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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Is there any difference between input and conditional input incase of neural networks?

In the research paper titled Conditional Generative Adversarial Nets, there is a notion of conditioning a neural network on class label. It has been mentioned in abstract that we need to simply feed ...
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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 later 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 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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Conditional probability between densities in normalizing flows

I've got a question regarding normalizing flows and how to model conditional probabilities involving them. Let' s say: $z_K = f_K(z_0)$ and where $f_K = f_1of_2of_3o...of_k$. I understand that the ...
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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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39 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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Self sufficient material(s) on maximum likelihood estimation

While studying techniques related to word embeddings, I came across an objective function named maximum likelihood. Word embeddings can be estimated using maximum likelihood as an objective function. ...
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Derivation of an probability expansion used in Word2Vec classifier model

We are using the following notations, for this question, to calculate the probability values \begin{array}{|c|c|} \hline \text{$w$} & \text{target word embedding vector} \\ \hline \text{$c$} &...
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Product of probabilities raised to own powers that can be used for entropy calculation

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? What does it signify? $$ N(X) = \...
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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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519 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 ...
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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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How to get the prediction probability of random sample image from multiclass classification model?

I am performing classification using AlexNet as transfer learning(simply say performing classification using CNN) for five types of class on 18000 images. These 18000 images are divided into Train, ...
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1answer
106 views

Can you use machine learning for binary data?

I am totally new to artificial intelligence and neural networks and have a broad question that I hope is appropriate to ask here. I am an ecologist working in animal movement and I want to use AI to ...
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37 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 ...
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29 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....
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41 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, $\...
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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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Bayes error rate formula clarification

My questions concern a particular formulation of the Bayes error rate from Wikipedia, summarized below. For a multiclass classifier, the Bayes error rate may be calculated as follows: $$p = 1 - \...
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51 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}(...
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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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35 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 $y \geq k$?
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74 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 ...
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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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26 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 ...
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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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74 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 ...
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1answer
253 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 ...
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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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64 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 ...
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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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Can anyone explain the pixelwise accuracy metric used in this paper? Also a question to the KL Divergence Loss

So I am making a project based on this paper: https://arxiv.org/ftp/arxiv/papers/1901/1901.07761.pdf In this paper, a U-Net is used to generate optimized mechanical structures. I am trying to ...
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2answers
191 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 ...
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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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1answer
216 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, ...
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48 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 ...
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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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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 ...
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294 views

Why are VAE's useful?

I am not sure I understand what is the advantage of using a VAE's over a deterministic Auto Encoder? For example, assuming we have just 2 labels, a deterministic Auto Encoder will always map a given ...
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209 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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2answers
203 views

How to make machine learning model that reports ambiguity of the input?

Suppose I want to build a neural network regression model that takes one input and return one output. Here's the training data: ...
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How to use SLAM on other sensor other than camera?

I have a sensor that reads electromagnetic field strength from each position. And the field is stable and unique for each position. So the reading is simply a function of the position like this: <...
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How do I combine two electromagnetic readings to predict the position of a sensor?

I have an electromagnetic sensor and electromagnetic field emitter. The sensor will read power from the emitter. I want to predict the position of the sensor using the reading. Let me simplify the ...