Questions tagged [mathematics]
Mathematics in a data science or machine learning context refers to the mathematical underpinnings for algorithms, optimization, statistics, and linear algebra etc.
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How Can a Mathematician with Programming Experience Transition to Hands-On Data Science and ML?
I have a strong foundation in mathematics and programming, but limited hands-on experience with the data science skills currently in demand in the industry. I am eager to start applying my knowledge ...
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Why does Generalized Mean Pooling (GeM) become Max Pooling as 𝑝 approaches infinity?
I've been studying various pooling methods in neural networks and came across Generalized Mean Pooling (GeM), which is defined as:
where pis a parameter that ...
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Courses or lectures or books on machine learning or AI in general that have a lot of theoretical and practical mathematics but also practical coding
I'm looking for deep learning, or machine learning more generally, or artificial intelligence more generally, courses or lectures or books, that have a lot of theoretical and practical mathematics but ...
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I need some advice about working as Mathematical Modeler/Data scientist [closed]
I have 10 years experience in studying mathematics in University, and I've just finished my Masters degree
I have some experience with LaTeX and Mathematica, what do I need to study to be able to ...
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How to analyze time series data and create time series model in Python?
I am trying to understand time-series data and model. In youtube tutorial and others, mostly univariate examples are shown. And they are applicable or suitable for those conditions. What if our ...
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Diffusion Models: Conditioning on Time vs. Noise Level
I am new to SE-Data Science, therefore I hope this is the right place to ask this rather theoretical question.
In diffusion models we usually have a time variable which determines the noise schedule (...
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Does performing k-NN on the centroids of clusters obtained from k-means make sense mathematically?
While playing around with some text embeddings, I used k-means clustering to get 4 clusters. I also have the labels for these embeddings, and I may simply use k-NN to classify new embeddings. However, ...
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Weighted average for multiple confusion matrix
I have problem and i have no idea how to resolve it.
I have 4 Confusion Matrixes and i need to calculate for example Matthews Correlation for each CM.
In second step i want calculate BIG KPI result ...
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What is the Understanding level required in mathematics to become a great data scientist?
I am a civil engineer and i got some undergraduate courses in linear algebra, probability and statistics.
I am pursuing some ML/DS courses in udemy so I'm just a beginner and I would like to become a ...
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AutoDiff on different operations?
How it is possible to use automative differentiation (computational graph) on operations like - convolution?
I know that 2d convolution can be represented by matrix multiplication. But what about 3d ...
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Trying to understand Ch.2.1 "2.1. Monads and their algebras" of "Categorical Deep Learning: An Algebraic Theory of Architectures"
I am trying to read article "Categorical Deep Learning: An Algebraic Theory of Architectures" https://arxiv.org/abs/2402.15332 and I am stuck with the Chapter 2.1 "2.1. Monads and their ...
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Time Series Analysis and Price Elasticity
Introduction:
As of now, I am a fourth year data science student. As of now, I also have my own company where I work parttime (8/12 hours per week) to gain some more experience in the domain. As you ...
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Question on theory from original GBM article
I am reading the original gradient boosting machine article and, maybe because my statistics are a bit rusty, have a few questions on one section.
In section ...
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Continuous Function from Binned Data with Consistent Integrals
I have binned energy production data (in Wh) in 5-minute intervals. This means that, at the timestamp of t + 5 minutes, the value represents the amount of energy generated in the interval from t to t +...
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Dimenson reduction from a cosine similarity matrix
I have a silly little question:
I have 200 press articles (string), I vectorize these articles with an embedding model (sentence embedding), so I have 1024 values per article.
I then have a 200 x 1024 ...
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Discuss kNN, test/train, random projection, unit vector, vectored matrix, hamming distance, stft, Y=(aAX1:M)
Suggestion Investigation
Looking for suggestions or guide for how to setup a clean approach and discussion on how to apply a python suggested way to solve this challenge
Looking for suggestions or ...
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Inverse Probability Fallacy of Maximum Likelihood Estimation
How can we justify that the parameters estimated via Maximum Likelihood Estimation are the optimal parameters for the data, given that MLE involves computing the data's likelihood as a function of the ...
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Intuition Behind Xavier Initialization
I am trying to understand the intuition behind why xavier works. So far I have pieced togther that $Var(Z)=n_{in}*Var(X)*Var(W)$ and so if we want the variance to mitigate the variance diminishing ...
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Why do we use the RELU activation function?
I reading about activation functions in feedforward neural networks.
ad a really old paper https://web.njit.edu/~usman/courses/cs677_spring21/hornik-nn-1991.pdf.
They prove that by using arbitrary ...
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Gradient function in LogisitcLoss class
I am going through a code for XGBoost from scratch and I am referring to this repository here
The log-loss function is given by
On differentiating the above function with respect to y_pred (referring ...
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Why do all the resulting curves from my function combining N-many random ReLUs look like quadratics?
I've written a function that generates a sum of N-many RelU functions, with random slopes and activation points.
I was expecting these resulting functions to be arbitrary, random curves, but for some ...
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Which machine learning models are rational to use on NP-hard and NP-complete "theoretical" problems?
Time and time again I run into "surprising" NP-hard problems that seem naturally simpler than they are. I recently worked on a weighted graph theoretical problem where the point is to ...
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Why both ChatGPT and Bard can't get a simple matrix calculation right?
I asked the following question to both ChatGPT 4 and Bard to see if they can get a simple matrix calculation right (after all Bill Gates said he was impressed by ChatGPT's math ability).
So I asked,
<...
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Suggestions to learn the Machine Learning models in greater depth?
I've been learning machine learning for the past few weeks from books and online courses. The books I've been reading, and currently still reading is "Hands-On Machine Learning with Scikit-Learn ...
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RetNet Paper Multi Scale Retention dimemsion question
From the paper:
https://arxiv.org/pdf/2307.08621.pdf
But since X is of size n by $d_{model}$.
How can we compute $XW_Q$? Since the row length of X which is $d_{model}$ is not the same as the column ...
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How in the heck should I tackle this classification problem? I'm not even sure if it's classification or regression
So, I'm currently a third year student in electrical engineering and I'm currently enrolled in a Mathematical Modelling and Machine Learning class and we're currently tasked to classify or use ...
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Question regarding Lecture 5 CS229
I was at the part where we are using one covariance matrix and two mean vectors for fitting our Gaussian. I understood that we are using one covariance matrix and we can use different ones that would ...
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How to split a range of numbers considering other variables as well?
Let's say that I have a vector of numbers and I'd like to split it into 3 most optimal ranges for example, then I suppose I can use k-means or Jenks natural breaks. If I'd like to do the same thing ...
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Handling error when returning from log transform
Before training the model, I convert a target value to the log scale since range of the target is quite large.
After training the model, the Absolute Mean error was estimated as, for instance, 0.5.
If ...
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Problem for a math formula in Weight Uncertainty in Neural Network
I am studying the paper https://arxiv.org/pdf/1505.05424.pdf and there is a formula I don't get page 4:
I don't understand how they obtain this formula. Moreover, with chain rule, I get $\frac{\...
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How do you appropriately measure the real mean squared error of a box cox transformed linear regression model?
My understanding is that it can make sense to transform the outcomes of a linear regression model to make them more normally distributed. That's because it could 1) help me find more linear ...
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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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Advice in career path [closed]
I'm currently in Argentina without any type of degree and knowledge in the field of data, maths, programming. My career goal is to get a starting job from here (Argentina) and eventually with some ...
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What is degree assortativity coefficient of a complete undirected graph?
Because it computes the correlation coefficient of degrees and the correlation coefficient of constant arrays is not defined, networkx library returns ...
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Influence functions on neural networks: Help with understanding of result and derivation
I'm working through a paper titled "Understanding Black-box Predictions via Influence Functions" where they introduce the notion of influence functions from robust statistics to approximate ...
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Understanding the ResNet paper
I am having trouble understanding the mathematical meanings behind the notations in the ResNet paper:
I believe that the function we are trying to optimize is the residual which is denoted as $\...
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Chi-Sqare test and Continuous values
How does chi-square test work for continuous variables. I see that it is used in most papers to test dependencies between continuous explanatory variables and the target variable. Please how does this ...
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Fast Fourier Transform in computer vision
Can someone explain me how does FFT works in computer vision, please. I know something about FFT as an algorithm of competitive programming but I can't understand how it perform an image in computer ...
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In WGAN paper, why does clipping weights approximate Lipschitz function?
In Wasserstein GAN, it's explained that maximizing a certain formula over a set of K-Lipschitz functions approximates the 1-Wasserstein distance and they model the functions as NNs. That much I ...
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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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Matrix factorization approximate products to solve math solution
Problem
Matrix factorization for approximating products how do we solve such that Z approximates products N, M. How to define the math formula for solve for Z approximtaes the products of N,M?
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Can't find this book [closed]
I came across the most comprehensive ML Mathematics book (700+ pages) with sections on Probability, Calculus, Linear Algebra and Mathematical Foundations of the famous tricks in Deep Learning on ...
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Are there deterministic problems a neural network can't learn?
I have a software which takes 5 input numbers and outputs a number, deterministically. I want to try and mimic this software precisely with a neural network, but I am finding it very difficult. The ...
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How does dropout behave like model averaging?
It is claimed Srivastava, Hinton, et al. that "dropout can be effectively applied in the hidden layers as well and that it can be interpreted as a form of model averaging" and that "...
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A mathematician from the outside looking in
I am wondering if anybody could give a survey of applications of approximation theory to data science. One application I am familiar with are, for example, wavelet neural networks. Does anybody know ...
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Is it possible to extract mathematical expression of an trained ML Model?
In Python & R, Linear Regression model gives the mathematical representation after learning the training data, typically in the form of intercept, coefficients of variables, and the p-value/t-...
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What is the difference between classification and regression metrices such as accuracy and MSE? [duplicate]
What is the difference between classification metrics such as accuracy and regression metrics such as MPE? & Why can’t accuracy be used as regression metric?
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What is the difference between accuracy in percentage (classification metric) and MPE (regression metric) as evaluation metrices?
What is the difference between accuracy in percentage (classification metric) and MPE (regression metric) as evaluation metrices?
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what are the hot areas/future in computer science/machine learning in the next decade? [closed]
what are the hot areas in computer science/machine learning in the next decade ? I am interested in knowing this since deep learning/machine learning which dominated in the last decade has saturated ...
user141819
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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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