Questions tagged [probability]

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur or how likely it is that a proposition is true.

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Maximum Likelihood Estimation - huge bias on certain values, advice?

First of all I profusely apologise for the lack of suitable ways to express myself, I lack the formal data science background and am trying to learn as I go along, so finding the right terminology 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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31 views

How to approach this: Percentage change in one KPI leading to change in other KPIs?

I want to know how can I approach or model this problem. I have 7 KPIs (3 of them dependent on each other) and one main KPI (total 8 KPIs). I want to understand effect of these 7 KPIs on the main KPIs....
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Identify causal feature in a classification model

Assume I have a model $f(x;b_1,b_2,b_3,b_4)$ which maps a 4-dimensional vector into a binary classifier e.g logistic regression with 4 parameters to create churn-classifier. Say, for instance, that $...
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Understanding forward process in diffusion models

I was reading a blog on diffusion models where I came across this expression. I didn't understand why it is \begin{align} \sqrt[]{1-\beta \small{t}}*\large{x}\small{t-1} \end{align} and what exactly ...
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Though process to calculate error rate for a classification algorithm with 1000 objects?

I am trying to solve this question A classification algorithm classifies 1000 objects in to one of two classes. It incorrectly classifies 13 out of 100 class 1 objects and 53 class 2 objects. (a) What ...
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How to perform a Monte Carlo simulation with continuous sampling using discrete quantiles?

Assume I have registered the duration of 10 tasks and built the table below with using this data: Duration For how many tasks it happened 4 days 5 task 6 days 2 task 8 days 2 task 10 days 1 task ...
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Weighted Probabilities

With numpy, how would I select an item with weighted probability? ...
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Tensorflow Probability Implementation of Automatic Differentiation Variational Inference with Mixtures

In this paper, the authors suggest using the following loss instead of the traditional ELBO in order to train what basically is a Variational Autoencoder with a Gaussian Mixture Model instead of a ...
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Multi-modal histogram and real-world measurements

I have a histogram of real-world measurements of the wind speed at a given site. There are many 0's in the dataset, presumably because the wind was far to gentle to trigger the sensor into reading ...
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Approach for analyzing marketing campaign

Consider my users has to do "Action A" at their own pace to be able to continue using our service. Then, we run a campaign to push the user to do "Action A" at a quicker pace by ...
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Predicting probabilities in Neural Networks

I have 1000 number of inputs in a sample each ranging between 0-1 as shown: ...
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Which is better KL- Divergence or Bhattacharya(Hellinger) Distance

I'm beginner in probability and statistics. I came across the concept of comparing two probability distributions. KL-Divergence and Bhattacharya(Hellinger) Distance are used to compare two probability ...
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Deep Learning book - trying to understand Bernoulli formulas

In the section 6.2.2.2 Sigmoid Units for Bernoulli Output Distributions of The Deep Learning Book there is a section: (z is defined as $z=w^Th+b$ and $\hat{y}=\...
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How to choose products based on Number of good, bad and total reviews?

Let us suppose, I have few scenarios for products with good and bad reviews. P1: 1000 Good, 1 bad P2: 100 good, 10 bad P3: 20 Good, 0 bad P4: 10000 good, 500 bad ...
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How to compare Poisson Point Process, ARIMA and LSTM?

I am trying to compare three forecasting techniques: A stationary stochastic Poisson-GEV: where the rate of occurrence of the events is given by a Poisson process and, it's intensity is given by a ...
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How to derive Evidence Lower Bound in the paper "Zero-Shot Text-to-Image Generation"?

Can someone share the derivation of Evidence Lower Bound in this paper ? Zero-Shot Text-to-Image Generation The overall procedure can be viewed as maximizing the evidence lower bound (ELB) (Kingma &...
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34 views

Training set Distribution and Activation function/Loss function correlation

How should the probability distribution of the training set influence the choice of the activation function / loss function? For instance if I have a Multinoulli distribution, which activation ...
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How useful is Bayesian Inference

Last few months, I had been exposed to Bayesian Inference in ML course With further investigation, I come to place where there is MCMC technique to simulate the ...
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Independence of Features assumption in Naive Bayes

How do we know if your features in my dataset are independent before applying Naive Bayes? Basically I want to know is it possible for us to get an idea before training our model if Naive Bayes will ...
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I need help to write an essay about: probabilistic method || Occam's razor || mathematics in the 21st

I am interested in one of the master's programs in Data Science. In the application process I need to submit an essay of 1,000 words about one of the following topics: Drawbacks of the probabilistic ...
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Cosine Similarity: Works with TF-IDF Vectors OR with Probability Vectors?

Using Cosine Similarity is a common method to calculate Semantic Textual Similarity. And it is particularly useful when comparing Sentence Embeddings provided by the Universal Sentence Encoder. ...
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Qunatify total time saved by prioritizing tasks based on the failure rate probability of each task

I am trying to solve a problem where I am trying to prioritize the tasks in a job based on the failure rates of each task. For ex: ...
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Use distribution probability as a feature in ML model

I built an LSMT model to predict sick cows. I also have risk factors like cow size and height (static risk factor) that I want to combine into the ML model. I found that size is geometrically ...
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Update of mean and variance of weights

I'm trying to understand the Bayes by Backprop algorithm from the paper Weight Uncertainty in Neural Networks, the idea is to make a NN in which each weight has it's own probability distribution. I ...
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Using softmax for multilabel classification (as per Facebook paper)

I came across this paper by some Facebook researchers where they found that using a softmax and CE loss function during training led to improved results over sigmoid + BCE. They do this by changing ...
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How to model the probability of detecting an image, given it is seen multiple times

Are there any existing methods/models describing the probability of an object being detected by a computer vision algorithm given it is seen $n$ times at similar angles and orientations? I know that ...
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52 views

derivation for expected value for variance

Hi Im taking a course about probability distribution in datascience and below is derivation of the expected value for the variance Variance = expected value of the squared difference from mean for ...
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What algorithms can handle probabilistic targets?

I have a classification problem where I want to want to use probabilities instead of classes to train my model to learn to output probabilities. In my dataset, I have instances where the probabilities ...
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1answer
32 views

Combining multiple probabilities from a classifier. Propagating probabilities

Let's say I have trained a classifier that classifies images of animals into 10 different classes. And let's say that I have 20 different images of a particular animal and because I know the ...
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32 views

Designing a network for multiclass regression

I'd like to model a continuous conditional probability distribution for two classes on a given data set. eg the height of men and women from a set of inputs. I can train a regression model (DNN, CNN, ...
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Distance between two time-dependent distribution

In my research, I want to use a meaningful and computationally tractable distance between two time-dependent probability distributions. For stationary distributions, several distance measures are used,...
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1answer
37 views

Creating a training dataset from analytical solution

I am currently redesigning an inverse problem on an experimental technique, but I am having doubts about how to create a training dataset. Here is the problem I am trying to solve: I have already ...
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Ensemble of different reservoirs (echo state networks)

Suppose I want to do reservoir computing to classify the input to the proper category (e.g. recognizing a handwritten letter). Ideally, after training a single reservoir and testing it, there would be ...
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Calculating classification metrics when "true" label is also generated by another classification model

I have a binary classification model $A$ and want to calculate its precision and recall for positive and negative classes. The "ground truth" or "true" labels for this model are ...
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different scored probability distributions for a classification model using python vs Azure ML Studio

I have a classification model which I initially built in Azure ML studio and then created a similar model in python (its similar because the algorithms in python VS Azure are a bit different so they ...
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54 views

Interpreting the results of the probabilistic neural networks (Monte Carlo dropout approach)

I have a Keras NN model where I apply the Monte Carlo dropout approach as a predictive method to evaluate the uncertainty of the model outputs. From my research in the probabilistic neural networks, I ...
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Error term in probabilistic interpretation of least squares update rule

I have read in Stanford's CS229 course notes that to justify the least-squares update rule with probability, the following is assumed: $$y^{(i)} = \theta^Tx^{(i)}+\epsilon^{(i)}$$ , where $\epsilon^{(...
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50 views

Compare cross validation values of Bernoulli NB and Multinomial NB

I'm testing the Multinomial NB and Bernoulli NB on my dataset and I'm using the cross validation score to better understand which of the two algorithms work better. This is the first classifier: ...
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1answer
49 views

How to implement conditional probability distribution on set-valued Random variables

I'm trying to implement conditional probability distribution when the events of two RVs are sets. If I try to extrapolate concepts from real or categorical variables to sets things become confusing ...
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How to set seed for random drawings with Numpy? [closed]

I'm trying to set the seed for a few lines of code in a jupyter notebook. However, when I tried running numpy.random.seed(0) in the initial cell, in the later cells the random generator was not '...
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Neural Network probabilities problem

I am using machine learnig to measure probability for the outcome of tennis matches. If the winer is 1 that means that p1 won otherwise p2 won. in Columns LG, SVC, RF and NN there are probaiblities ...
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23 views

Classifier Performance - Binomial proportion confidence interval

I am solving a binary classification task. As an output of Random Forest classifier, I get a probability of how sure RF is that class is 0 or a 1. How can I calculate the needed threshold, to be 95% ...
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1answer
68 views

What is a distribution-wise asymmetric measure?

I was trying to understand KL-Divergence, $$D_{KL} \langle P(X) \Vert P(Y) \rangle,$$ and was going through its Wikipedia article. It says the following In contrast to variation of information, it is ...
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35 views

Which probability distribution will you use to model outliers?

I was asked this question in a recent interview for the position of a Data Scientist: Which probability distribution will you use to model outliers ? I told him outliers are like rare events which ...
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R code that gives results like Wolfram Alpha for the expectation of a function of a random variable? [closed]

When I ask Wolfram Alpha to calculate $E[f(X)]$ where $f(x) = e^{-x^2}$ and $X \sim \mathcal{N}(1,4)$, it gives the result $$ E[f(X)] = \frac{1}{3\sqrt[9]{e}} \approx 0.29828, $$ and the following ...
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how to interpret this 'lift chart'? prediction and true labels

i am trying to compare the prediction from my classifcation model and it's true label either 0 or 1. ...
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1answer
25 views

What is the most common practice of generating (X,Y) from an arbitrary CDF or PDF?

So I can generate X from arbitrary CDF F(x) by the procedure above. Can it be generalized to two variables? How, exactly? If not, what's the best way to generate <...
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Learn smoothly varying mean and variance of a variable over a 2d domain

For a problem which I am working on at the moment, I'm interested in learning how the mean and variance of some response variable y changes with two independent ...
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How to generate a random sample and distribute values based in an probability distribution?

I want to generate a random sample based on this probability distribution: The line is the KDE of the histogram. My random sample will have n values, the value is ...

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