is known, the dependency is linear, such as: $$...
Martin G's user avatar
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2 answers
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What are the reasons for drawing initial neural network weights from the Gaussian distribution?

Are there theoretical or empirical reasons for drawing initial weights of a multilayer perceptron from a Gaussian rather than from, say, a Cauchy distribution?
Stephane Bersier's user avatar
4 votes
1 answer
6k views

What mu and sigma vector really mean in VAE?

In standard autoencoder, we encode data to bottleneck, then decode with using initial input as output to compute loss. We do activate matrix multiplication all over the network and if we are good, ...
Stenga's user avatar
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Parameter of Conditional Gaussian Distribution

I'd like to understand how to determine the parameter of conditional gaussian distribution. Following is the network architecture of VUNET which learns the conditional gaussian distribution $q(z|x, \...
Beverlie's user avatar
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Why are observation probabilities modelled as Gaussian distributions in HMM?

HMM is a statistical model with unobserved (i.e. hidden) states used for recognition algorithms (speech, handwriting, gesture, ...). What distinguishes DHMM form CHMM is the transition probability ...
Roberto Pierson's user avatar
1 vote
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Training Gaussian Restricted Boltzmann Machines with Noisy Rectified (nrelu or ssu) linear hidden units

I'm not sure how to implement this architecture. I'm following this thesis (pages 17-19) or this paper but I'm not sure how to train it. I want to use this to extract features from raw audio. I know I ...
Isaac's user avatar
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3 votes
1 answer
118 views

Mixture Density Network: determine the parameters of each Gaussian component

I am reading Bishop's Mixture Density Network paper at: https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/bishop-ncrg-94-004.pdf This is a good paper, but I am still confused about ...
Edamame's user avatar
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Where can we find the application of bayes's theorem in Bayesian optimiation with gaussian processing

I am trying to learn bayesian optimisation by following this tutorial. However, until now I don't get the relation between bayes's theorem to the gaussian process formalism. Any ideas?
ChiPlusPlus's user avatar
1 vote
1 answer
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Understanding GMM-MMI

While studying Gaussian mixture models and the expectation maximization algorithm, I also came across a number of studies that used 'Discriminative training' for the models that addressed some ...
Sairaam Venkatraman's user avatar
1 vote
2 answers
916 views

How to tune bandwidth in machine learning kernel model?

Gaussian kernel $k(x,y) = \exp(-\lVert x-y \rVert^2/\sigma^2)$ has a hyperparameter $\sigma$. I know grid search cross validation, but this would require a lot of computation since computational ...
ArtificiallyIntelligent's user avatar
1 vote
0 answers
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Gaussian Process Regression: does feature normalization affect final log-likelihood of model?

I'm trying to learn a Gaussian Process Regressor in SKLearn. I tried it both with and without feature (and output) normalization, and even though results seem similar-ish, the reported log marginal ...
Ben's user avatar
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2 votes
0 answers
208 views

Wasserstein distance between Gaussian and the empirical distribution

Wasserstein distance between two gaussians has a closed form solution. Does the same hold for the distance between a Gaussian with a fixed variance(say 1) and the empirical data distribution? ...
user3838440's user avatar
1 vote
0 answers
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results from "Google Vizier: A Service for Black-Box Optimization"

In Google Vizier: A Service for Black-Box Optimization it is show what kind of optimizers google uses internally. Figure 6 shows some benchmark results compared to Random Search. Am I right in ...
HennyKo's user avatar
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1 answer
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How do i use the Gaussian function with a Naive Bayes Classifier?

I would like some help with the maths and to check I have understood the algorithm correctly. So I’ve been learning off of a video and I tried my own example. At the end of it I got dodgy results; I ...
Finn Williams's user avatar
8 votes
3 answers
15k views

Why does PCA assume Gaussian Distribution?

From Jon Shlens's A Tutorial on Principal Component Analysis - version 1, page 7, section 4.5, II: The formalism of sufficient statistics captures the notion that the mean and the variance ...
Math J's user avatar
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5 votes
2 answers
6k views

Working with Data which is not Normal/Gaussian

What happens if my data/feature is not normal? Can I still use machine learning algorithms to utilize such data for predictions? I noticed in many data sciences courses, there is always a strong ...
Newbie01's user avatar
-3 votes
1 answer
771 views

Which Normal distribution a point belongs to?

I have estimated normal distributions for two classes (0 and 1). The distributions for the two classes are, \begin{align} X_0 &\sim \mathcal{N}(\mu=549.96,~~ \sigma=549.96) \\ X_1 &\sim \...
Muhammad Adeel Zahid's user avatar
2 votes
1 answer
510 views

Replacing missing value by class conditional mean

I have two classes, $p(x|y=0)$ and $p(x|y=1)$ with ${{\mu }_{0}}$ and ${{\mu }_{1}}$ as mean and shared covariance matrix $\Sigma $. Now, I have a missing feature ${{x}_{n}}$ for a particular ...
KAY_YAK's user avatar
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1 vote
1 answer
2k views

ValueError ill-defined empirical covariance when running a Gaussian Mixture Model

I am getting the following error when running a Gaussian Mixture Model: ...
M. Barbieri's user avatar
1 vote
1 answer
4k views

GausianNB: Could not convert string to float: 'Thu Apr 16 23:58:58 2015'

I'm beginner in python so please bare with me. I'm trying to solve one machine learning problem using GaussianNB. I've certain fields which are not in proper date format, so I converted it into UNIX ...
Rohit Mourya's user avatar
1 vote
1 answer
204 views

Classification followed by regression to handle response variable that is usually zero

I have a data set consisting of a bunch of predictors (mostly unbounded or positive real numbers) and a single response variable that I wish to predict. The response is typically exactly zero -- ...
haroba's user avatar
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1 vote
2 answers
524 views

How are the positions of the output nodes determined in the Kohonen - Self Organizing Maps algorithm?

In the Cooperative stage of Kohonen's SOM, the neighborhood for a winning neuron(output node). In most cases, the neighborhood function happens to be the Gaussian Function. For example, $$h_j,_i = exp(...
Viswanath Hariharan's user avatar
3 votes
1 answer
555 views

Inductive Bias in Gaussian process

All supervised learning techniques have some kind of an inductive bias. What is the inductive bias in Gaussian process models ?
raK1's user avatar
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3 answers
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How to check if a data is in gaussian distribution in R or excel?

I know about the fitdist() function from the fitdistrplus package in R, however, I am not able to use it to predict a gaussian ...
Chandresh Gupta's user avatar
4 votes
3 answers
14k views

Transform a skewed distribution into a Gaussian distribution

I have a skewed distribution that looks like this: How can I transform it to a Gaussian distribution? The values represent ranks, so modifying the values does not cause information loss as long as ...
bkoodaa's user avatar
  • 323
1 vote
1 answer
96 views

EM parameter estimation for conditional Gaussians

Let $$X_1\sim N(\mu_{X_1},\sigma_{X_2}^2)$$ $$X_2\sim N(\mu_{X_2}, \sigma_{X_2}^2)$$ where $\mu_{X_2}=c+aX_1$. Also, I have data $D$ (with missing values on $X_1,X_2$). How can I update/estimate the ...
snowave's user avatar
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3 votes
1 answer
300 views

Gaussian Mixture Models EM algorithm use average log likelihood to test convergence

I was investigating scikit-learn's implementation of the EM algorithm for fitting Gaussian Mixture Models and I was wondering how they did come up with using the average log likelihood instead of the ...
nyro_0's user avatar
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