Questions tagged [bayesian]
Bayesian statistics is a statistical paradigm that contrasts with that of frequentist statistics. Bayesian methods rely on prior information do determine the degree of belief in the probability of a value.
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Bayesian Linear regression for non-gaussian distribution
Which distribution should be considered for non-gaussian distribution while building Bayesian Linear regression. I am trying to build this model using Pymc3 library but since I have just started to ...
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Parameter outside specified range using HGboost/Hyperopt library
I am trying to use the HGboost library which uses the Hyperopt library for doing hyperparameter optimization of an XGboost model. The script runs fine but the optimized parameter for "...
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Prediction intervals for future timestamps - out-of-sample
I've created a model for out-of-sample forecasting that uses multistep recursive strategy to reduce my problem to regression, the predictions are sufficient but I was wondering if there is any ...
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Using Bayesian statistics in time series forecasting
I would like to forecast demand count time series of taxi fleets at different locations on the map at different points in time. I.e. multivariate demand Time series forecasting.
Given hierarchinal ...
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Is there no reason to ever use naive bayesian learning?
I found this slide in the university course on machine learning I am currently taking. The reasons seem sound but I have not found this confirmed anywhere everywhere I read that for certain types of ...
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Model uncertainty quantification
I'm reading a paper about model uncertainty quantification. Specifically, it says epistemic uncertainty is a kind of uncertainty due to lack of knowledge about a particular region in the input space.
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How to interpet the bolded lines in bayesopt
I am using bayesopt to maximize a function that is everywhere less or equal to zero $(f(x) \leq 0)$. The score is essentially a negated Mean Absolute Error because the default behavior of bayesopt is ...
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Problem for a math formula in Weight Uncertainty in Neural Network
I am studying the paper https://arxiv.org/pdf/1505.05424.pdf and there is a formula I don't get page 4:
I don't understand how they obtain this formula. Moreover, with chain rule, I get $\frac{\...
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Bayesian Neural Network Inference
In a paper about Bayesian Neural Network, I saw the following algorithm:
Algorithm 1 Inference procedure for a BNN.
Define $p(\theta\mid D)$;
for $i = 0$ to $N$ do
Draw $θ_i \sim p(\theta\mid D)$;
$...
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bayesian neural network and the flipout estimator
i was reading the flipout paper and i stumbled over this passage. I will summarize the main point here:
In bayesian neural networks the weights are random variables sampled from a distribution.
W is ...
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Does a classifier based on optimal bayes classifier equation classify every new instance the same way?
I'm trying to understand how optimal bayes classifier works and I was wondering if, given that the function we try to maximize when making a new prediction does not depend on the instance we are ...
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Understanding the calculations of bayesian classification rule given features with known distribution
I have some difficulties using the Bayes rule and the calculations used for estimation of a given class in a classification task if we know the distribution (and its parameters) of the feature vector:
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Bayesian linear regression using pymc
Assume three features: $x_1,x_2,x_3,$ and a continuous label $y.$ I want to use pymc in python to fit a ...
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Adressing uncertainty of a spatio-temporal multivariate timeseries with random temporal gaps
Imagine there are multiple locations of interest from where water samples are gathered manually. Each sample is immediately analyzed, converted to a numerical value (a real number) and fed into a ...
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Sklearn Dirichlet Mixture
I'm using sklearn.mixture.BayesianGaussianMixture to fit a Dirichlet Process Mixture Model, and my data is 64 dimensional and have sample size 10000. However, the ...
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Techniques for choosing datasets from pool of datasets to create priors(time-series data, DTW? spike and slab?)
Let us consider a scenario where we have a pool of 100 datasets from various customers, with varying sizes containing sales and budgeting(mutiple channels) data per date. The datasets can range from ...
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how do i compute the predictive covariance matrix from the posterior samples?
I have generated with EMCEE some posterior samples from a statistical model whose likelihood is a multivariate gaussian. it's a regression problem.
can you explain me how I can use these samples to ...
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How Naive Bayes makes prediction based on scikit-learn?
I need to understand, how multinomial-naive-bayes can make prediction based on scikit-learn implementation.
I saw the source code but I want to understand the math behind it. Could you please explain ...
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find the parameter that minimize a multivariate distribution
i was trying to use scipy's minimize scalar to find the value of the parameter T that minimize the negative log-likelihood of a multivariate distribution with covariance matrix C. if i understood ...
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Framing a probabilistic time dependent problem
I need help framing the following problem:
I have a dataset where I know for each day, at customer level, that someone with device X bought device Y.
Example:
At day 1
50 people with device X bought ...
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help with comparison between the prediction of a bayesian neural network and an analytical model
i am in a weird situation where i have a bayesian neural network used for regression and a polynomial model $f(a,b,c,d) that depends on 4 parameters and that is fitted through monte carlo methods.
i ...
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How can I deal with a computationally expensive simulator method in Sequential Monte Carlo/Approximate Bayesian Computation?
I am doing Approximate Bayesian Computation with Sequential Monte Carlo with PyMC in a way that is similar to what is described in this example of the ...
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Python Impute using BayesianRidge() sklearn impute.IterativeImputer regression impute analysis value error
PROBLEM
Use interativeImputer from sklearn.impute.IterativeImputer, to get regression model fit for for BayesianRidge() for impute missing data in variable 'Frontage'.
After the interative_imputer_fit ...
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Can Pybats' Analysis function make a prediction on a future DateTime object that is only one step beyond the final point of the existing data?
I was able to utilize the Bayesian approach of statistics in Pybats in order to make a forecast model on a timeseries dataset. While the model is learning from the ...
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Weighting Regularisation Term in Aleatoric Uncertainty Loss Function
I am currently digging into Uncertainty Quantification and try to implement Aleatoric Uncertainty estimation into a regression model.
Given this publication we can model the Aleatoric Uncertainty by ...
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Understanding the uncertainty in gaussian processes
Consider the following image:
which is an fitted GP. Note how $0 <= x <= 2$ yield a much higher uncertainty than e.g $5 <= x <= 8$.
Thus gps are good when dealing with the exploration vs ...
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Force predictions of 2 time series models with different time steps to be consistent
Suppose I have a time series. Let's say it is of the number of sales in a shop. Suppose I am looking to make two models - model 1 which predicts future values by weekly time steps (total sales per ...
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Practical example of difference between p(y|x) and p(x|y)
I've been reading about the difference between generative models and discriminative models. I know that for generative models we learn the joint probability p(x,y) or just p(x|y) and p(y). For a new ...
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What is the Bayesian distribution of two p.d.f's?
I whant to make this:
Theese are the inputs
I'm traying to replicate this for my app, but don't know how its done.
As you can see, there must be a preset value for the sigma with the inputs of type ...
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Probability for Nth Place in Race from Bradley-Terry Model Inputs and Outputs
I have created a motorcycle race prediction model that is given pairs of racers and outputs the probability of each rider beating the other in each pairwise comparison. That info is then processed ...
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Bayesian state description in Reinforcement Learning
What's the best approach to feed a bayesian description of an observed state to a Reinforcement Learning agent?
Brief context: I have an agent situated in an environment, which it perceives through a ...
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Why aren't Bayesian models straightforwardly superior to all/most other models if they model the real-world better?
Why aren't Bayesian models straightforwardly superior to all/most other models if they model the real-world better?
As possibly displayed by the following chart:
source
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How "much" should belief be weighted against numerical measures of accuracy/correctness?
How "much" should belief be weighted against numerical measures of accuracy/correctness?
It's possible to devise numerically low-quality models, but that have very good empirical validity, ...
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How to guide exploration in reinforcement leanring/model predictive control/dual control problem
Consider the following optimization/control problem:
We aim to maximize the cumulative reward R during the horizon H by every day allocating a portion of total budget B to our two different investment ...
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How calculate probability when we have continuous features?
Suppose that we have a dataset with four features and each feature follows different distribution (normal,beta,gamma...). All features are continuous. So, how we can calculate the probability of any ...
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Problem understanding the forward algorithm for HMMs
I found a recursive version of the forward algorithm on wikipedia, however I don't understand the notation given in the pseudocode:
What means $$x_{t-1}$$ under the summation sign? What do I need to ...
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What methods I could use to analyze the contingency table?
I am data science beginner, and I have a question about methods that I could use to analyze the following data. It is a simple case, I am trying to check the influence of cohabitation before marriage ...
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What are the requirements for a word list to be used for Bayesian inference?
Intro
I need an input file of 5 letter English words to train my Bayesian model to infer the stochastic dependency between each position. For instance, is the probability of a letter at the position 5 ...
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Incorrect example of applying Bayes theorem
I have been reading the book "The Data Science Design Manual" (by Steven S. Skiena) and I came across an example that explained how the Bayes theorem can be applied that confused me and made ...
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Why and how Variational Inference underestimates variance?
I referred to the Quora link here as well, but could not understand clearly.
Can anyone please help me understand why and how variational inference underestimates the variance of the true posterior ...
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Confusion regarding which distribution Monte Carlo considers for sampling
Considering Bayesian posterior inference, which distribution does Monte Carlo sampling take samples from: posterior or prior?
Posterior is intractable because the denominator (evidence) is an ...
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Confused on Naive Bayes classifier
In the last part of Andrew Ng's lectures about Gaussian Discriminant Analysis and Naive Bayes Classifier, I am confused as to how Andrew Ng derived $(2^n) - 1$ features for Naive Bayes Classifier.
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What thought processes do people use for generating priors on a variable's probability distribution?
Example
Consider a block of text with a variety of sentence types within it, of which there are 7. Within a text these sentences will be more or less likely to appear, dependent on where in the text ...
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Probability distributions for Directed Cyclic Graphs
Given a directed cyclic graph where vertex A is 'infected', and there are different infection probabilities between each node, what is the best approach towards computing the conditional probability $...
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Combine prior knowledge probability with ML model probability results
I want to combine prior knowledge to improve my machine learning model. According to Bayes rule, max posterior is obtained when multiply prior with MLE.
I multiply prior probability with the machine ...
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Markov Process and transition matrix
I would like to find some good courses but also a quick response on how to model transition matrix given the states.
Imagine having 4 states and the following array [1,2,4,1,3,4,2 etc etc]. What ...
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Are there any implementations of non Naive Bayes Classifier in Python?
Naive Bayes assumes that predictors are independent. Though this assumption is quite powerful, in some scenarios it fails miserably . So are there any implementations of non Naive Bayes in Python ? ...
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Bayesian Linear Regression using the Kernel Trick vs Constructing features using Kernels as Prototypes
How different is it to do Bayesian linear regression using the GP approach (kernel trick) versus constructing features using kernels to prototypes? As far as I know, this very basic question is ...
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Bayes theorem on the probability of an object drawn at random using percentages (not Naive Bayes)
It's the normal Bayes equation but I'm not sure if I've calculated this correctly or how to check my work, here is a somewhat similar question but I wasn't sure if our math was the same, the question ...
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Multivariate testing
I'm going to run a test with 4 different variants (3 variants and a control group), and we want to find the variant with the highest conversion.
Are there any resources/methods in R/python to:
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