Questions tagged [vector]

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What is the derivative of a matrix with regard to a vector defined?

I had this question when I read equation (C.20) in Appendix C of "Pattern Recognition and Machine Learning" written by Christopher M. Bishop. Here I copy the equation below for reference: ...
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How should vector notation with multiple indices be interpret?

This is a question about the interpretation of mathematical notation in statistical models. Let's say that this equation represents a panel model: $y_{it} = \alpha + \boldsymbol{\beta}' \mathbf{X}_{it}...
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Update cointegration vector

Hello everyone and thanks in advance for your interest. I have a time series of length T, and I compute the cointegration vector though the Johansen's methods over one section of the series itself, ...
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How do I calculate the variance of a Hermitian form?

Suppose $\mathbf{x}\sim\mathcal{CN}\left(\mathbf{0},\mathbf{I}_n\right)$ is a circular complex Gaussian random vector, and $\mathbf{Q}$ is a Hermitian matrix. How do I calculate the variance of the ...
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Scalar similarity measure between two vectors including both angle and magnitude

I have different models, predicting a vector $\boldsymbol{v}\in\mathbb{R}^3$. Now I would like to compare the performance of these models against a baseline vector $\boldsymbol{b}\in\mathbb{R}^3$, for ...
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Product of elements of a vector which has very large values and very low values ordered in decreasing order (MATLAB)

I have to compute the product of the elements in a vector V. The elements of my vector are in decreasing order and go from very large numbers (eg 5e^5) to very small numbers (e.g 1.8e^-8). I am using ...
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Why can the hyperdimensional plane be discribed as $\textbf{w} \cdot \textbf{x} - b$ for support vector machines

So given the picture and the related definitions from this answer: How does the equation $\textbf{w} \cdot \textbf{x}^{(i)} - b = -1$ hold for several vectors $\textbf{x}^{(i)}$ when $\textbf{w} \...
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How to define distance for vector of angles?

I have a vector of angles and I am looking for a method to compute the distance of my vector with any other vector of angles? I am looking for something similar to Euclidean distance but I know that ...
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Removing duplicate training vectors?

As an extension to this question, for ML problems where it makes sense to remove duplicates (ie: identical data & target variables) from your distribution, in which scenarios would it (if at all) ...
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What is the difference between the dot product and the element-by-element multiplication?

What is the different between the dot product "$\cdot$" and the element-by-element multiplication notation $\odot$ in Statistics? I referred to Hamilton's Time-Series Analysis, and these ...
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rank of an expected value of a matrix

x is (a * 1) vector y is (b * 1) vector x and y are independent then what is rank(E[xy']) I know that xy' should be (a*b) matrix and since they are independent. , however I am not sure about the rank
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Expected value of a product of two dependent random variables

Let me preface this by saying that I'm an engineer, and by no means a mathematician, so please excuse any mathematical "wrong-doing" in my explanation. I have two vectors $V_1$ and $V_2$, ...
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Length of a probability vector?

I'm doing some work on probability vectors, and came across the idea of probability vector length as a measure of how deterministic a probability vector is, as calculated using this equation: The ...
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How do I take the derivative to $\gamma $ of $(y-x^{\gamma})^T(y-x^{\gamma})$?

I have to solve the least squares for $\gamma$ in the following problem. The model is described as $y_i = \beta x_i^{\gamma} + u_i$, where $u_i $ is i.i.d. normal with mean zero and variance $\sigma^2$...
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Matrix and vectors, why different notation for dimensions?

If we collect data and put it into a matrix of size (100,3), we tend to say we have three-dimensional data. We think of each column as a dimension. On the other side, if we have a vector of size (100,...
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What is the entropy of multivariate data multiplied by a vector?

It is a general rule that for multivariate data $\boldsymbol{X}$ and a matrix $\boldsymbol{A}$, their entropy is $$h(\boldsymbol{A} \boldsymbol{X}) = h(\boldsymbol{X}) + \ln |\det \boldsymbol{A}|$$ (...
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what is the expected value of the dot product of two vectors

I have a little question, but I don't know that well how to answer it. I have a random walker with position vector $\vec{r} = \sum_{i=1}^N \vec{r}_i$, where i is the random walker's step. Every vector ...
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Estimation of a vector with a big covariance matrix

I have a Gaussian vector with a known covariance, given by a Covariogram (covariance function). Inverting this matrix (let's say of size 5000x5000 and above) is not reasonable. Is there any known ...
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