# Questions tagged [bayes-optimal-classifier]

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### 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 ...
43 views

### Use Naive Bayes to label unlabeled data

I have an Excel file that includes all product information (web scraped from Zalando) of 10k dresses. So for each dress/line I have multiple features available (brand, color, neckline, length...) I ...
22 views

### Posteriori Probability, Parameter Vectors and the explicit form of Bayes Classifier

I'm working on some linear discriminant analysis problems to develop a better understanding of the underlying mechanisms for machine learning algorithms. I'd like to develop a better understanding of ...
1 vote
47 views

### Derive the criterion for minimizing the expected loss when there is a general loss matrix and general prior probabilities for the classes

In the book "Pattern Recognition and Machine Learning" I am trying to do exercise 1.23 (p.63): Derive the criterion for minimizing the expected loss when there is a general loss matrix and ...
1 vote
236 views

### What is the relation between Linear Classifier and Linear Decission Boundary (or Non Linear Decision Boundary)?

As we know (Wikipedia Definition): Linear Classifier makes a classification decision based on the linear combination of the feature vectors. Mathematically : $y = f(\sum w_i x_i)$ So , $f$ is our ...
1 vote
434 views

### How would you find a p threshold for a binary classification prediction?

Lets say that there's a binary classification problem where $X$ ∈ $R_p$ and $Y ∈ \{0,1\}$ and $Pr(Y = 1 | X = x) = p$ for $p$ in $[0,1]$. There is a loss function $L_{falseneg} > 0$ for false ...
118 views

### This decision is the best we can do if we have no prior information about the probabilities of the two classes?

I am currently studying the textbook Learning with kernels: support vector machines, regularization, optimization and beyond by Schölkopf and Smola. Chapter 1.2 A Simple Pattern Recognition Algorithm ...
199 views

### How is this a "Bayes classifier"?

I am currently studying the textbook Learning with kernels: support vector machines, regularization, optimization and beyond by Schölkopf and Smola. Chapter 1.2 A Simple Pattern Recognition Algorithm ...
58 views

### How $\dfrac{P_t(\mathbf{\mathrm{x}}, y)}{P_s(\mathbf{\mathrm{x}}, y)} = \dfrac{P_t(\mathbf{\mathrm{x}})}{P_s(\mathbf{\mathrm{x})}}$?

Related: Empirical Risk Minimization: Rewriting the expected loss using Bayes' rule and the definition of expectation I am currently studying Transfer Learning by Qiang Yang, Yu Zhang, Wenyuan Dai,...
264 views

### Empirical Risk Minimization: Rewriting the expected loss using Bayes' rule and the definition of expectation

I am currently studying Transfer Learning by Qiang Yang, Yu Zhang, Wenyuan Dai, and Sinno Jialin Pan. Chapter 2.2 Instance-Based Noninductive Transfer Learning says the following: As mentioned ...
762 views

### Improve Adaboost that using weighted logistic regression instead of decision trees

I implemented Adaboost that using weighted logistic regression instead of decision trees and I managed to get to 0.5% error, I'm trying to improve it for days with no success and I know it possible to ...
82 views

### Use different Naive Bayes classifiers to target different data

I am practicing using the Naive Bayes classifier to predict whether people get a stroke or not, but, I am confused with two classifiers. One is categorical Naive Bayes, another is Gaussian Naive Bayes....
1 vote
157 views

### How to proof that the bayes optimal classifier is optimal for a continuous domain

Exercise 3.7 from the book »Understanding Machine Learning: From Theory to Algorithms«, Shalev-Shwartz and Ben-David, states the following: The Bayes optimal predictor: Show that for every ...
1 vote
230 views

### Bayes Optimal Classifier for multinomial classification

I understand the meaning and how to deduce a Bayes optimal classifier in binary classification, but I am not sure how to derive this in the context of multinomial classification. Do we use the naive ...
856 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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### 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 ...
613 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 ...
1 vote
58 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 ...
1 vote
183 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 ...
1 vote
55 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 $$h(x) = 1\{... 0 votes 0 answers 202 views ### Is the Bayes optimal classifier well defined? The Bayes optimal classifier (BOC) is defined as follows. When data D is given, the classifier returns the value$$\text{argmax}_{y\in Y} \sum_{h} P(y\mid h) P(h\mid D)\text{,}$$where the Y is a ... 1 vote 0 answers 610 views ### Finding the error probability of an optimal bayes classifier analytically I have two classes \omega_1,\omega_2 with equal prior probability P(\omega_1)=P(\omega_2)=0.5. And the points in 2D are distributed \mathcal{N}(\mu_i,\Sigma), \mu_1=(0,0)^T, \mu_1=(4,4)^T, \Sigma=... 1 vote 1 answer 195 views ### error probability of decision function If I have a binary calssification task with prior probability p(0) = 0.6, and I make two decisions. 1) solely based on the prior probability i.e. I make prediction 0 60% of the time and prediction ... 9 votes 1 answer 7k views ### Bayes optimal classifier vs Likelihood Ratio I am getting slightly confused by all the probabilistic classifiers. The bayes optimal classifier is given as  max (p(x|C)p(C))  and if all classes have equal prior then it reduces to  max (p(x|C))... 1 vote 1 answer 622 views ### Can the Bayes Optimal Predictor be generalized? I'm reading Understanding Machine Learning by Shai and Shai. In it, the Bayes Optimal Predictor is defined as$$f_{\mathcal{D}}(x) = \mathbb{1}[\mathbb{P}[y = 1 | x] \geq 1/2]$$Where \mathcal{D} ... 2 votes 1 answer 546 views ### Why classifiers report the class with maximum posterior probability as the predicted class? When we train a classifier to predict y \in \{1, \dots, K\} given an input x, classification is done by reporting the class with the highest posterior probability as the prediction; that is:$$ \...
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 ...