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.)

21 questions with no upvoted or accepted answers
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How can we prove this inequality, related to the generalization error, without using the Rademacher complexity?

This is an inequality on page 36 of the book Foundations of Machine Learning, 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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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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38 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 ...
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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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1answer
52 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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34 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 ...
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1answer
149 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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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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1answer
99 views

Why do I get small probabilities when implementing a multinomial naive Bayes text classification model?

When applying multinomial Naive Bayes text classification, I get very small probabilities (around $10e^{-48}$), so there's no way for me to know which classes are valid predictions and which ones are ...
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39 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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27 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 ...
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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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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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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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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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47 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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15 views

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
33 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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1answer
54 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 ...