Questions tagged [naive-bayes]

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Find conjugate and posterior distributions where data is from Normal distribution

The data $X$ is from $N(0, \cfrac{1}{\theta})$ distribution where $\theta$ is the model parameter. Find $\theta$'s bayesian conjugate prior distribution and the appropriate posterior distribution. ...
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Likelihood calculation for Naive Bayes classifier

I am reading the Generative models for discrete data chapter in Kevin P Murphy's book(Machine Learning: A Probabilistic Perspective) Here for calculating the MLE of naive Bayes (pg no: 83) the ...
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Bayes' Theorem in Naive Bayes Classifier

Bayes' Theorem states that: $ P\left(y \mid x_1, \cdots, x_n\right)=\frac{P\left(x_1, \cdots, x_n \mid y\right) \cdot P(y)}{P\left(x_1, \cdots, x_n\right)} $ In Naive Bayes Classifier we can say the ...
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Prove $P(B|A) = P(B)$, if $A$ and $B$ are independent [closed]

How can I show that $P(B|A) = P(B)$, given that $A$ and $B$ are independent?
Shubhang Gupta's user avatar
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Negative Log likelihood and Derivative of Gaussian Naive Bayes

I am trying to derive negative log likelihood of Gaussian Naive Bayes classifier and the derivatives of the parameters. So there are class labels $y \in {1, ..., k}$, and real valued vector of $d$ ...
DHH's user avatar
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Solving Bayes' Theorem

I am provided $P(A|B) = 0.980$, $P(B) = 0.0005$, $P(A'|B') = 0.987$ and I calculated $P(B') = 0.9995$. I am asked to calculate the overall probability of $P(A)$. I tried to solve it by rearranging the ...
John's user avatar
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In naive Bayesian classification, what happens if the likelihood ratio is 1?

This is a question on my assignment, I have arrived at an answer but I'm starting to second-guess myself. The grammar in the question is a bit wonky, so I'll type out the question and my ...
requiemman's user avatar
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What is the model parameters in Naive Bayes?

I just lead the Naive Bayes learning, the form is $$ P(y, x_1, \dotsc, x_n) = p(y) \prod_{i=1}^n p(x_i \mid y). $$ In this lecture, it says Each factor $ p(x_i \mid y) $ can be completely described by ...
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How to compute the probability using Naive Bayes assumption?

I am struggling a bit with this question (and it's on a practice test -- not an actual test). ...
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Independent and Identically distributed, conditional independent and Naive bayes

I'm reading about Naive Bayes classification concept, noting that we make the conditionally independence assumption. But isn't this the general assumption that is always made dealing with machine ...
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Show that if $\Sigma_0 = \Sigma_1$ this classifier is linear?

I have $Y \in \{ 0;1 \} $ $$ P(Y=1 \mid X = x)= \frac{1}{ \left[ 1 + \frac{\det(\Sigma_0)}{\det(\Sigma_1)} \cdot e^{-\frac{1}{2} \left[ (x-\mu_1)^T\Sigma^{-1}_1(x-\mu_1) - (x-\mu_0)^T \Sigma^{-...
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2 answers
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Plot the decision boundary for Bayes

Let $X=(X_1,X_2) \in [0,1]×[0,1]$ and $Y \sim Bernoulli(p=X_1⋅X_2)$. The Bayes decision boundary $\{(x_1,x_2):P(Y=1|X=(x_1,x_2))=0.5\}$ in the regions $[0,1]×[0,1]$ whose points would be classified as ...
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Naive Bayes Classifier - With Lagrange Variable- Derivation

I am running through this link to understand better the derivation for MLE for Naive Bayes: https://mattshomepage.com/articles/2016/Jun/26/multinomial_nb/ In particular, i am confused as to this part: ...
Alex Walton's user avatar
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Independence and Conditional Probability Confusion

I am trying to understand the derrivations associated with the Naive Bayes assumption. One document I read starts off by stating this: \begin{align} P(x | C_k) &= P(x_1, x_2, \dots , x_D |C_k) ...
Universal Thinker's user avatar
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How to compute co-occurence probability from a co-occurence matrix?

I have a co-occurence matrix in this format: ...
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What is the “learning” step in Gaussian Naive Bayes classification?

For conditionally independent features $f_i$, Naive Bayes Classification gives me the classifier $Classifier(f) := \arg \max_{k} P(C=k) · ∏^n_{i=1} P(f_i|C=k)$ for classes $k$. I understand that ...
MJimitater's user avatar
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How can I read the multinominal naive bayers in simple english?

I trying to studying about text classifier but I have some problems to understand the math representations of scikit.learn implementation: How can I describe this using simple english?
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Regression or naïve Bayes for irregular matrix?

I am writing an application to predict exam scores given at least one tuple, where the tuple represents the results of a practice exam: ...
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Compute the posterior probability in a Naive Bayes classifier

Consider a binary classification with one binary output $y$ and two binary features $x_1$ and $x_2$. The Naive Bayes classifier assumes the following distribution for a pair: $$ p(y,x_1, x_2) = p(x_1|...
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Bayesian Statistics: how do I calculate this probability?

Given a research with the following results: Favorite vegetable is spinach for 30% of the participants, and carrots for 70% of the participants. 40% of the participants play the drums, 50% play the ...
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Naive Bayes classifier question [closed]

A spam filtering system has a probability of 0.95 to classify correctly a mail as spam and 0.10 probability of giving false positives. It is estimated that 0.5 % of mails are actually spam. Suppose ...
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In-depth explanation of the multinomial Bayes classifier

I am new to machine learning and am trying to understand the different classifiers. I have searched the internet and books for a comprehensive explanation of the Multinomial Bayes classifier, but I ...
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In Naive Bayes classifier how is P(sneezing,builder|flu) = P(sneezing|flu)P(builder|flu)?

Please refer to this literature: According to Naive Bayes classification algorithm: $P(sneezing,builder|flu) = P(sneezing|flu)P(builder|flu) $ where sneezing and builder are independent events. ...
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Derivation of the formula for the probability of a class, given conditionally independent attributes.

The following is a formula that finds the posterior probability of a class (i.e. yes or no) given four conditionally independent attributes: $$P(c|X) = P(x_1|c)\cdot P(x_2|c)\cdot P(x_3|c)\cdot P(x_4|...
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Relationship between Naive Bayes and MLE

I have found various references describing Naive Bayes and they all demonstrated that it used MLE for the calculation. However, this is my understanding: $P(y=c|x)$ $\propto$ $P(x|y=c)P(y=c)$ with $...
Shrike Danny's user avatar
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Agreeing to disagree "simple" example

I'm looking at Aumann's work "Agreeing to Disagree", and trying to understand the very first numerical example. So, the paper starts with definitions [L]et $(\Omega, \mathcal{B}, p)$ be a ...
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Arriving at Maximum Likelihood Estimates

I am trying to develop a text classifier and I'm reading about MLE to help me understand the process. I came across this example: and I wanted to try this myself. I'm running into a problem and so ...
Ayumu Kasugano's user avatar
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Why does $P(A,B | C) = P(A|C) \cdot P(B|C)$

I'm in an NLP course learning about naive bayes statistics. We briefly went over joint and conditional probabilities. Why does $P(A,B | C) = P(A|C)\cdot P(B|C)$
maddie's user avatar
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Bayes' theorem on continuous interval

I'm reading up on naive Bayes' classifiers, and it's just an application of Bayes' theorem. Which makes sense in a discrete space; example: counting the number of apples versus oranges, and predicting ...
Mohammad Athar's user avatar
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1 answer
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Combining two probablities based on context

I have written an object detection algorithm which can localize different classes on a given image. For each class, the output is given as a list of bounding boxes around each detected class along ...
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Naive Bayes Algorithm with floating weights or zero weights

What happens on those cases on Naive Bayes Algorithm : 1.one of the weights are zero ? 2.one of the weights are float? I am asking because i am trying to use Naive Bayes to develop small ...
jsor's user avatar
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Probability for text classification

I have a list of sentences and each sentence is classified with a number of emotions ex: I loved the movie Happiness $= 1$ Disappointment $= 0$ I hated the move Happiness $= 0$ Disappointment $= 1$ ...
user42967's user avatar
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What is p(biased coin given heads) in 2 Fair coin, 1 biased coin experiment

In "Conditional probability with Bayes" theorem in Khan's academy, in 2nd experiment, where author has 2 fair coins, and 1 biased coin, he tries to calculate probability of biased coin, after first ...
Parthiban Rajendran's user avatar
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Is my derivation for the maximum likelihood estimation for naive bayes correct?

I think I have I gotten the wrong formula for the following derivation, but I don't know where. here is my explanation: For a task on sentiment analysis, suppose we have some classes represented by $...
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Bayes theorem usage for Ham/Spam detection

I am trying to understand the probability calculations using Bayes theorem for a ham/spam classification problem (that uses Naive Bayes). I have a training set of ham and spam data with appropriate ...
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How can I predict Naive Bayes data(spam or ham)?

For example, I have Naive Bayes data like data : probability Fastest : 1 digit : 0 Find : 0.643234 Forum : 0.562904 Free : 0.857344 I might say if there is a word "data" in a certain ...
Tot's user avatar
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Naive Bayes classifier big O complexity

I am trying to learn about The Naive Bayes Classifier as defined by the following: where $\textbf{x} \in \{1, ... , K\}^{D}$ $K$ is the number of different values a feature can have $D$ is the ...
Josh's user avatar
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4 votes
1 answer
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Bayes classification with a simple example of mail classification

Every mail is described by a bag of words: $x = (x_1, . . . , x_l)$, where $x_i \in \{0, 1\}$ indicates whether the $i$th word is present or not. We have $n$ training samples ${(x^1,y^1),....(x^n,y^n)}...
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1 answer
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Naive Bayes problem applied to text

Assume that you are using a Naïve Bayes classifier to classify some documents into two classes, Sports and Health docs. Assume that there are only $5$ words used in your model. Let us denote these 5 ...
Harsh's user avatar
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1 answer
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Naive Bayes Classification Example

Given the following data: $$\begin{array}{c|c|c|c|c|} \text{Instance} & \text{A} & \text{B} &\text{C} &\text{Class} \\ \hline \text{1} & 1 & 2 & 1 & 1 \\ \hline \text{...
Sophie Filer's user avatar
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How is the right term derived in this conditional probability statement?

Does anyone know how to get the right term? It seems like the right term is actually $P(C, x_1, x_2, \ldots, x_n)$ and not $P(C \mid x_1, x_2, \ldots, x_n)$?
jlcv's user avatar
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3 votes
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How can the following $\arg \max$ function be reduce?

Let $\theta \sim \mathcal{U}$ and $A(x)$ be defined by the random variable $x$ by: $$A(x)=x-\lfloor x\rfloor$$ Calculate the MAP estimator $\hat \theta_{MAP}$ for the inputs $A(x)\in [0,0.001]$ $$...
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2 votes
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Finding the naive Bayes classifier

Let $Y$ have a Bernoulli distribution with P(Y=0)=0.2 and $X$ have a Bernoulli distribution with: $$f(X|Y) = \begin{cases} 0.7 & \quad X=Y\\ 0.3 & \quad \text{ else}\\ \end{...
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Interpreting the results of a Naive Bayes classifier.

Using the Naive Bayes formula to classify text I have something like... $$ P(Cat|Word1) = \frac{P(Word1|Cat) * P(Cat)}{P(Word1)} $$ Using a small example ... ...
Simon Goodman's user avatar
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Naïve Bayes Classifier

For the Data Mining - Naïve Bayes Classifier for the case of "Numberless values for an attribute", the conditional probability is modeled with the normal distribution (see below). Probability Density ...
chrisych's user avatar
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Bayesian Nets and weird probability

I have to solve the following problem: Suppose we have a bayesian net in which we have the following variables: R, PA and PR Let: P(R) = 0.1, P(PA) = 0.5, P(PR|R, PA) = 0.6, P(PR|¬R, PA) = 0.4, P(...
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Probability with a joined condition

I want to know the probability $P(A|X,Y)$, given that I know $P(A|X)$, $P(A|Y)$, $P(A)$, $P(X)$, $P(Y)$ and given, that $X$ and $Y$ are independent. I'm also going to assume that $X$ and $Y$ are ...
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Bernoulli Naive Bayes Classification

I am having trouble understanding the following text regarding Bernoulli Naive Bayes. Specifically, the author mentions that $i$ is a feature. However, what is the difference between $x_i$ and $i$?
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How to solve conditional probability problem using bayesian algorithm

I am trying to solve An agent learning to categorise news articles in two topics, World (W) and Finance (F). Out of $100$ articles, $40$ were classified as W, and $20$ of the articles were ...
ARG's user avatar
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5 votes
1 answer
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What assumptions did I make when I strengthened my independence criterion across a new random variable?

I have an algorithm which tries to calculate some $\operatorname{Pr(X | Y_1 Y_2 \dots )}$ (where juxtaposition means event intersection, "given $Y_1$ and $Y_2$ and ... have happened".) We have some ...
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