Questions tagged [probability]
For question involving probability as related to AI methods. (This tag is for general usage. Feel free to utilize in conjunction with the "math" and more specific probability tags.)
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Can Diffusion Models denoise an unseen probability distribution during inference?
I am trying to understand if it is possible to condition the reverse condition process with a weight tensor. Normally this weight tensor is more restrictive (binary) and could be used for downstream ...
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Showing Axis-Aligned Rectangles With Noise Are PAC-Learnable (FML, Problem 2.6)
I asked the following in Math Stack Exchange and was told "You may be more likely to get an answer on stats.stackexchange.com". I figured this is a more suitable place.
In what follows, an ...
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How does this distribution change in "Understanding Diffusion Models: A Unified Perspective"?
In the paper Understanding Diffusion Models: A Unified Perspective, how did we go from equation $(44)$ to $(45)$? I couldn't find the details in the paper. How does the distribtuion for, the ...
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Same prediction result with little probabilities change
I built a job prediction system leveraging data scrapped from LinkedIn with Random Forest and compared it to XGBoost. XGBoost was used due to its high accuracy after training.
When I made a prediction,...
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How to guess a card in the game of Cambio with limited information?
I need help with a probability problem in the card game of Cambio. In this game, two players are dealt four cards each from a deck of 52 cards . At the start of the game, the bottom cards of each ...
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Trying to understand the definition of environment in this paper on monte carlo approximation of AIXI
Here is the link to the paper https://www.davidsilver.uk/wp-content/uploads/2020/03/mc_aixi_long.pdf
Definition 2. An environment $\rho$ is a sequence of conditional probability functions $\{ \rho_0, \...
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What makes ChatGPT a generative model?
I'm working my way through how ChatGPT works. So I read that ChatGPT is a generative model. When searching for generative models, I found two defintions:
A generative model includes the distribution ...
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Are softmax outputs of classifiers true probabilities?
BACKGROUND: The softmax function is the most common choice for an activation function for the last dense layer of a multiclass neural network classifier. The outputs of the softmax function have ...
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How to classify data into organised groups by using a resulting classification vector and a set of probabilities? [closed]
I am trying to figure out the best way to calculate the probability a sentence belongs to some category.
For simplicity sake, lets assume that the sentence is "yellow fruit".
Next, I use the ...
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Is it possible for PixelCNN to tell us what it generates?
I coded PixelCNN with the help of Keras official website. Also, I read the paper. I can use PixelCNN, similar to a decoder or generator (to generate samples). My question is, "is it possible to ...
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Question for the derivation of the probability of a trajectory
I'm studying reinforcement learning now and I'm quite a newbie to this field.
I have some questions about how to derive the equation as below.
$p_{\theta}(s_{1},a_{1},\dots,s_T,a_T)=p(s_1)\prod_{t=1}^...
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Given A and B, C are independent of each other. Given A, B and C, D and E are independent of each other. What is the minimal number of parameters?
Assuming all variables $A, B, C, D,$ and $E$ are random binary variables. I come up with Bayes net: $D \rightarrow B \rightarrow A \leftarrow C \leftarrow E$ which has the minimal number of parameters ...
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How to convert prediction probabilities of 2D images (initially 3D image) to 3D image predictions?
Classification: binary
Model: CNN (ResNet50V2)
During our research we've had 91x109x91 images (3-dimensional). We've used 2D CNN to train and evaluate our images and make predictions on labelled cases,...
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Use soft-max post-training for a ReLU trained network?
For a project, I've trained multiple networks for multiclass classification all ending with a ReLU activation at the output.
Now the output logits are not probabilities.
Is it valid to get the ...
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Does generator in conditonal GAN obey probability laws?
In probability, we have two types of probability functions: unconditional probability $p(x)$ and conditional probability $p(x | y)$. Both are fundamentally different and the latter can be obtained by ...
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What exactly is a Parzen?
I came across the term "Parzen" while reading the research paper titled Generative Adversarial Nets. It has been used in the research paper in two contexts.
#1: In phrase "Parzen window&...
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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 ...
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How can the probability of two disjoint events be non-zero?
Let $A$ and $B$ be two models for a classification task. Let $x$ be a test set and $M$ be a metric for the classification task. $X$ be a random variable on test sets.
Now,
$M(A,x) = $ Score of model $...
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How would the probability of a document $P(d)$ be computed in the Naive Bayes classifier?
In naive Bayes classification, we estimate the class of a document as follows
$$\hat{c} = \arg \max_{c \in C} P(c \mid d) = \arg \max_{c \in C} \dfrac{ P(d \mid c)P(c) }{P(d)} $$
It has been said in ...
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What does the product of probabilities raised to own powers used for entropy calculation quantify?
Suppose $X$ is a random variable taking $k$ values.
$$Val(X) = \{x_1, x_2, x_3, \cdots, x_k\} $$
Then what is the following expression of $N(X)$ called in literature if exists? What does it signify?
$$...
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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 ...
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How do I calculate the probabilities of the BERT model prediction logits?
I might be getting this completely wrong, but please let me first try to explain what I need, and then what's wrong.
I have a classification task. The training data has 50 different labels. The ...
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PPO2: Intuition behind Gumbel Softmax and Exploration?
I'm trying to understand the logic behind the magic of using the gumbel distribution for action sampling inside the PPO2 algorithm.
This code snippet implements the action sampling, taken from here:
<...
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Aren't scores in the Wasserstein GAN probabilities?
I am quite new to GAN and I am reading about WGAN vs DCGAN.
Relating to the Wasserstein GAN (WGAN), I read here
Instead of using a discriminator to classify or predict the probability of generated ...
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In RL as probabilistic inference, why do we take a probability to be $\exp(r(s_t, a_t))$?
In section 2 the paper Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review the author is discussing formulating the RL problem as a probabilistic graphical model. They ...
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How to calculate probability from fuzzy membership grade?
Suppose we have the fuzzy membership grade for a person $x$ with a set $S = \text{set of tall people}$ be $0.9$, i.e. $\mu_S(x)=0.9$.
Does this mean that the probability of person $x$ being tall is $0....
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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, $\...
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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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How does $\mathbb{E}$ suddenly change to $\mathbb{E}_{\pi'}$ in this equation?
In Sutton-Barto's book on page 63 (81 of the pdf):
$$\mathbb{E}[R_{t+1} + \gamma v_\pi(S_{t+1}) \mid S_t=s,A_t=\pi'(s)] = \mathbb{E}_{\pi'}[R_{t+1} + \gamma v_\pi(S_{t+1}) \mid S_{t} = s]$$
How does $...
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Importance sampling eq. 5 in paper "Residual Energy-based Models for Text Generation"
In the paper "Residual Energy-Based Models for Text Generation" (arXiv), on page 5, they write that equation 5 is an instance of importance sampling.
Equation 5 is:
$$ P(x_t \mid x_{<t}) = P_{LM}(...
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Why is probability that at least one hypothesis out of $k$ being consistent with $m$ training examples $k(1- \epsilon)^m$?
My question is actually related to the addition of probabilities. I am reading on computational learning theory from Tom Mitchell's machine learning book.
In chapter 7, when proving the upper bound ...
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What is the most efficient data type to store probabilities?
In ML we often have to store a huge amount of values ranging from 0 to 1, mostly being probabilities. The most common data structure to do so seems to be a floating point? Indeed, the range of ...
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Why does the error ensemble use the ceiling of the number of classifiers?
What is $y$? Why is $k$ the ceil of $n/2$? What is $y \geq k$?
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What are the prerequisites to start using the TensorFlow Probability library? [closed]
I have some familiarity with the regular Tensorflow library and have been able to create a number of working models with it. There are more than enough resources out there to get up and running and ...
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Expected duration in a state
I am going through Rabiner 1989 and he writes that the discrete probability density function of duration $d$ in state $i$ (that is, staying in a state for duration $d$, conditioned on starting in that ...
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Neural network seems to just figure out the probability of a specific result
I am really new to neural networks, so i was following along with a video series, created by '3blue1brown' on youtube. I created an implementation of the network he explained in c++. I am attempting ...
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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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Predicting probabilities of events using neural networks
I've got a few thousands of sequences like
1.23, 2.15. 3.19, 4.30, 5.24, 6.22
where the numbers denote times on which an event happened (there's just a single ...
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How can supervised learning be viewed as a conditional probability of the labels given the inputs?
In the literature and textbooks, one often sees supervised learning expressed as a conditional probability, e.g.,
$$\rho(\vec{y}|\vec{x},\vec{\theta})$$
where $\vec{\theta}$ denotes a learned set of ...
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How to Prove This Inequality, Related to Generalization Error (Not Using Rademacher Complexity)?
This is an inequality on page 36 of the Foundations of Machine Learning by Mohri, but the author only states it without proof.
$$
\mathbb{P}\left[\left|R(h)-\widehat{R}_{S}(h)\right|>\epsilon\right]...
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Convert a PAC-learning algorithm into another one which requires no knowledge of the parameter
This is part of the exercise 2.13 in the book Foundations of Machine Learning (page 28). You can refer to chapter 2 for the notations.
Consider a family of concept classes $\left\{\mathcal{C}_{s}\...
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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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What are some approaches to estimate the transition and observation probabilities in POMDP?
What are some common approaches to estimate the transition or observation probabilities, when the probabilities are not exactly known?
When realizing a POMDP model, the state model needs additional ...
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How can I convert the probability score between 0 to 1 to another format?
I have trained a multi-class CNN model using fastai. The model splits out probabilites for each of the three classes, which, of course, sum up to 1. The class with highest probability becomes the ...
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Is there an algorithm for "contextual recognition" with probabilities?
Example 1
An object is composed of 3 sub-objects.
Object 1: 90% looks like an eye 10% looks like a wheel
Object 2: 50% looks like an eye 50% looks like a wheel
Object 3: 90% looks like a mouth 10% ...
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Probabilistic classification - normalize results
I have a probabilistic classifier that produces a distribution over my 3 classes - C1, C2, C3.
I want to compare some new points I'm classifying to each other, to see which one is the best fit for a ...
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Why is the entire area of a join probability distribution considered when it comes to calculating misclassification?
In the image given below, I do not understand a few things
1) Why is an entire area colored to signify misclassification? For the given decision boundary, only the points between $x_0$ and the ...
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What to do when PDFs are not Gaussian/Normal in Naive Bayes Classifier
While analyzing the data for a given problem set, I came across a few distributions which are not Gaussian in nature. They are not even uniform or Gamma distributions(so that I can write a function, ...
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Unique game problem (ML, DP, PP etc)
Looking for a solution to my below game problem. I believe it to require some sort of reinforcement learning, dynamic programming, or probabilistic programming solution, but am unsure... This is my ...
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Is there an AI model with "certainty" built in?
If I see a hundred elephants and fifty of them are grey I'd say the probability of an elephant being grey is 50%. And my certainty of that probability is high.
However, if I see two elephants and one ...
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