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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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How do I determine how likely some data was drawn from a distribution?

I have a sampled data, say, many vectors $m_1, \cdots, m_i \in R^{d}$. I want an objective function that rates the probability of this data being drawn from certain distribution (here, specifically ...
Da1sy petals's user avatar
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0 answers
26 views

Distribution Based Mapping of Augmented (Noisy) Image and Clean image?

I have a task of training a Denoising Autoencoder which will be augmented MNIST dataset and and I have to reproduce the clean image, I have to use the ResBlocks in the Encoder(Conv Layer) as well as ...
Jivitesh's user avatar
1 vote
1 answer
134 views

Trying to understand some derivation in the paper: Deep Unsupervised Learning using Nonequilibrium Thermodynamics

I have recently been learning about diffusion models and trying to derive all the results in the paper by Sohl-Dickstein, et. al, "Deep Unsupervised Learning using Nonequilibrium Thermodynamics&...
ahxmeds's user avatar
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2 votes
2 answers
82 views

If $p(s'|s,a) = 0$, would the reward the reward $r(s,a,s')$ be infinite? [duplicate]

In chapter 2 of Barto and Sutton's RL book, the four argument probability function $p: S \times R \times S \times A \to [0,1]$ is reduced to three arguments $p: S \times S \times A \to [0,1]$ as ...
Jahid Chowdhury Choton's user avatar
2 votes
2 answers
135 views

What is the meaning of log p(x) in VAE math and why is it constant

I was reading the article on medium, where the author cites this equation for Variational Inference: \begin{align*} \text{KL}(q(z|x^{(i)})||p(z|x^{(i)})) &= \int_z q(z|x^{(i)})\text{log}\frac{q(z|...
Kiran Manicka's user avatar
1 vote
1 answer
87 views

How does using the ELBO in VAEs make the problem tractable?

I'm studying Variational Autoencoders and a lot of the literature says that the posterior is intractable because the marginal distribution p(x) is intractable since the space of z is so large we ...
Kiran Manicka's user avatar
0 votes
1 answer
28 views

Independence of random variable in Gaussian Process context

From Bishop's Pattern Recognition and Machine Learning: $t_n = y_n + \epsilon_n$, where $\epsilon_n$ is a random noise variable whose value is chosen independently for each observation $n$. Consider ...
piero's user avatar
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Resulting quantiles from Quantile Regression DQN

In my QR-DQN application, the resulting quantiles for a state s and action a take the form of the blue line in the figure. The ...
Amav's user avatar
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1 vote
3 answers
99 views

What is the difference between q and p in Statistical Notation(used in VAE)?

I'm looking at general visuals of Variational Autoencoders and I'm seeing that the encoder is typically expressed as q(z|x) with phi as a subscript while the decoder is p(x|z) with theta as a ...
Kiran Manicka's user avatar
3 votes
0 answers
320 views

Relation between SDE diffusion and DDPM/DDIM

Background & Definitions In DDPM, the diffusion backward step is described as follows (where $z\sim \mathcal{N}(0,I)$ and $x_{T}\sim \mathcal{N}(0,I)$): and in DDIM we have while in the SDE ...
snatchysquid's user avatar
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Filter distribution of Latent variable models

In this paper https://arxiv.org/pdf/1907.00953.pdf, about stochastic latent variable models, the paper says "We use the reparameterization trick to sample from the filtering distribution". I ...
chadmc's user avatar
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3 votes
1 answer
91 views

How can I make an MNIST digit recognizer that rejects out-of-distribution data?

I've done an MNIST digit recognition neural network. When you put images in that are completely unlike its training data, it still tries to classify them as digits. Sometimes it strongly classifies ...
river's user avatar
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1 vote
0 answers
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How does the skin color follow Gaussian distribution in YCBCR?

I am still new to image processing and machine intelligence. I wanted to make a Python program that can isolate an image of a hand from the background to detect a specific hand gesture, so I came to ...
abdo Salm's user avatar
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Do Neural Networks tend to have Zero Mean Errors in each Output?

My NN (a few linear layers with ReLUs + batch normalization, no activation in the last layer) learns to approximate vector-valued labels $y_z$ from data $z\sim\rho_z$ in a supervised way, i.e. net$(z)=...
joinijo's user avatar
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0 answers
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Calculating Curiosity with Friston's Free Energy in Reinforcement Learning

I'm trying to implement the paper A Curiosity Algorithm for Robots Based on the Free Energy Principle in a reinforcement learning environment using PyTorch, but I am unclear how curiosity is ...
Ted Tinker's user avatar
1 vote
1 answer
116 views

How is the variance for a diffusion kernel derived for a diffusion model?

So I'm watching this video tutorial from CVPR this year on diffusion models, and I am confused by the variance term in the distribution on the left on the video. I understand that in the forward ...
Cynthia Kim's user avatar
1 vote
0 answers
112 views

Why does importance sampling work with latent variable models?

Caveat: importance sampling doesn't actually work for variational auto-encoders, but the question makes sense regardless In "L4 Latent Variable Models (VAE) -- CS294-158-SP20 Deep Unsupervised ...
Foobar's user avatar
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1 answer
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What should be taken as random variables in the distributions of datasets?

Consider the following two paragraphs taken from the paper titles Generative Adversarial Nets by Ian J. Goodfellow et.al #1: Abstract We propose a new framework for estimating generative models via ...
hanugm's user avatar
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0 votes
1 answer
240 views

What is the distribution of autoencoder embeddings?

Is there any result on the distribution of autoencoder embeddings? For example, the following image (taken from this article) visualizes the latent space with t-SNE. As you can see, images from the ...
nalzok's user avatar
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1 answer
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What is the meaning of $p_{\text {data }}(y)$ in the CycleGAN?

In the original CycleGAN paper, on the second page, there is a sentence that I didn't quite understand In theory, this objective can induce an output distribution over $\hat{y}$ that matches the ...
Lukas Pezzei's user avatar
1 vote
1 answer
952 views

PPO: policy loss becomes nan [closed]

I'm implement PPO for a very specific problem, and it seems to be working somewhat, but after a few epochs, I always get something like this: ...
Antonis Karvelas's user avatar
0 votes
0 answers
175 views

Neural network for an output in the form of a probability distribution

I am not an expert in machine learning. Recently, I want to construct a data-driven model based the neural network. The problem is that I want from my algorithm to learn an output in the form of a ...
marouane bouadi's user avatar
0 votes
1 answer
405 views

Are there any scale invariant activation functions that outputs probability distribution?

Softmax activation function is used to convert any random vector into a probability distribution. So, it is generally used as an activation function in the last layer of deep neural networks that are ...
hanugm's user avatar
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0 votes
1 answer
64 views

Why are Directed Graphical Models considered ML methods?

Consider the following problem. The probability of being born in countries [1,2,3,4] is given by [a, b, c, d] respectively. This is a categorical problem. Now, assume that the height of a person ...
user1029384756's user avatar
1 vote
0 answers
14 views

How does the distribution of the parameters change in logistic regression?

I have my own data to train a logistic regression model (for a multi-class classification task), and I want to know how the distribution of weight parameters changes after each update with gradient ...
Seewoo Lee's user avatar
2 votes
3 answers
213 views

Are the authors of the VAE paper writing the PDFs as a function of the random variables?

Usually, I see the conventions: discrete random variable is denoted as $X$, the pmf is written as $P(X=x)$ or $p(X=x)$ or $p_{X}(x)$ or $p(x)$, where $x$ is an instance of $X$ a continuous random ...
a12345's user avatar
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1 vote
1 answer
218 views

What is the analytical formula for "Kaiming He" probability density function?

A probability density function is a real-valued function that roughly gives the density of probability at a particular value of a random variable. For example, the probability density function of a ...
hanugm's user avatar
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4 votes
1 answer
1k views

How does the VAE learn a joint distribution?

I found the following paragraph from An Introduction to Variational Autoencoders sounds relevant, but I am not fully understanding it. A VAE learns stochastic mappings between an observed $\mathbf{x}$...
a12345's user avatar
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0 votes
2 answers
88 views

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 ...
hanugm's user avatar
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2 votes
1 answer
139 views

Which of the following probability distribution is generating an iid dataset?

Let $X_1, X_2$ be two discrete random variables. Each random variable takes two values: $1, 2$ The probability distribution $p_1$ over $X_1, X_2$ is given by $$p_1(X_1=1, X_2 = 1) = \dfrac{1}{4}$$ $$...
hanugm's user avatar
  • 3,850
1 vote
2 answers
408 views

How can we "draw i.i.d" from any probability distribution?

Consider the following paragraph from 2 Learning in High Dimensions in from of the paper titled Geometric Deep Learning Grids, Groups, Graphs, Geodesics, and Gauges ...
hanugm's user avatar
  • 3,850
0 votes
1 answer
163 views

How to calculate policy probability ratio in multiple action space

I try to solve a navigation problem with PPO; my actions space have three-part: robot linear velocity that is in [-3,3] range (getting from a tanh activation func) robot linear angular that is in [-...
m031n's user avatar
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0 votes
2 answers
382 views

Where can I read about the multinoulli distribution?

I encountered the term multinoulli distribution in the following sentence from Chapter 4: Numerical Computation of the deep learning book. The softmax function is often used to predict the ...
hanugm's user avatar
  • 3,850
1 vote
0 answers
45 views

Are there any other metrics available for calculating the distance between two probability distributions other than those mentioned?

The divergence between two probability distributions is used in calculating the difference between the true distribution and generated distribution. These divergence metrics are used in loss functions....
hanugm's user avatar
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1 vote
1 answer
337 views

Is it abuse of notation to use tilde operator in this context?

The following is a way to use tilde (∼) in context of random variables or random vectors. In statistics, the tilde is frequently used to mean "has the distribution (of)," for instance, $X∼N(...
hanugm's user avatar
  • 3,850
1 vote
0 answers
245 views

Which probability distribution a generator in Generative Adversarial Network (GAN) is capturing: dataset or ground truth?

Consider the following statement from the abstract of the paper titled Generative Adversarial Nets We propose a new framework for estimating generative models via an adversarial process, in which we ...
hanugm's user avatar
  • 3,850
1 vote
1 answer
1k views

How to define a continuous action distribution with a specific range for Reinforcement Learning?

Specifically for continuous control PPO, let's say my action space range is between $X$ (low) and $Y$ (high) and they are all sampled from a Gaussian Action Distribution with mean $\mu$ and standard ...
hridayns's user avatar
  • 233
1 vote
0 answers
29 views

Rotationally independent distributions

Maxwell's theorem states that multivariate normal distribution $\mathcal{N}(\mathbf{0}, \sigma^2\mathbf{I})$ is the only distribution of a random vector that is invariant and have independent ...
skypitcher's user avatar
0 votes
0 answers
224 views

Predicting the probability of a periodically happening event occurring at a given time

I have encountered this problem on how to predict the probability of a periodically happening event occurring at a given time. For example, we have an event called being_an_undergrad. There are many ...
Leonard's user avatar
4 votes
1 answer
294 views

Why do we sample vectors from a standard normal distribution for the generator?

I am new to GANs. I noticed that everybody generates a random vector (usually 100 dimensional) from a standard normal distribution $N(0, 1)$. My question is: why? Why don't they sample these vectors ...
dato nefaridze's user avatar
1 vote
1 answer
388 views

Why are CNN binary classifier output probability distributions often skewed?

I've been working on a lot of simple resnet18 binary classifiers lately and I've started to notice that the probability distributions are often skewed one way or the other. This figure shows one such ...
Alexander Soare's user avatar
3 votes
1 answer
325 views

How can a probability density value be used for the likelihood calculation?

Consider our parametric model $p_\theta$ for an underlying probabilistic distribution $p_{data}$. Now, the likelihood of an observation $x$ is generally defined as $L(\theta|x) = p_{\theta}(x)$. The ...
hanugm's user avatar
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2 votes
1 answer
99 views

What is emperical distribution in MLE?

I was reading the book Deep Learning by Ian Goodfellow. I had a doubt in the Maximum likelihood estimation section (Pg 131). I understand till the Eq 5.58 which describes what is being maximized in ...
ANIRUDH BUVANESH's user avatar
8 votes
2 answers
3k views

Why is KL divergence used so often in Machine Learning?

The KL Divergence is quite easy to compute in closed form for simple distributions -such as Gaussians- but has some not-very-nice properties. For example, it is not symmetrical (thus it is not a ...
Federico Taschin's user avatar
3 votes
1 answer
89 views

Is this referring to the true underlying distribution, or the distribution of our sample?

I am currently studying the paper Learning and Evaluating Classifiers under Sample Selection Bias by Bianca Zadrozny. In the introduction, the author says the following: One of the most common ...
The Pointer's user avatar
3 votes
2 answers
1k views

When should one prefer using Total Variational Divergence over KL divergence in RL

In RL, both the KL divergence (DKL) and Total variational divergence (DTV) are used to measure the distance between two policies. I'm most familiar with using DKL as an early stopping metric during ...
mugoh's user avatar
  • 531
1 vote
0 answers
55 views

Estimating $\sigma_i$ according to maximum likelihood method

Let be a Bayesian multivariate normal distribution classifier with distinct covariance matrices for each class and isotropic, i.e. with equal values over the entire diagonal and zero otherwise, $\...
David's user avatar
  • 113
1 vote
1 answer
414 views

How to calculate v min and v max for C51 DQN

Background: In C51 DQNs you must specify a v-min/max to be used during training. The way this is generally done is you take the max score possible for the game and set that to v-max, then v-min is ...
Leon's user avatar
  • 163
1 vote
1 answer
500 views

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 $\mu$ ...
M.S.'s user avatar
  • 11
1 vote
1 answer
60 views

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?
C Lu's user avatar
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