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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Reinforcement Learning: Formally, does an exponentially decaying epsilon satisfy GLIE?
I am aware that exponentially decaying exploration constants (epsilon) are used practically. Formally, though, do they satisfy the GLIE condition?
Specifically, relating this to the Borel-Cantelli ...
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What does maximize average log probability mean?
In the word2vec paper (https://arxiv.org/pdf/1310.4546.pdf) that introduces the skip-gram algorithm we encounter this phrase:
which says that we maximize the average log probability.
Can someone help ...
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Conditional density estimation for sequences using conditional random fields
I am looking to estimate the conditional distribution of the next observation $x_{t+1} \in \mathbb{R}_+$ of a discrete-time process, given the current observation and $l$ previous observations. I am ...
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Check the validity of the distribution in the proof of No-Free-Lunch Theorem
I'm reading the proof of No-Free-Lunch Theorem (quoted at the end of this question) in Understanding Machine Learning: From Theory to Algorithms, Cambridge University Press, p.37, the author wrote:
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Is probabilities mean of predicted class (RandomForest) a consistent estimator of class recall?
I'm working on a classification problem in order to predict among 50 different classes.
I'm using a Random Forest classifier and I'm using the predict_proba method ...
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Hi, I need help with this question. This quesion is based on Markov Chains. I want to answer it without using any simulation
Alinah is spending the summer at her grandparents’ farm in a small town in Iowa. The town is known for frequent changes in its weather. Each day starts off as either sunny or rainy. There’s a 50% ...
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Confusion over taking gradients in Variational Autoencoder (VAE)
I am confused as to when to hold certain parameters constant in a VAE. I will explain with a concrete example.
We can write $\operatorname{ELBO}(\phi, \theta) = \mathbb{E}_{q_{\phi}(z)}\left[\log
\...
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How to prove equation (7)(8) in paper A Review of the Gumbel-max Trick and its Extensions for Discrete Stochasticity in Machine Learning?
I couldn't derive the formula (7)(8) in paper
https://arxiv.org/pdf/2110.01515.pdf
They didn't seem obvious to me.
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Edit friendly DDPM noise space
I was reading this paper, "An Edit Friendly DDPM Noise Space: Inversion and Manipulations". In page no. 4, they have mentioned that in DDPM, noise maps of consecutive steps are highly ...
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How to visualize a changing distribution overtime, given non-uniformly sampled data with timestamps
Assume that there is a bernoulli distribution whose probability is unknown to us and may occasionally change.
What we have on hand are non-uniformly sample results (0/1) with timestamp information.
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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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Intuition behind Jensen Shannon divergence between deep features of two images?
Jensen Shanon divergence is mainly used to determine the divergence between two probability distributions. Can it be used to calculate the difference between the deep feature vectors of two images?
I ...
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Looking for suggestions on how to distinguish between two different distributions in my data when no labels are available
My data consists of medical claims from thousands of providers across the country. The data contains how much they were paid for each service they performed and how many units of each service they ...
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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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Does the central limit theorem and confidence intervals apply to any distribution, including memoryless distributions?
Is it possible to assign a 1 or a 0 to values in any distribution, be it a memoryless power law or pareto distribution to match some criteria such as if a value is under 10 it gets a 1, otherwise it ...
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Common cross-validation code: why does it work?
The following Python code is common practice when creating a folds column for multi-label stratified k-fold cross-validation:
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Do models of social systems suffer from prediction drift?
Background
I've created a binary classification model that predicts the probability of fraud for a given sample.
The choice of threshold allows me to set how many frauds are captured in the training ...
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Problem formulation of future timeframe prediction based on current time
I have a problem where I want to predict "when is the next action happening" based on the time.
Example problem: Imagine you have a dataset of transactions per user, your goal is to predict ...
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Getting probability to finish in the last 3 ones after each game week
I'am working on a dataframe with five differents features :
team
game_week
season
cum_points : pre game cumulative number of points
final_position
Those datas are covering 10 seasons of Premier ...
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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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Probability of a Maximum in a Time Series Given Past Data
I'm trying to predict the peak power usage of an EV charging station. I would like figure out probability bounds given the peak power throughout the month.
Imagine that our EV time series consists of ...
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Trying to extrapolate info from a partial data set - statistical inference
I am wondering if my logic is OK here or not.
98% of a group without a device has an event occur
2% of group with device has an event occur
Since we know that correlation isn't causation I can't say ...
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Kernel Density Estimation and performance evaluation
I am doing a data science project about Kernel Density Estimation, specifically about finding the best bandwidth and kernel function to use.
I need to use data that I don't know the actual underlying ...
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probability distribution
Just wanted to know if the value we get by passing, say, random.normal(shape=(3,2)) in the Tensorflow, etc, are normally distributed or if they are randomly chosen ...
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Precision vs probability
Say I have a model which predicts a class $C_i$ from an input $X$, with a probability of 0.95 i.e $P(C_i| X)=0.95$. That would mean that if we do this over and over, then 95/100 times we would be ...
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Predicting probability of reaching a milestone -- How much data should I use from production universe to train/test model?
If I am predicting probability of a business to reach (x) milestone (classification 1), but the only data I have is live production data, how much of the production data should I use to train the ...
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Evaluating models which classify on rolling time intervals
TLDR: I am trying to predict the probability of an incident occurring within a specific time interval. I have data from multiple years, and I know the exact time of year that incidents occur. I have ...
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Get dependant probabilities in multiclassification
After training my CatBoostClassifier model I call get_proba function which returns me list of probabilities. The problem starts from an another point... I transfer that data into dataframe then to ...
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What does it mean to "condition' a net's output?
Graves talks about conditioning the predictions of a net based on inputs. What does that mean, and how is it done?
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How to demonstrate two variables are orthogonal with respect to the output in a 3-D Python dataset?
I have a Python dataset with 300 samples and 3 columns: 2 independent integer variables X,Y and the dependent continuous variable ...
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Calculationg perplexity (in natural language processing) manually
I am trying to understand Perplexity within Natural Language Processing as a metric more fully. And I am doing so by creating manual examples to understand all the component parts. Is the following ...
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whats the difference between these two value function definisions?
I've seen in literature two different yet similar approaches when writing the value function in an MDP:
$V_\pi(s)=\sum\limits_{a\in A}\pi(a|s)\sum\limits_{s'\in S}\sum\limits_{r\in R} Pr[s',r|s,a][r+\...
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Good models for predicting whether a customer would make a purchase given details like age, gender, ethnicity, salary, etc?
I have around 30,000 data points and for those data points I have some numerical fields like customer_age, ...
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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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How is Probability Used in Data Science? [closed]
This is my first Question so apologies if I do not stick to the standards.
What I want to understand is how is all of the following topics:
Probability
Different Probability Distributions.
Baye's ...
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Mathematically rigorous NLP
I'm looking for resources (books/articles/whatever) that provide mathematical formalization of NLP and statistical language theory. By that I mean clear exposition of the subject in terms of ...
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Strategy to choose maximum value from an unknown array of n numbers
Suppose you have an array of n normally distributed numbers whose values are initially unknown(and the probability parameters are unknown too). You must choose one number and you want it to have ...
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Compute the pdf from pandas kde
I have data (features/targets in machine learning terminology), e.g. X1(t), X2(t), ... XN(t) and dependent variable y(t). I can use pandas to plot the kde's of the independent variables (X1(t),...).
I ...
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How can I obtain the mean of a Poisson distribution given the first improbable point of the distribution?
I generated a Poisson distribution with mean equal to 3 and 10000 samples by using np.random.poisson(3,10000). The plot is the following:
from this plot I see that ...
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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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How does factoring probability distributions help?
I'm trying to make sense of machine learning and am reading Deep Learning by Goodfellow, Bengio and Courville. In section 3.14 they show an example of factoring a distribution then say "These ...
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Threshold tuning with one-vs-rest for multi classification python
I’m currently using a One vs Rest Random forest algorithm for multi class classification problem using Python, and I want to find the optimal threshold for each class, How can I do this with OVR (One-...
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approximating probability mass function from a large data
I am learning elementary probability; especially I am interested in learning how to find probability mass functions and density functions from data.
I think I perfectly understand the theory: For ...
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Inject external prior distribution to my dataset
Input:
External Information - distribution between the feature_i & binary_target
Internal Dataset - tabular data. ...
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Correct way of calculating probability
I have some data which shows how many orders were made by a certain customer group that bought a certain product type:
And the same format but showing how many refunds were made:
I am trying to ...
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XGBClassifier's predictions are not probabilities with objective='binary:logistic'
I am using a XGBoost's XGBClassifier, a binary 0-1 target, and I am trying to define a custom metric function. It supposedly receives an array of predictions and a DMatrix with the training set ...
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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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