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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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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 ...
Harry's user avatar
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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 ...
Ali Qaqan's user avatar
1 vote
0 answers
33 views

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, \...
TomT800's user avatar
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2 votes
2 answers
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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 ...
Ai4l2s's user avatar
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18 votes
2 answers
3k views

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 ...
Snehal Patel's user avatar
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1 answer
38 views

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 ...
Damir Olejar's user avatar
1 vote
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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 ...
Pouyan's user avatar
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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}^...
Feel's user avatar
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1 answer
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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 ...
BOB's user avatar
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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,...
Amadej Šenk's user avatar
1 vote
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106 views

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 ...
user452306's user avatar
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1 answer
96 views

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 ...
hanugm's user avatar
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1 answer
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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&...
hanugm's user avatar
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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 ...
hanugm's user avatar
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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 $...
hanugm's user avatar
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2 votes
1 answer
155 views

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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1 answer
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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? $$...
hanugm's user avatar
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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 ...
Leonard's user avatar
2 votes
1 answer
9k views

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 ...
iso_9001_'s user avatar
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2 votes
0 answers
251 views

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: <...
Micha Christ's user avatar
2 votes
1 answer
317 views

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 ...
Stefano Barone's user avatar
1 vote
1 answer
145 views

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 ...
David's user avatar
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1 answer
158 views

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....
Hadi GhahremanNezhad's user avatar
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
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2 votes
0 answers
173 views

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 ...
Marc's user avatar
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3 votes
1 answer
104 views

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 $...
ZERO NULLS's user avatar
1 vote
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64 views

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}(...
rubencart's user avatar
1 vote
1 answer
83 views

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 ...
calveeen's user avatar
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2 votes
0 answers
92 views

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 ...
Ray Walker's user avatar
0 votes
1 answer
55 views

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 $y \geq k$?
Mr-Programs's user avatar
0 votes
1 answer
79 views

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 ...
SuperCodeBrah's user avatar
2 votes
0 answers
52 views

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 ...
jstycrpsc's user avatar
1 vote
0 answers
30 views

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 ...
finlay morrison's user avatar
2 votes
0 answers
133 views

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 ...
Prashant Govindarajan's user avatar
1 vote
4 answers
454 views

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 ...
maaartinus's user avatar
3 votes
2 answers
2k views

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 ...
Jammy's user avatar
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2 votes
0 answers
80 views

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]...
j200932's user avatar
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2 votes
0 answers
221 views

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}\...
j200932's user avatar
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1 vote
1 answer
131 views

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 ...
JohnDoe122's user avatar
2 votes
0 answers
100 views

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 ...
MScott's user avatar
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1 vote
2 answers
389 views

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 ...
user1631306's user avatar
1 vote
0 answers
16 views

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% ...
zooby's user avatar
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1 vote
0 answers
28 views

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 ...
Amir Graitzer's user avatar
1 vote
1 answer
118 views

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 ...
sage76's user avatar
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2 votes
1 answer
432 views

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, ...
Soumee's user avatar
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1 vote
0 answers
60 views

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 ...
Michael Ramos's user avatar
1 vote
1 answer
103 views

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 ...
zooby's user avatar
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3 votes
1 answer
180 views

Viterbi versus filtering

In Chapter 15 of Russel and Norvig's Artificial Intelligence -- A Modern Approach (Third Edition), they describe three basic tasks in temporal inference: Filtering, Likelihood, and Finding the ...
vdbuss's user avatar
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1 vote
1 answer
595 views

The problem with the Gambler's Problem in RL

Recently I simulated the Gambler's Problem in RL: Now, the problem is, the curve does not at all appear the way as given in the book. The "best policy" curve appears a lot more undulating than it is ...
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