Questions tagged [probabilistic-programming]

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What are some interesting applications of probabilistic / Bayesian modelling in health innovation? [closed]

I hope this is the right board for this question. I am completing an MSc in Applied Statistics over the next 12 months and am looking for interesting problems from health innovation and medical ...
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In what ways do conjugate priors compose?

A lot of conjugate priors are known for a lot of likelihood distributions (mostly the exponential family). But most Bayesian models in practice don't just consist of one distribution. Usually, you ...
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Generating a truncated normal distribution

I want to write code, say in Python to generate a truncated normal distributed random variable on the interval $[a,b]$. I have a standard function, call it N which will generate a normally distributed ...
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Conditioning of join gaussian over a line

I need to compute the conditional probability of bivariate normal distribution over a line. Let's suppose that X and Y both are normal distributions and that they are independent. Let's suppose that ...
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Acceptance-Rejection Technique Theorem Proof

I am assigned to discuss the acceptance-rejection technique in our class. I have trouble understanding the last part of proving its theorem. The theorem goes like this: The acceptance-rejection ...
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4 answers
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Estimate negative binomial dispersion parameter $k$ using mean and proportion of zeros

I came across supplemental methods of a paper estimating the mean ($R$) and dispersion ($k$) of a negative binomial distribution that stated: Page 8: "Given estimates of the mean ($\hat{R}$) and ...
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Bayesian paired samples difference estimate

Let's say I have some observational clinical data of $N$ patients. They have a score (from 1 to 7) which is their level of symptom severity (1 being no symptoms, 7 being extremely symptomatic) at ...
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Probability of drawing N elements from M elements with per element draw probability without replacement

I have a list of M elements with per element draw probability, summing to 1.0. Example (M=10): L = [0.3, 0.2, 0.01, 0.05, 0.02, 0.02, 0.2, 0.05, 0.05, 0.1] Now I ...
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probabilistic regression in existing packages

I know that typical machine-learning packages (such as scikit-learn or TensorFlow) contain plenty of functions for probabilistic classification: given a training set of pairs $(x_i,y_i)$, where $y_i$ ...
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Differentiating entropy in Reinforcement Learning as Probabilistic Inference

I am studying the paper Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review (https://arxiv.org/abs/1805.00909) and I do not understand how the author differentiate the ...
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Uncertainty Estimation with Bayesian Inference

I am modeling a generalized extreme value distribution with the code below in PYMC3. I have defined my own distribution as the gev is still not available in pymc3. The function defined is the PDF of ...
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Regarding Gibbs sampling and HMC in fitting Bayesian model, their differences and advantages

I have a question regarding the two MCMC algorithms, Gibbs sampling and Hamiltonian Monte Carlo (HMC) for performing the Bayesian analysis. If using Gibbs sampling, my understanding is that we need to ...
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Observation dependency in pymc3 models

I have a model, which can be simplified conceptually to: $$ a \sim TruncNormal(\mu = 1.0, \sigma=0.01, min = 0.9, max = 1.1)$$ $$y = a \cdot sin(b) $$ I can make observations about $y$, but these ...
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Calculate the probability $P(S^2_{n-1}<s^2_{n-1})$ by Monte-Carlo simulation of the population distribution

i am struggling with the following problem, i have posted my attempt below, i am apparently supposed to get an answer of 0.632 with a random seed of 25 however i get a 1 as the answer. Please help i ...
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Probabilistic Record Linkage [duplicate]

Record linkage is the task of identifying which records from different data sources refer to the same entities. Without the common identification key among different databases, this task could be ...
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Can I use AdaBoost Regressor with Gaussian Process Regressor as base estimator, as my Surrogate Function?

I am using a text-extraction model whose hyperparamters I want to optimise. The model takes time(on average 1 hr) for training on the dataset. The algorithm I am using for hyperparameter tuning, is ...
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Is there a way to supress p-values in tbl_regression function in R? [closed]

I want to make tables including exponentiated parameter coefficients with CIs, but not with p-values. Right now i am using : ...
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How do I fit a multiple linear regression where I know the relationship between some of the coefficients

I want to fit a linear regression with multiple independent variables. Say that I know that the coefficient of one variable is twice as large as the coefficient of another variable, or that one ...
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What does it mean to create predictions on predicted probabilities?

Background: I have a particular dataset of presence and absence of a specific bird. This data went through various means of simplification for machine learning techniques, for example random forests ...
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How do you write factor operations for rule-based conditional probability distributions?

Supposing I have rule-based conditional probability distributions (CPDs), $\{P(X|\text{Pa}_{X}), \cdots\}$, in a graphical model each represented as a set of rules $\mathscr{R}$ such that: For each ...
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1 answer
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How to implement conditional probability distribution on set-valued Random variables?

A Random Set is a set-valued RV, i.e. a map $X:\Omega\to\mathcal{C}$ from a probability space $(\Omega,\Lambda,P)$ to the family of measurable closed sets $\mathcal{C}$ on a $\sigma-$algebra $\Lambda$ ...
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Bayesian meta-analysis of multiple ranked lists?

Let's say I go around and ask a bunch of my friends to rank 30 movies. Each one returns me a list. Now the obvious treatment is to average the rankings, but I'm wondering if anyone has seen a more ...
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What is the benefit of adding control flow to probabilistic programming?

I was watching an interesting video on the Pyro package in Pytorch for probabilistic programming. One of the things that they ...
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Are nodes outside the markov blanket unconditionally independent?

Apologies if my question is deeply flawed, I've been working through a lot of material in the past few weeks and have a few blind spots here and there. On one level my question is this - given a ...
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If given a table of samples from a multivariate distribution, can you get multivariate marginals by just extracting the columns you are interested in?

If we let $p(x)$ be the joint probability density where of r.v. $x$ where $x \in \mathbb{R}^{10}$ I am interested in looking at the joint marginal $p_{x_3, x_4, x_5}(x_3, x_4, x_5)$ I know that ...
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What are the limmitations of reparametrization gradients for discrete random variables? (Gumbel-softmax)

We know that one approach for re-parametrizing gradients for variational inference is taking the Gumbel-softmax estimator proposed in [1] and [2]. In [3], that is a talk on SVI, D. Blei at around 29:...
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Plotting a probability density based on the ratio of two random variables in PyMC3

I am trying to graphically represent the ratio of two probability distributions: $$f(x) = \frac{1}{\sqrt{2\pi}} \exp{(\frac{(-x)^2}{2})}$$ $$g(x) = \frac{1}{2} \exp{(-|x|)}$$ I'm a bit confused about ...
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Statistical relationship between the stages of a stochastic optimization problem

What exactly do the "stages" of a stochastic program say about the statistical relationship between the problem variables? From what I understand, the stages imply both an "ordering&...
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REINFORCE for VAE Implementation Question

I want to compute the VAE loss through REINFORCE since my model's decoder is a deterministic program and is non-differentiable. The only REINFORCE implementation for VAE I was able to find used the ...
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Program analysis of a coin toss simulator

Here's a problem I'm trying to solve (it's a problem from the CS109 course, assignment 2): Suppose we want to write an algorithm fairRandom for randomly ...
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Variance of evidence lower bound(ELBO) loss function

When using Bayesian optimisation in a neural network our loss function is equal to: Here the first term is the KL divergence between the approximate and true posteriors. The second term is the ...
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MAP of Gaussian Process Classification in Tensorflow Probability

I'm attempting to implement Gaussian Process Classification learning in tensorflow-probability, but my estimator turns out to be very biased toward zero. As opposed ...
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Unique game problem (ML, DP, PP etc) [closed]

Looking for a solution to my below game problem. I believe it to be some sort of dynamic programming, machine learning, or probabilistic programming challenge, but am unsure... This is my original ...
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How to get quantiles/probabilities of time series forecasts?

my problem is as follows : I am creating demand forecasts for some goods with different methods (ARIMA, ETS,..) The issue is that I would like to forecast the probabilities of those forecasts since ...
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applied papers on probabilistic generative models and inference engines

I am looking for applications papers where people choose some task on which they will do Bayesian inferencing and graphical modeling, and then build an inference engine to infer latent parameters. And ...
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What property must a RNG have to be used in Monte Carlo simulations?

For example, every cryptographically secure pseudo-random number generator (CSPRNG) is required to satisfy the next-bit test and withstand "state compromise extensions". This makes me wonder what ...
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How to validate your loss function when it is not a simple regression or classification?

Assuming I have loss function f(y_pred,y_target) that I will use to train my neural network. In this case the loss function is a regression, and let's say it should ...
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Examples of applications of Markov random fields to data with a small number of variables

I am learning about some of the common applications of Markov random fields (a.k.a. undirected graphical models) to data science. A common feature of many applications I have read about is that the ...
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What is the connection between Bayesian Networks and the models done in Probabilistic Programming?

For what I’ve read about them, they are very similar. Both model probabilistic models in which the nodes are random variables and the edges are dependencies among them. However, the literature I’ve ...
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Plate notation for a hierarchical regression model (bayesian)

I've been recently studying hierarchical bayesian regressio (with pymc3), and I was wondering, how does the following example: http://twiecki.github.io/blog/2014/03/17/bayesian-glms-3/ look like ...
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Probabilistic programming vs "traditional" ML

I was browsing the github repo for Pymc and found this notebook: Variational Inference: Bayesian Neural Networks The author extols the virtues of bayesian/probabilistic programming but then goes on ...
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Predicting a Twitter user from individual tweets probabilities

Let's say I have three tweets and those three tweets are all from either Mary or John. There is no possibility for mixed result. ...
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Unbiasedness of confounding variable models

This is a question based on work in this paper: https://dl4physicalsciences.github.io/files/nips_dlps_2017_14.pdf I am interested in causality and representations using probabilistic graphical ...
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What is Probabilistic Programming Used for?

I am hearing a lot about probabilistic programming. Turns out its just a way to specify probabilistic graphical models. Like Tensorflow is to neural networks. So, why use it? Do you know of any ...
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Why is MCMC not reliable when compared to stochastic gradient descent?

I came across the following quote on enter link description here if we made MCMC as reliable as stochastic gradient descent now is for deep networks, that could mean a resurgence of more explicit ...
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How Deep Probabilistic (Graphical) Models differs from the usual Probabilistic Graphical Models?

How Deep Probabilistic (Graphical) Models differs from the usual Probabilistic Graphical Models? What are the main applications and state of art results of Deep Probabilistic Models?
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"Blocking" effects in probabilistic programs

I'm trying to estimate a regression where: I can only see the sex of a subset of the population I do know the total population size I'd like to know how many events are driven my men vs women, using ...
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Are there any seemingly simple probability question that are actually intractable?

Are there any good examples of a seemingly simple probability problem, which is actually intractable? I am trying to motivate the use of simulation, and would like to come with an example of when it ...
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multi-stage stochastic programming interpretation

In multi-stage stochastic programming a two-stage approach is sequentially repeated. In general a two-stage model contains first-stage decisions (e.g. production quantity) and second-stage decisions ...
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Hamiltonian Monte Carlo vs. Sequential Monte Carlo

I am trying to get a feel for the relative merits and drawbacks, as well as different application domains of these two MCMC schemes. When would you use which and why? When might one fail but the ...
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