Questions tagged [bayesian-statistics]
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Out-sample error for disjoint input spaces
I am trying to understand the fundamentals of Bayesian machine learning and I found an interesting task, which I have tried to solve:
We are in the setting of a binary classification problem with $Y=\{...
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Problem with Bayesian Optimization for SVM's hyperparameters
I'm trying a few hyperparameter optimization methods for SMV.
Random search manages to usually get pretty good hyperparameters with 0.95+ accuracy.
However Bayesian Optimization gets ~0.5 because in ...
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SMO, Random forest and Bayes net algorithms: why does Random forest perform better?
I analyzed a dataset using those 3 different algorithms.
As I can see, Random forest performs better in most cases.
My dataset is composed of 4000 instances of two classes (class A 2000 elements, ...
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What is the time complexity of the SGVB estimator?
In the context of variational autoencoders, we want to maximize the evidence lower bound and this is typically done using Stochastic Gradient Variational Bayes (SGVB). I was curious if there is any ...
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Density of uniform distribution over two disjoint squares
A probability distribution $P$ over $X \times \{0, 1\}$. $P$ can be defined in term of its marginal distribution over $X$ , which we will denote by $P_X$ and the conditional labeling distribution, ...
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Gaussian distribution with condition?
What does this expression mean?
Normal distribution with condition
I am reading a research paper and found the following expression (Eq.28 in the paper below).
It means a Gaussian distribution, but ...
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how many parameters do we need to estimate for a general probabilistic model
Its a question from a test in machine learning.
I have 3 binary variables x1,x2 and x3 (which means that each one of them can be either 1 or 0), each one of them has a binary output y (can be 0 or 1).
...
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Bayes theorem probability doesn't make sense
I try to use Bayes Theorem to calculate the probability of $P(A|B)$. I have $P(A)$ in column1, $P(B|A)$ in colmn2, $P(B)$ in column 3. I get the following:
my calculations were:
$$P(B/A) = 0.8\times ...
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Solomonoff's theory of induction, Kolmogorov complexity and Bayesian Inference
My motivations for asking this question are philosophical in nature. I'm by no means a computer scientist though, and I feel as though this question should be answered by someone who is since it's one ...
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Bayesian updating for multivariate Gaussian
I am reading http://www.yisongyue.com/courses/cs159/lectures/LinUCB.pdf and come across this slide
What has been confusing me boils down to showing that multivariate Gaussian is conjugate to itself ...
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How to choose value of additive smoothing in naive Bayes and why a higher value gives bad accuracy?
In Naive Bayes we often do additive smoothing as a fail safe. Consider the following expression:
Lets say
$$P(X_i) = \frac{count(X_i) + \alpha}{\sum_i^n count(X_i) + \alpha*total\_size}$$
How to tune ...
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Not grasping Bayesian Monte Carlo
I've read several sources of information that describe the process of Bayesian Monte Carlo Quadrature but am just not understanding the details enough to be able to implement it.
For instance two ...
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Unsupervised learning: necessity of labels and dependency between features and labels?
I have logs of activities without labels, which describe whether an activity is normal or not. Assuming that normal behaviors will follow a Gaussian distribution, I fit Gaussian distributions on ...
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What is meant by the term "prior" in machine learning
I am new to machine learning. I have read several papers where they have employed deep learning for various applications and have used the term "prior" in most of the model design cases, say prior in ...
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Using counting to build a grid world
For this question, I have tried everything that I can think of, but cannot solve it. What I want to do is iterate over all possible values of $z_1$, but every method I use, it requires me to know ...
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Convergence of Markov model
I was learning Hidden Markov model, and encountered this theory about convergence of Markov model.
For example, consider a weather model, where on a first-day probability of weather being sunny was 0....
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Is there any example of Regression Tree driven optimization (or active learning)?
Bayesian Optimization is the classic example of meta-model driven optimization where new observations are used to train a Gaussian process that provides a clue to where to optimize next.
LEM (...
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Variable elimination in Bayesian network
I'm trying to check if my understanding of variable elimination is correct.
Assume the above Bayesian network is factorized as:
$p(a,b,d,e,l,s,t,x) = p(a)p(t|a)p(e|t,l)p(x|e)p(l|s)p(b|s)p(d|b,e)p(s)$...
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Are the Confabulation Theories of Thaler and Hecht-Nielsen Isomorphic?
Both S. L. Thaler and R. Hecht-Nielsen have set forth neural-based theories of "confabulation" applicable to machine learning.
The essential mathematics of Hecht-Nielsen is set forth in his paper "...
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What ML methods exist to categorize signal from noise? Red noise? Spatially correlated noise?
Let's say we are given measurements of some sort.
In many cases, it is safe to assume that noise is white noise, serially uncorrelated, and zero mean with some finite variance.
But in other cases, ...
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Expectation Maximization Algorithm for simple naive Bayesian network
I am trying to understand the following network
A has two children - B & C (aka common cause)
All the variables are binary and can be either 0 or 1.
In data values are missing only for some ...
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How can a distributed system cooperate to determine rules of its environment?
I'm sorry if this question is silly or elementary. I'm not a computer scientist so I don't know the vocabulary to use to ask this question. Thus I've produced an analogy to explain the challenges I'm ...
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Simple Bayesian classification with Laplace smoothing question
I'm having a hard time getting my head around smoothing, so I've got a very simple question about Laplace/Add-one smoothing based on a toy problem I've been working with.
The problem is a simple ...
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Why naive Bayes performs better?
I have found that naive Bayesian classifier performs much better than classification using mixture of multivariate Gaussians.
Here is the problem: I have a set of objects with attached features (10 ...
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Difference between Bayesian Networks and Dynamic Bayesian Networks
I'm studying Bayesian networks and want to clarify a couple of things with people who are more knowledgable in the area than me.
As far as I understand it, a Bayesian network (BN) is a directed ...
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Approximate Bayesian Computation VS Monte Carlo Simulation
I am a little confused about the differences between Approximation Bayesian Computation (ABC) and Monte Carlo Methods (MCM). Citing from wikipedia:
Approximate Bayesian computation (ABC) constitutes ...
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Bayes nets - calculating probabilities
Given a Bayesian network, say a -> b -> c, all binary random variables (I won't show the CPTs, assume they are given). You are told b and c are true. How do you calculate the P(a=True)?
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Bayesian Nets & Markov Blanket
As i passed PHD entrance exam, some days ago, i want to find solutions for challenging problem.
In Bayes network on X={X1,...Xn} each random variable has P parents and Q child's. for Xi we want to ...
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Can you use a Bayes classifier to determine if something is NOT in a defined class?
I know I can use a Bayes classifier to determine if something is one of N classes, but can I also determine if something is NOT in any of the predefined classes? Or will a Bayes classifier only find ...
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