# Questions tagged [probability-distribution]

For questions related to AI theory that relies on the knowledge of a distribution of probabilities across one or more dimensions affecting probability. Such a distribution may be in discrete buckets, such as quartile, octile, or percentile conventions or continuous functions based on some closed form (algebraic formula). Distributions of probability are key in planning, natural language handling, and other AI objectives.

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### Is knowing underlying probability distribution mandatory for deciding iid property of random variables?

Consider the following information regarding iid random variables The acronym IID stands for "Independent and Identically Distributed". A sequence of random variables (or random vectors) is ...
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### Are there any deep learning tools so that can be used to estimate long-tail distributions?

Are there any deep learning tools so that can be used to estimate long-tail distributions? update: my context is there are is there is a long-tail distribution (probability distribution) in my data of ...
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### In continuous action spaces, how is the standard deviation, associated with Gaussian distribution from which actions are sampled, represented?

I have a question about implementing policy gradient methods for problems with continuous action spaces. Assume that actions are sampled from a diagonal Gaussian distribution with mean vector $\mu$ ...
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### Intuitively, why can the training of a neural network be formulated as a probability estimation problem?

Neural network training problems are oftentimes formulated as probability estimation problems (such as autoregressive models). How does one intuitively understand this idea?
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### Is the generator distribution in GAN's continuous or discrete?

I have some trouble with the probability densities described in the original paper. My question is based on Goodfellow's paper and tutorial, respectively: Generative Adversarial Networks and NIPS ...
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### Why do we regularize the variational autoencoder with a normal distribution?

When we define the loss function of a variational autoencoder (VAE), we add the Kullback-Leibler divergence between the sample taken according to a normal distribution of parameters:  N(\mu,\sigma)...
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### Generalization error: Inputs drawn from distributions

I am currently studying Deep Learning by Goodfellow, Bengio, and Courville. In chapter 5.2 Capacity, Overfitting and Underfitting, the authors say the following: Typically, when training a machine ...
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### Solving the supervised learning problem of learning $p(y \vert \mathbf{x})$ by using traditional unsupervised technologies to learn $p(\mathbf{x}, y)$

I am currently studying Deep Learning by Goodfellow, Bengio, and Courville. In chapter 5.1.2 The Performance Measure, $P$, the authors say the following: Unsupervised learning and supervised learning ...
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### Many of the best probabilistic models represent probability distributions only implicitly

I am currently studying Deep Learning by Goodfellow, Bengio, and Courville. In chapter 5.1.2 The Performance Measure, P, the authors say the following: The choice of performance measure may seem ...
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### Why does the machine learning algorithm need to learn a set of functions in the case of missing data?

I am currently studying the textbook Deep Learning by Goodfellow, Bengio, and Courville. Chapter 5.1 Learning Algorithms says the following: Classification with missing inputs: Classification ...
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### Formulation of a Markov Decision Process Problem

Given a list of $N$ questions. If question $i$ is answered correctly (given probability $p_i$), we receive reward $R_i$; if not the quiz terminates. Find the optimal order of questions to maximize ...
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### Why we multiply probabilities with support to obtain Q-values in Distributional C51 algorithm?

In 'Deep Reinforcement Learning Hands-On' book and chapter about Distributional C51 algorithm I'm reading, that to obtain Q-values from the distribution I need to calculate the weighted sum of the ...
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### Why am I getting the logarithm of the probability bigger than zero when using Neural Spline Flows?

I am using a normalizing flow (Neural Spline Flows) to approximate a probability. After some training, the average loss is around 0.5 (so the logarithm of the probability = -0.5). However, when I am ...
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### Deciding std. deviation for policy network output?

When I try to fit a Normal Distribution to the output of a policy network, for a continuous action space problem, what should be its standard deviation? mean for the distribution will directly be the ...
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### What is a probability distribution in machine learning?

If we were learning or working in the machine learning field, then we frequently come across the term "probability distribution". I know what probability, conditional probability, and ...
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### How does maximum approximation of the posterior choose a distribution?

I was learning about the maximum a posteriori probability (MAP) estimation for machine learning and I found a nice short video that essentially explained it as finding a distribution and tweaking the ...
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### Why is Jensen-Shannon divergence preferred over Kullback-Leibler divergence in measuring the performance of a generative network?

I have read articles on how Jensen-Shannon divergence is preferred over Kullback-Leibler in measuring how good a distribution mapping is learned in a generative network because of the fact that JS-...