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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22 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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1answer
73 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 $...
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1answer
68 views

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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26 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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1answer
49 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 ...
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28 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 ...
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1answer
26 views

Why error ensemble uses ceiling of number of classifiers?

What is y? Why is k the ceil of n/2? What is ‘y ≥ k’
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1answer
64 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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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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25 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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58 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 ...
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1answer
42 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
85 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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38 views

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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30 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}\...
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1answer
41 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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25 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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35 views

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
63 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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14 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% ...
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2answers
295 views

What is probability distribution in machine learning?

If we were learning or working in machine learning field then we frequently come across this term probability distribution. I know what probability, conditional probability and probability ...
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17 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 ...
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1answer
65 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 ...
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1answer
107 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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45 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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1answer
67 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 ...
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1answer
60 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 ...
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2answers
199 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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1answer
99 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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3answers
330 views

How can I develop a prediction algorithm for a game of chance?

How can I develop a prediction algorithm in the case of games of chance? Suppose there is a 50:50 chance of winning. Is there way of creating a prediction algorithm?
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2answers
41 views

Was Nils Nilsson wrong with probabilistic knowledge representation?

He starts his paper from 1987 [1] with a reference to the PROSPECTOR expert system which was using Bayes rules to handle uncertain knowledge. Then he explains the idea behind probabilistic logic which ...
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2answers
93 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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15 views

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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2answers
62 views

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 ...
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5answers
395 views

Reinforcement Learning (RL) how to obtain $p(s',r|s,a)$

I am trying to study the book Reinforcement Learning: An Introduction (Sutton & Barto, 2018). In chapter 3.1 the authors state the following exercise Exercise 3.5 Give a table analogous to that ...
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1answer
104 views

What are the meanings of these (P(x;y), P(x;y,z),P(x,y;z))?

I was reading a machine learning book that uses probabilities like these: $P(x;y), P(x;y,z), P(x,y;z)$ I couldn't find what they are and how can I read and understand them? Apart from the context, ...
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1answer
42 views

SEIF motion update algorithm doubt

I want to implement Sparse Extended information slam. There is four step to implement it. The algorithm is available in Probabilistic Robotics Book at page 310, Table 12.3. In this algorithm line no:...
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1answer
648 views

How does the Dempster-Shafer theory of evidence differ from the Bayesian reasoning under uncertainty?

Dempster–Shafer theory (wiki) Bayesian probability (wiki) How do these two methods handle uncertainty in regard to information fusion?
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1answer
2k views

Is Nassim Taleb right about AI not being able to accurately predict certain types of distributions?

So Taleb has two heuristics to generally describe data distributions. One is Mediocristan, which basically means things that are on a Gaussian distribution such as height and/or weight of people. The ...
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1answer
55 views

How important will statistical learning be to a conscious AI?

Deep learning is based on getting a large number of samples and essentially making statistical deductions and outputting probabilities. On the other hand we have formal programming languages like ...
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1answer
91 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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1answer
269 views

Reinforcement Learning over an MDP that is actually a POMDP

Look at Breakout: We know that the underlying world behaves like an MDP, because for the evolution of the system it just need to know which is the current state, i.e. position, speed and speed ...
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2answers
293 views

What does the argmax of the expectation of the log likelihood mean?

What does the following equation mean? What does each part of the formula represent or mean? $$\theta^* = \underset {\theta}{\arg \max} \Bbb E_{x \sim p_{data}} \log {p_{model}(x|\theta) }$$
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1answer
196 views

How can I improve this word-prediction AI?

I'm relatively new to AI, and I've tried to create one that "speaks". Here's how it works: 1. Get training data e.g 'Jim ran to the shop to buy candy' 2. The data gets split into overlapping 'chains' ...
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2answers
285 views

Are probabilistic models dead ends in AI?

I am a strong believer of Marvin Minsky's idea about Artificial General Intelligence (AGI) and one of his thoughts was that probabilistic models are dead ends in the field of AGI. I would really ...
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2answers
3k views

What is a Markov chain and how can it be used in creating artificial intelligence?

I believe a Markov chain is a sequence of events where each subsequent event depends probabilistically on the current event. What are examples of the application of a Markov chain and can it be used ...