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Questions tagged [gaussian]

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19 views

Gradient equations of gaussian kernel discriminant trained with gradiant descent

I am having a hard time trying to find the gradient equations for the weight $\alpha^t$ and $w_0$ for a gaussian kernel discriminant trained with gradient descent with the following error function $$E(...
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1answer
25 views

What is a latent space vector?

I do not understand this about GANs. Apparently the Generator is supposed to receive a latent space vector as its input. Yet I couldn't find an example of how I can implement it in Pytorch. This is a ...
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13 views

Co-joining multi-peak histograms

I am analysing a bunch of data files which represent responsiveness of cells to addition of a drug. If a drug is not added, cell responds normally, if it is added, it shows abnormal patterns: , . We ...
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1answer
25 views

What is a “variable index” in the Gaussian perspective?

I was going through this article about Gaussian processes, in which the author explains about the "variable index" in the form of a plot while writing about 2D Gaussian. The explanation and plot are ...
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0answers
15 views

Normalization of Distribution of numeric features and target

Here, I am talking about the Normalization of Distribution of Features/Target, not normalization/scaling of them. I've been seeing Notebooks which normalize some features and the target variable, ...
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0answers
19 views

Is it possible to train probabilistic model to return several distributions?

I have nonlinear data of function y(x), which is let's say parabolic. At some points of x there are several y's (look at the picture). Is it possible to train a probabilistic model to return several ...
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0answers
19 views

How can detect and highlight outliers by using gaussian function and normalize the data elegantly?

I tried to normalize the data by using Gaussian function 2 times on both positive and negative numbers of each parameter of this dataset. The dataset includes missing data as well. The problem is I ...
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9 views

Which distribution should I use for Naive Bayes algorithm(Gaussian or Rayleigh)? What to do with categorical data?

I am predicting whether credit card application of an individual would be approved or not given his/her credentials. I have the following dataset: The variable descriptions are as follows: I need ...
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1answer
108 views

A2C Continuous for Pendulum-v0 working implementation, negation for loss and entropy calculation

very good implementation of A2C continuous for Pendulum-v0 Code has snippet to stop execution when mean of last 10 or 20 is higher than -20 but the results look like: ...
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1answer
142 views

Prove GDA decision boundary is linear

My attempt: (a) I solved that $a=\ln{\frac{P(X|C_0)P(C_0)}{P(X|C_1)P(C_1)}}$ (b) Here is where I'm running into trouble. I'm plugging the distributions into $\ln{\frac{P(X|C_0)P(C_0)}{P(X|C_1)P(C_1)...
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20 views

How is the standard deviation of VAE's obtained?

I am trying to build a Variational Autoencoder. I was looking at various codes online and found most of them in some way or another copy Francois Chollet (Google researchers) code. Now my main ...
7
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1answer
747 views

Why Gaussian latent variable (noise) for GAN?

When I was reading about GAN, the thing I don't understand is why people often choose the input to a GAN (z) to be samples from a Gaussian? - and then are there also potential problems associated with ...
2
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1answer
449 views

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 ...
5
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1answer
584 views

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 ...
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0answers
74 views

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 "...
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0answers
38 views

When using the sklearn.gaussian_process module, how can I choose a non-zero mean function of Gaussian Process?

When using sklearn.gaussian_process module, only the parameter normalize_y is related to the mean process. So, my question is how to set the form of the mean function using this module?
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59 views

How to set the mean function's form of Gaussian Process using sklearn module in Python?

I want to compare the difference of prediction error between linear mean process and the polynomial mean function using the sklearn.gaussian_process.GaussianProcessRegressor. However, only the ...
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0answers
199 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 ...
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0answers
20 views

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/...
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1answer
51 views

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 ...
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1answer
45 views

Limits of using a normal distribution in Bayesian inference

When applying a Bayesian inference method such as Gaussian Process Regression (GPR), the assumption of a prior and likelihood function following a normal distribution is inherent. One can use an ...
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1answer
3k 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. ...
2
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1answer
148 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: $$...
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0answers
26 views

What are the reasons for drawing initial neural network weights from a Gaussian?

Are there theoretical or empirical reasons for drawing initial weights of a multilayer perceptron from a Gaussian rather than from, say, a Cauchy distribution?
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1answer
880 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, ...
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0answers
19 views

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, \...
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0answers
49 views

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 ...
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0answers
25 views

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 ...
3
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1answer
64 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 ...
2
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1answer
39 views

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?
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1answer
128 views

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 ...
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2answers
202 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 ...
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0answers
115 views

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 ...
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0answers
159 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? ...
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0answers
74 views

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 ...
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1answer
132 views

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 ...
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2answers
3k 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 ...
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2answers
2k 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 ...
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1answer
118 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 \...
2
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1answer
278 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 ...
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0answers
545 views

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

I am getting the following error when running a Gaussian Mixture Model: ...
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1answer
1k 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 ...
1
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1answer
104 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 -- ...
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2answers
249 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(...
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1answer
255 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 ?
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3answers
729 views

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 ...
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2answers
8k 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 ...
1
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1answer
90 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 ...
3
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1answer
246 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 ...