# All Questions

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### In Hidden Markov Model (HMM), is the transition matrix known, inferred, or assumed?

I'm reading Kevin Murphy's Probabilistic Machine Learning, which explains the forward algorithm to do filtering in HMM as follows (pp 610): The very first line says that the transition matrices ...
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### Linear regression with redundant features (perfect multicolinearity)

Suppose $X \sim N(0,1)$, $Z=X$, and $Y=X$. An ordinary least squares regression problem is solved: $min_{(b1,b2)} \|Y-(b1*X+b_2*Z)\|_{2}^2$ This is a strictly convex function which must have a ...
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### Can someone explain briefly application of PCA for estimating parameters in GMM

I am having some difficulty in seeing connection between PCA of second order moment and parameters of GMM ( mean components) . The claim is mean components are in the span of eigenvectors. Can some ...
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### How to generate decision boundaries for the (3,1) nearest nighbhor classfier

I have two training sets: ...
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### Tukey HSD, insignificant p-value when the confidence interval does not contain 0?

I am using TukeyHSD to do multiple comparisons. I am seeing strange results for some of the pairs: the adjusted p-value is greater than the specified significance level but the corresponding ...
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### Issues plotting a fitted SVM model's decision boundary using ggplot2's stat_contour()

I'm trying to figure out how to plot a decision boundary for a fitted svm model in ggplot2. Right now, I'm attempting to do so by using stat_contour. Here is my code with an example call to my ...
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### Arctangent, Tanh, Concavity.. How can I find the derivatives?

I want to find the first and second derivative (https://www.youtube.com/watch?v=dIE22eL6q90 (Inflection Points and Concavity Intuition video)) of a linear regression like this article shows ...
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### How to use a linear model with two factors and repeated measures?

Suppose I have a date set of the form: ...
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### Number of variables for decision trees

I have a data with just 5 independent variables and a response. I am dealing with a classification problem. Will decision trees perform well or the number of variables have to be higher to get ...
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### Combining pca and classification algorithms

For some classification algorithms, assuming independence of data helps reduce the number of parameters to estimate. Why then not just to apply a method like pca or ica to the original features to get ...
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### define prior probabilities in naive bayes with unbalanced classes and asymetric cost

I'm trying to apply Naive bayes to the following supervised problem: It's a binary classification problem The classes are unbalanced. The target class represents the 0.004266432 of the total and the ...
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### Proving a linear model is not identified

Suppose there is a linear model: $$Y_i=\beta_0+\beta_1X_i+\varepsilon_i$$ How do I formally prove that without further assumptions $\beta_1$ is not identified. I thought to define a new set of ...
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### Portfolio VaR with Copula?

Let the portfolio be given by: $$X=X_1+X_2$$ $(X_1,X_2)$ are dependent through a Copula function $C(u_1,u_2)$, such that the joint distribution is given by: $$F(x_1,x_2)=C(F(x_1),F(x_2))$$ What is ...
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### What distribution is this? Activated process

A particle randomly hops a discrete distance from one position to another. I have measured, for 200 hops, the time between each hop. Here is the histogram: What distribution is this? To look at, ...
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### Does mean = median imply that a unimodal distribution is symmetric?

For a unimodal distribution, if mean = median then is it sufficient to say that distribution is symmetric? Wikipedia says in relationship between mean and median: "If the distribution is ...
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### Similarity datasets

Given two (or maybe more) datasets with the same samples/members, but with different variables. Is there a general way to compare the information available in the two datasets without looking into the ...
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### Machine learning : learn feature value range for a classification

Which domain the problem belongs to? Given a set of products some are classified as cheap and some not. The task is to determine the price range (probablistic) for cheap products ? Supervised ...
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### Sampling from a portion of the normal distribution?

I have a a conditional distribution $p(X_1 | \theta) \propto MVN(\mu, \Omega) \pi(X_1)$ where $X_1=[x_1, x_2, \dots, x_n]'$ and $\pi(X_1)=1$ when all $x_i \in [0,a)$ and $0$ otherwise. Is there any ...
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### Survival Analysis on Telecom Churn in R

I am working on Telecom Churn problem and here is my dataset. http://www.sgi.com/tech/mlc/db/churn.data Names - http://www.sgi.com/tech/mlc/db/churn.names I'm new to survival analysis.Given the ...
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### Unstandardize the slope of standardised variables in a linear regression

If I standardize my dependent and independent variable, and run a linear regression between them, the slope estimate which I have will be standardised. The variables were standardised by subtracting ...
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### SPSS one way ANOVA

I'm using SPSS version 20 in the statistical analysis of my study. It's a case-control study, within the cases there are three polymorphisms (TT, Tt, tt) and their correspondent vitamin D level. I ...
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### How to check $H_0$ hypothesis using Pearson's criteria?

How to check hypothesis by using Pearson's criteria, that $H_0:$ random variable $X$ is normally distributed given that $k=7$ (count of intervals) and $\alpha=0.1$ (significance level). I do ...
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### Likert Scale , SPSS and hypothesis

We made an online research that aimed to see if "have a pet" could influence "good perception about self". 69 participants answered 21 direct questions with this likert points (5.totally agree, ...
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### Forcing a heteroskedastic error in R [on hold]

I'm looking assign a particular value to my error term (making it heteroskedastic) in a regression within R. How would I go about doing this? Thanks for your help.
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### Machine Learning for Text Classification

I am new to Machine Learning.I am working on a project where the machine learning concept need to be applied. Problem Statement: I have large number(say 3000)key words.These need to be classified ...