All Questions
6 questions
3
votes
1
answer
65
views
Modeling the probability distributions for the Bayes classifier
According to the Wikipedia, the Bayes classifier assumes knowledge of the distributions of $X | Y$, where $X$ and $Y$ are the random variables of the features and the classes, respectively. Let's ...
- 371
1
vote
0
answers
69
views
How do I minimize the cost from errors?
Bayes' Optimal Classifier is known to achieve the minimum error rate for a dataset $x_1, \ldots, x_n, x_i \in \mathbb{R}^d$. Suppose that each error had a cost associated with it. For example, in a ...
- 255
3
votes
0
answers
71
views
Question about using Bayesian rule as a classification for continuous data set
Please note that my question is not about coding.
I am now learning Bayesian classification and I think I understand it in a discrete case. I have trouble understanding it for multivariate continuous ...
- 316
1
vote
1
answer
1k
views
Finding the error probability of an optimal bayes classifier analytically
I have two classes $\omega_1,\omega_2$ with equal prior probability $P(\omega_1)=P(\omega_2)=0.5$.
And the points in 2D are distributed $\mathcal{N}(\mu_i,\Sigma), \mu_1=(0,0)^T, \mu_1=(4,4)^T, \Sigma=...
- 11
1
vote
1
answer
232
views
error probability of decision function
If I have a binary calssification task with prior probability $p(0) = 0.6$, and I make two decisions.
1) solely based on the prior probability i.e. I make prediction 0 60% of the time and prediction ...
- 297
2
votes
1
answer
642
views
Why classifiers report the class with maximum posterior probability as the predicted class?
When we train a classifier to predict $y \in \{1, \dots, K\}$ given an input $x$, classification is done by reporting the class with the highest posterior probability as the prediction; that is:
$$
\...
- 2,261