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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Machine Learning for conditional density estimation

Suppose I have a set of examples $X = (x_1,x_2,..,x_n)$ with continuous numeric targets $Y = (y_1,y_2,..,y_n)$. While it is standard to use regression models to make point predictions of $y_i$ as $f(...
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Is there any way to artificially create a probability calibration for data coming from another model?

I have predictions, which come from a survival model, this model gives me very low probabilities, and I am not sure if they fulfill the real probability of the phenomenon. For example, I calculate $P\...
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Best metric to evaluate model probabilities

i'm trying to create ML model for binary classification problem with balanced dataset and i care mostly about probabilities. I was trying to search web and i find only advices to use AUC or logloss ...
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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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Aggregated probability based on multiple predictions on independent samples using the same classifier

i have a understanding question regarding the interpretation of a aggregation of a machine learning classifier. Lets assume i have trained a binary classifier and it was validated with a accuracy of ...
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how to deal with features in pairwaise comparison models?

I am working on a dataset of ATP (Association of Tennis Professionals - men only) tennis games over several years. I want to predict the outcome of tennis so one way to do that is using a Bradley-...
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the mean and standard deviation aren't the same as those of the input data i provided after sampling

I have a log-normal mean and a standard deviation. after i converted them to the underlying normal distribution's parameters mu and sigma, I sampled from the log-normal distribution however when i ...
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Maximum entropy optimization for approximating image quality score distribution - as in Google's "Neural Image Assessment" paper

I am asking this question after a thorough research on the internet and having read every single detail of "NIMA: Neural Image Assessment" by Hossein Talebi and Peyman Milanfar. Before ...
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Log odds vs Log probability

Log-odds has a linear relationship with the independent variables, which is why log-odds equals a linear equation. What about log of probability? How is it related to the independent variables? Is ...
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Understanding of odds

Odds is the probability of an event occurring against the event not occurring. Suppose I play 10 games & I win them all. So my odds of winning are obviously 100%. According to the formula, odds of ...
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Is this a successful implementation of KL Divergence from scratch, and how can I graph all distributions?

I'm attempting to implement a KL Divergence on two imaginary dice from scratch and I'm not sure if it is correct. By 'how do I graph all distributions' I'm wondering if the KL Divergence just a number ...
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Odds vs Likelihood

Odds is the chance of an event occurring against the event not occurring. Likelihood is the probability of a set of parameters being supported by the data in hand. In logistic regression, we use log ...
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How are the weights defined in a (linear-chain) Conditional Random Field?

Edit: i saw that i mixed up i (in the graph) and t (in the formula), in the following i equivalent to t I am trying to understand the theory behind linear chain Conditional Random Fields. I have now ...
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How to test likelihood hypothesis on dataset?

How to test the following hypothesis? The larger the fare the more likely the customer is to be travailing alone. Using the data below, how would one be able to test the hypothesis? ...
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memory error- python N-th order Markovian transition matrix from a given sequence

Ok. What is wrong with you code! I am trying to calculate transition probabilities for each leg. The code works for small array but for the actual dataset I got memory error. I have 64 g version ...
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Probability of the occurrence of an event over time

I need to answer the following question: What is the probability that the event 1 will occur at some point in the time for a new sample? At which time point is this more likely to occur? 1: event ...
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Predictions using calibrated classifer

I find myself asking alot of calibration related questions recently - but i cannot find adequate material on it! I am training a binary classifier to predict default. This probability will be used in ...
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How can I interpret my rho risk values when performing probabilistic time series forecasting?

I am currently exploring different probabilistic time series forecasting models for car sales data and have planned to evaluate the probabilistic forecasts with the metrics rho-risk as described on ...
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Policy from an ensemble tree model?

I'm trying to output a policy (pdf on a fixed number of finite labels) from a Random Forest model. What is the best way to achieve this? I'm thinking that I can just normalize the votes from all the ...
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Generating a random numpy ndarray of 0 and 1 with a specific range of 1 values

I want to generate a random numpy ndarray of 0 and 1. I want that the number of occurrences of 1 in every specific rowto range between 2 and 5. I tried:...
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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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Imbalanced data: understanding example from Bishop PRML book?

I'm trying to understand the 3-step procedure to compensate for the effects of imbalanced data described in Section 1.5.4 - pg 45 of Bishop's PRML book. Please refer to the following excerpt from the ...
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How come the cost function changed in linear regression in andrew Ng stanford course in two different videos?

I'm a little bit confused, here is the cost function Andrew gave at the first place to minimize but when he derived using probability, we minimize the same one but in a different sign here h(theta) ...
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Probability Distribution on the Test Set

How can one interpret the probability distibution of the predictions for the target of the test set? For example if we wanted to interpret the plot below, can we say it is overfitted? Here x axis ...
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Why use Bayesian network instead of joint probability distribution table?

Is there a reason, except the number of parameters why one prefers to use a bayesian network instead of just a joint probability distribution table ?
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clustering - purchase probability - machine learning

I'm looking for a machine learning scenario: Data: time, when a customer enters the store weight, how much the customer bought Can I use machine learning to train an algorithm, which will give me a ...
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Probability vs Odds

I know what Probability & Odds ratio is, but I want to know under what circumstances each is used. When is Odds preferred over Probability?
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Analysis of probability distribution of each features and Machine Learning

While I know that probability distributions are for hypothesis testing, confidence level constructions, etc. They definitely have many roles in statistical analysis. However, it is not obvious to me ...
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Estimating the Probability of Sequence of Events Based on the Historical Data

I am working on the project where I need to estimate the delivery time(PICKUP to DROPOFF) based on the delivery route data by individual deliverers. So, I might need to figure out: How many packages ...
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Shannon Information Content related to Uncertainty?

I'm a data scientist student currently writing my master thesis which resolves around the Cross Entropy (CE) Loss Function for neural networks. From my understanding, the CE is based on the Entropy, ...
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Train a parametrized model to sample from a known target distribution

I wonder if there is a way to train a parametrized model to sample from a known distribution such as Gaussian. We usually don't need a model to sample from a known distribution (if we know the CDF for ...
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Approximation of a confidence scores from a neural network with a final softmax layer: Softmax vs other normalization methods

Say that there is a neural network for classification and the 2nd to last layer are 3 nodes, and the final layer is a softmax layer. During training the softmax layer is needed, but for inference it ...
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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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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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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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