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17 views

Computing Object Classification with bayesian statistics

Say I want to know if there is a zebra $\theta$, in an image $x$. According to Bayes statistics applies to image recognition, I should be computing: ...
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1answer
133 views

Expression for Sum of Multivariate Gaussian Random Vectors

Consider two multidimensional random vectors $x$ and $z$ having Gaussian distributions $P(x)=N(x\mid\mu_x,\Sigma_x)$ and $P(z)=N(z\mid\mu_z,\Sigma_z)$, respectively, together with their sum $y=x+z$. ...
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1answer
88 views

Dimensionality effect on Fisher's Score

Consider Fisher's Linear Discriminant Analysis (LDA). Let $\mu_0 \in \mathcal{R}^D$ and $\mu_1 \in \mathcal{R}^D$ be means of the two classes. Similarly, let $\Sigma_0 \in \mathcal{R}^{D\times D}$ ...
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1answer
260 views

Stuck with handling of conditional probability in Bishop's “Pattern Recognition and Machine Learning” (1.66)

I've just started working through the book, and I'm stuck with how the author handles conditional probability in (1.66). The context is as follows. In this chapter we are working with a curve ...
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444 views

Math problem in Pattern Recognition and Machine Learning

I had been carefully following Bishop's Pattern Recognition book and came across some of difficulties due to my merely basic math ground.First begin by the Gaussian section on page 80. The ...
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141 views

Theoretical proof of convergence of sequential weight update procedure (Neural Networks and Machine Learning)

My question is at the bottom. (Most of the descriptive words come from Chris. Bishop's Neural Networks for Pattern Recognition) let $w$ be the weight vector of the neural network and $E$ the error ...