Questions tagged [bayesian]

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If I use Gibbs sampling with a Bayesian model, what do I have to check is memoryless?

Right now I am trying to better understand how Bayesian modeling works with just the basics. I found through reading tutorials that some very basic Bayesian models like Bayesian Hierarchical Modeling ...
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1answer
81 views

How to update the posterior belief when we are observing a stream of correlated data from a fixed but unknown data source

I want to build a [probabilistic] model that aims to infer the true value of an unknown categorical variable, $y \in \{1,2,..., K\}$. We have a dataset $(X,y): \mathbb{R}^d\rightarrow \{1,2,..., K\}$ ...
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61 views

When to use bayesian linear regression instead of linear regression?

When does it make sense to use a bayesian approach, maybe in context to linear regression? To be more concrete: Assume you measure a certain number of devices and you wanna' check the linear ...
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2answers
236 views

Is k-means with Mahalanobis a valid option for clustering?

I want more info into if k-means with Mahalanobis distance is a mathematically/methodologically correct option for datasets with different variance clusters. The steps are: Create aggregate datasets (...
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106 views

What are the tradeoffs between Bayesian Deep Learning and Deep Gaussain Processes?

I understand the differences between Deep Gaussian Processes(DGPs) and Bayesian Deep Learning(BDL): DGPs are essentially feed-forward neural networks where each node is a Gaussian Processes, which BDL ...
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385 views

Bayesian linear regression / categorical variable / Laplace prior

I'm trying to do feature selection in the bayesian framework with a Laplace prior with the following code in Python; Code: ...
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0answers
52 views

information leakage when using empirical Bayesian to generate a predictor

Consider the following problem: I want to predict the next bat of a set of baseball player. I have a training data set, where it contains the historical bat records (0-1 encoded, which is our target ...
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471 views

Implement gaussian mixture model with stochastic variational inference

I am trying to implement Gaussian Mixture model with stochastic variational inference, following this paper. This is the pgm of Gaussian Mixture. According to the paper, the full algorithm of ...
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9 views

Tracking time-series latency using conjugate priors

I need to do a project using Bayesian statistics for a class and I am trying to apply it to my work. I help manage a time series database with 40,000+ different time series that we collect. The time ...
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43 views

Poisson model with overdisperssion

I'm working with a dataset $X$ (of length $N$) of count data, which looks like: I developed a statistical model which can be improved, so I'm asking for any suggestions, for instance, differnet ...
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25 views

Custom Loss Function for Mixing Sparse and Dense Features for a Prediction Problem

I have a largely uncorrelated feature space of about 40 dichotomous features, using which I'm trying to predict a continuous target variable. Now, some of these features are very sparse (Active less ...
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17 views

Improve confidence interval accuracy

I am doing a linear regression on log-transformed data and I use the bayesian approach to model the predictive distribution and construct my 90% prediction Interval. The problem with this approach is ...
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61 views

Firebase AB testing algorithm

We have run an AB test at firebase which has the following results: I was also building my own Bayesian AB-test suite and was wondering how they came to these conclusions. What I was doing was ...
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29 views

GMM with Dirichlet prior

I'm learning about the variational inference - mean field approximation on from this online course DeepBayes2019 page 30 The probabilistic model is written as follows: $p(X, Z \mid \pi, \mu, \lambda) =...
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18 views

Derivation of Bayes classifier in Murphy's book

I am reading Kevin Murphy's Machine Learning book (MLAPP, 1st printing) and want to know how he got the expression for the Bayes classifier using minimization of the posterior expected loss. He wrote ...
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2answers
62 views

Parallel hyperparameter optimization techniques?

Most hyperparameter optimization technique want to evaluate points one by one. I have an expensive optimization problem, but i can run hundreds of evaluations in parallel. The dimension of the problem ...
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0answers
894 views

Bayesian optimization for a Light GBM Model

I am able to successfully improve the performance of my XGBoost model through Bayesian optimization, but the best I can achieve through Bayesian optimization when using Light GBM (my preferred choice) ...
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31 views

Bayes posteriograms

My main objective is to predict the posterior probability of an individual belonging to one of the classes, using Bayes theorem. The information I have is: value of the data point mean and stdev of ...
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49 views

PyMC3: how to efficiently regress on many variables?

I am sorry ahead of time if this seems like a basic question, but I had difficulty finding resources online addressing this. In PyMC3, when building a basic model of a few variables, it is easy to ...
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1answer
389 views

How to do hidden variable learning in Bayesian Network with Python?

I learned how to use libpgm in general for Bayesian inference and learning, but I do not understand if I can use it for learning with hidden variable. More precisely, I am trying to implement approach ...
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40 views

When to model a problem by using the Bayes' theorem?

I have a labeled training dataset where each observation has a sentence either in English or in French as its predictors and its label (target value) is whether this sentence is English or French. The ...
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25 views

Algorithms behind “smartlinks” for online traffic distribution

Several traffic networks offer "smart links", where you can send online traffic, and the traffic will be sent to the most profitable segment. These networks include Monetizer, Glize etc. I.e. if you ...
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689 views

Correct calculation of BIC (Bayesian Information Criterion) to determine K for K-Means

I am trying to calculate BIC in python. In python, there is no inbuilt library for computing BIC. I referenced the following link to compute variance and BIC further:- https://stats.stackexchange.com/...
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110 views

How to integrate out hyperparameters of Gaussian process for Bayesian optimization?

I read this paper (https://arxiv.org/pdf/1206.2944.pdf) discussing about practical issues of Bayesian optimization and they mentioned that integrating out hyperparameters of Gaussian process using ...
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136 views

Custom regularisation for logistics regression

My understanding of l2 regularisation: Weights of the model are assumed to have a prior guassian distribution centered around 0. Then MAP estimate over data adds an extra penalty in cost function. My ...
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27 views

How to interpret long equations in Deep Learning papers

For eg. I've been studying a paper on Recommender systems using collaborative deep learning and I've just started learning. The paper revolves around the NN representation as shown below The ...
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185 views

How to use pymc3 to sample the mean of a Pareto random variable?

I Have a variable which is Pareto-ly distributed 'x', with unknown alpha and m. I want to find out the distribution of its mean, so I use the following model: ...
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10 views

I think a learning rate schedule would be counter-productive with AdaBelief. Am I wrong?

I just tried an experiment where instead of Adam, I used Adabelief, but with the same learning rate schedule hyper-parameters. The outcome was so much worse than using Adam that I am inclined to ...
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14 views

Hypothesis Space of Bayes' Optimal Classifier?

What is the hypothesis space for an Optimal Bayes' Classifier and why do the assumptions of a Naive Bayes' Classifier (that features are conditionally independent of each other) narrow the search ...
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32 views

Practical difference between Bayesian Neural Networks and Feed Forward Neural Network with Gaussian Noise

To my understanding, a BNN's weights come from a Gaussian with trained mean and standard deviation, while a FFNN of the following form, comes from a learned weight, which acts as a 'mean', and is ...
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26 views

Bayesian Regression Model

I am new to Bayesian modeling. I am running Bayesian regression model in R using brm function from brms library, which is powered by STAN. I have a data with 10 million records. I took 10% sample out ...
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10 views

Machine learning. Input: set of distributions, Output: distribution

I have a set of features where typical machine learning techniques do not work very good. All features have very different distributions, some heteroscedasticity is also present. The distribution ...
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39 views

Classification of OLS regression coefficients

A variable $A$ (reaction time) is log-normally distributed, i.e. $\log(A) \sim \mathcal{N}(0,\sigma^2)$ and is linearly dependent of $n$ variables $X = (X_1,\ldots,X_n)$, i.e. \begin{align} A &= \...
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8 views

what does “Tree” refer to in Tree-structured Parzen Estimators

I am going through the literature of Hyperparameter optimization techniques and came across TPE. There is very little to no explanation on why the name has "Tree" in it. What is Tree referring to? and ...
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34 views

Specifying priors in rstanarm for hierarchical model

We are given the model $$ \begin{align*} y_{ij} & \sim \mathsf{Normal}(\alpha_j + \beta x_i, \sigma^2)\\ \alpha_j & \sim \mathsf{Normal}(\gamma_0 + \gamma_1 u_j, \tau^2) \end{align*} $$ with ...
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29 views

Bayesian Network - a practical example of marginal probability calculation?

I was watching an online course on the topic Bayesian Networks and I have a question regarding the calculation of marginal probabilities. Hier is the given network: and the corresponding course video ...
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16 views

Bayesian/Frequentist “philosophies” in relation to common ML models

Starting to think about questions tout could come up in a data science job interview, there is this one question that is bugging me since i don't have a deep background in statistics. I have a ...
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12 views

what R and Python package can predict a word list with certain probability after one known word?

I have a lot of documents, I need to know after one know word, which words occurs with which probability. For example: ...
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25 views

Bayesian test for classification problems?

I am using two classification algorithms in Weka i.e. Logistic Regression and Naive Bayes and want to know which algorithm has better performance? I need a statistical test like Bayesian, so which ...
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1answer
75 views

How to test dev set on Time Series data via forecasting

I'm implementing $3$ Bayesian Deep Learning models (links below) for my masters. I'm supposed to test them on a civil engineering time series data. My models ...
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1answer
163 views

Estimating class prevalence in unlabelled data after predicting labels with a binary classifier

I'm looking to get an estimate of the prevalence of 1's (i.e. the rate of positive labels) in a very large dataset that I have. However, I am hoping to report this percentage as a 95% credible ...
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1answer
53 views

Limits of using a normal distribution in Bayesian inference

When applying a Bayesian inference method such as Gaussian Process Regression (GPR), the assumption of a prior and likelihood function following a normal distribution is inherent. One can use an ...
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68 views

RNADE vs MDR vs BART vs Bayesian Linear Regression

I'm looking at a collection of problems where I need to forecast the probability of a continuous variable. My dependent variables are a combination of categorical and continuous. It looks like there ...