5

It means that $z$ has a (multivariate) normal distribution with 0 mean and identity covariance matrix. This essentially means each individual element of the vector $z$ has a standard normal distribution.


3

I am using the convention of uppercase $X$ for random variable and lowercase $x$ for an individual observation. It is possible your source material did not do this, which might be causing your confusion. However, it is the convention used in Sutton & Barto's Reinforcement Learning: An Introduction. What I didn't understand what is đť‘‹ here. i.e., what is ...


2

The notation $p(x)$ is widely used in machine learning (e.g. here) and even statistics (e.g. here). People often use $p(x)$ to refer to a probability distribution (either pmf, pdf, or cdf) rather than just $p$. There is also the notation $p_x$ (or things like $p_{x \mid y}$ for conditional p.d.s), which you will find in some statistics books. Of course, if ...


2

From the stanford CNN class (http://cs231n.github.io/neural-networks-2/): Blockquote Initializing the biases. It is possible and common to initialize the biases to be zero, since the asymmetry breaking is provided by the small random numbers in the weights. For ReLU non-linearities, some people like to use small constant value such as 0.01 for all ...


2

Learning is possible without random thoughts and actions. Knowledge can be encapsulated in predetermined forms and passed through predetermined knowledge transfer mechanisms. Much of civilization is based on these predeterminations. Without them, humanity would be thrown back possibly 120,000 years. However, initial discovery requires trials and review of ...


2

The point is even you know the distribution, sometimes you can't prove that the sampled data is i.i.d. or not! (more details in https://stats.stackexchange.com/q/130381/144441). Hence, without knowing the distribution, you have less information, and of course, you can't prove any identically distributedness property of the sampled data. Note that i.i.d. is ...


2

In general term yes. Because what the ML algorithms do in general is to learn the hidden probability density function of the target examples (cats, dogs..). And that is done by learning the conditional probability function between inputs, $X$, and target outputs, $y$, for discriminative models or by learning the joint probability function for generative ...


1

Independent and identically distributed random variables share the same probability distribution and each item doesn’t influence or provide insight about the value of the next item you measure. The most common example is a coin toss: as you flip the coin, one outcome does not influence or predict the next one. As for a dataset of flowers, we assume that the ...


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