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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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### 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 ...
15 views

### Computing confidence score using probability and IoU

I am trying to fuse two detections with the help of a probability model and, to know that both detections belong to the same object, I use the Intersection over Union (IoU) score. So, the confidence-...
22 views

### 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,...
10 views

1 vote
50 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 ...
23 views

### 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. ...
23 views

### 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{$c$} &...
55 views

1 vote
58 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 ...
33 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 ...
40 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 $y \geq k$?
75 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 ...
46 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 ...
1 vote
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 ...
89 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 ...
111 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 ...
512 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 ...
71 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]...
72 views