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Questions tagged [bayes-optimal-classifier]

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Bayes Optimal vs Naive Bayes

I am a 3rd year CS student and I am currently studying machine learning. We have recently been covering Bayes classifiers and I am very confused by the Bayes Optimal Classifier. For Naive Bayes, we ...
23 views

LDA and Fisher LDA - are their weight vectors always equivalent?

Linear Discriminant Analysis (LDA) and Fisher Linear Discriminant Analysis (FLDA) both project high-dimensional observations to univariate classification scores using different rationals and ...
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28 views

Training and test data set with Bayesian classfier

I have a simple question and try to make sure that I understand the classification process. Assume that I have a data set with three different classes (say iris ...
48 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 ...
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Linearity of Bayes Optimal Classifer

Given a Bayes optimal classifier, that is, the classifier that decides: $$arg\,max_{c \in C} ~p(c|X)$$ What are sufficient condition for that classifier to be linear? My understanding is that using ...
88 views

Combining Classifiers with different Precision and Recall values

Suppose I have two binary classifiers, A and B. Both are trained on the same set of data, and produce predictions on a different (but same for both classifiers) set of data. The precision for A is ...
57 views

Can we increase the accuracy of a classifier using sketches?

I am using a sketch technique to improve the memory of a standard classifier (naive Bayes) with data streams. The sketch technique is composed of a sketch table (hash table) means the true values can ...
92 views

What is D in Optimal Bayes Classification (Machine Learning by Tom Mitchell Ed2)?

I'm reading chapter 6 from "Machine Learning" by Tom Mitchell, 2nd edition. It seems like the author changes in each paragraph what "D" is without saying anything, but it becomes really confussing at ...
42 views

For simplicity I will only discuss binary classification. If $p_k(x) = P(X \mid Y = k)$ for $k = 0,1$, then Bayes classifier $h$ minimizes the risk $P(h(x) \neq Y)$. It is well known that $$h(x) = 1\{... 0answers 174 views Is the Bayes optimal classifier well defined? The Bayes optimal classifier (BOC) is defined as follows. When data D is given, the classifier returns the value$$\text{argmax}_{y\in Y} \sum_{h} P(y\mid h) P(h\mid D)\text{,}$$where the Y is a ... 0answers 390 views Finding the error probability of an optimal bayes classifier analytically I have two classes \omega_1,\omega_2 with equal prior probability P(\omega_1)=P(\omega_2)=0.5. And the points in 2D are distributed \mathcal{N}(\mu_i,\Sigma), \mu_1=(0,0)^T, \mu_1=(4,4)^T, \Sigma=... 1answer 152 views error probability of decision function If I have a binary calssification task with prior probability p(0) = 0.6, and I make two decisions. 1) solely based on the prior probability i.e. I make prediction 0 60% of the time and prediction ... 1answer 4k views Bayes optimal classifier vs Likelihood Ratio I am getting slightly confused by all the probabilistic classifiers. The bayes optimal classifier is given as  max (p(x|C)p(C))  and if all classes have equal prior then it reduces to  max (p(x|C))... 1answer 419 views Can the Bayes Optimal Predictor be generalized? I'm reading Understanding Machine Learning by Shai and Shai. In it, the Bayes Optimal Predictor is defined as$$f_{\mathcal{D}}(x) = \mathbb{1}[\mathbb{P}[y = 1 | x] \geq 1/2]$$Where \mathcal{D} ... 1answer 319 views Why classifiers report the class with maximum posterior probability as the predicted class? When we train a classifier to predict y \in \{1, \dots, K\} given an input x, classification is done by reporting the class with the highest posterior probability as the prediction; that is:$$ \...
I have a class assignment to provide a proof that Bayes classifier for the two label version is optimal in that it's error rate is always ${\le}$ any other classifier. I've never worked through a ...
If two classes $w_1$ and $w_2$ have normal distribution with known parameters ($M_1$, $M_2$ as their means and $\Sigma_1$,$\Sigma_2$ are their covariances) how we can calculate error of the Bayes ...