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.

Filter by
Sorted by
Tagged with
0 votes
0 answers
18 views

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 ...
  • 101
1 vote
0 answers
12 views

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 ...
  • 11
1 vote
1 answer
85 views

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 groups with devices have an event occur. Since we know that correlation isn't causation, I can't ...
  • 63
0 votes
0 answers
14 views

Why do you need more subjects than levels in RM ANOVA?

Honestly, I'm hoping I even asked this question appropriately. It's one of those things I never quite grasped, but just accepted to be true, that when running a within-subjects ANOVA, you have to have ...
0 votes
0 answers
8 views

Rotate vector anticlockwise

I'm learning mathematics for Machine Learning, and there given a vector [ 1 0 ] and [ 0 1 ]. The vector is packed on a matrix, ...
0 votes
0 answers
14 views

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? ...
0 votes
0 answers
8 views

Plus sign inside circle, there seem to be many meaning. Are they all related?

In Linear algebra plus sign inside a circle refers to direct sum. In a paper "Towards Neural Mixture Recommender for Long Range Dependent User Sequences" it seems to refer to concatenation. ...
  • 385
0 votes
0 answers
19 views

How to replicate MMCV conv layer with integrated batch norm using PyTorch

Question How do I replicate the following convolution layer from MMCV using PyTorch? I cannot find any reference in the MMCV docs on how norm_cfg works. ...
  • 46
0 votes
0 answers
14 views

Can I describe likelihood of prediction model using P(D | theta)?

Generally, to optimize model using MLE, you should find $\theta$ that maximizes $P(D | \theta)$. In prediction model that gets input and predicts output, you should find $\theta$ that maximizes $P(Y|X,...
0 votes
1 answer
36 views

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 ...
0 votes
0 answers
27 views

Mathematics for Machine Learning by A. Aldo Faisal is too abstract for machine learning?

I'm currently studying mathematics to jump into machine learning courses, and I'm taking the mathematics for machine learning specialization on Coursera while simultaneously reading the mentioned book....
2 votes
3 answers
51 views

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 ...
  • 31
0 votes
1 answer
32 views

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 "...
  • 1
1 vote
0 answers
33 views

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 ...
  • 111
1 vote
1 answer
23 views

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-...
0 votes
0 answers
13 views

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?
0 votes
1 answer
26 views

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?
0 votes
0 answers
16 views

compare decision tree vs extended gradient boosting mathematically?

If we want to compare decision tree vs extended gradient boosting vs xgboost mathematically, what are their differences?
  • 1,754
0 votes
0 answers
12 views

If a machine learning model can be trained to obtain B from A, and another to obtain C from B, could a final model obtain A from C?

I've recently been working on a regression model based on some physics to obtain some numbers C from a set of features A, although with little success. Knowing that the formula that relates A to C ...
0 votes
1 answer
40 views

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 ...
user avatar
-1 votes
1 answer
66 views

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 ...
0 votes
0 answers
17 views

Journals to publish a proof of a math result used for neural-network algorithms

I would like to know which journal is an appropriate outlet for the results described below. I recently came across a particular neural-network training algorithm. The algorithm is based on a result ...
  • 1
1 vote
1 answer
23 views

Why there is so few research on neural code of artificial neural networks and are there alternatives to the neural code approach?

I feel that the neural code/neural coding (how neurons or biases enode the symbolic concepts of the chains of concepts, e.g. each feature is chain of symbolic functions and their parameters) is the ...
  • 131
1 vote
0 answers
58 views

What is the meaning about the $\alpha$ in TD3 algorithm

I am study the paper with TD3 algorithm. I am curious about the meaning of $\alpha$ while the paper prove that overestimation will be happened in a critical situation. The contents about mathematical ...
  • 11
2 votes
0 answers
26 views

Discretize interval into fixed number of bins while minimizing error

Background I have been working on an optimization problem related to the following function: $$ y = f(x) = c_{1}(1-e^{-c_{2}(x-x_{0})})^{2}$$ where $c_{1}$, $c_{2}$ and $x_{0}$ are constants. Assume ...
0 votes
0 answers
17 views

How do Neural Networks take advantage of Tensor Contraction?

I'm trying to write a Convolutional network that runs on a Compute Cluster. I've already written a DNN using basic matrices, and need to start working with higher-order data structures. I've come ...
0 votes
0 answers
12 views

Sigmoid Cross Entropy Implementation Min Value

When looking through the TF API docs I was reading the Sigmoid Cross Entropy Implementation I wanted to do a sanity check by checking the min/max value of the function which should be 0 loss at each ...
  • 245
0 votes
0 answers
20 views

How to find the exponent in Zipf's Law?

Currently I am following the online d2l.ai book and I am stuck doing the exercise 2 of chapter 9.2. . The question is: ...
0 votes
0 answers
15 views

Test statistic (t-test or z-test)

Suppose we have some data of person's reaction time after drinking energy drink, that is: r = c(22.04, 22.16, 21.47, 22.99, 21.99, 22.94, 22.47, 21.46, 24.23, 22) Assume that the average reaction ...
1 vote
0 answers
18 views

Resources for Symbolic Regression

What are some good resources/recommendations related to symbolic regression? (In terms of predicting analytic mathematical equations from neural networks)
1 vote
1 answer
24 views

How do we derive our loss function from the gradient objective?

I've been dwelling through RL theory and practice and one particular part I find hard to properly understand is the relation between the practical loss function and ...
0 votes
1 answer
12 views

How can I transform or plot my data to see power consumption more easily?

I have two heating tapes installed in my setup and they provide heat to maintain the reaction at a certain setpoint temperature. Basically, the heating tapes go on a cycle of on/off to maintain the ...
0 votes
0 answers
13 views

Application of eigenvalues, eigenvector, transposed matrix

Can you give me please some application of eigenvectors, eigenvalues and matrix transposition in data science? I guess for eigen-values/vectors it would be linear regression PCA and NLP, alongside ...
0 votes
0 answers
10 views

Zernike moment calculations

I am trying to work with Zernike moments and am after all my efforts not able to understand a few things. Following is the formula I found in literature: I cannot understand what the impact of p (...
  • 21
1 vote
1 answer
16 views

Problem understanding the forward algorithm for HMMs

I found a recursive version of the forward algorithm on wikipedia, however I don't understand the notation given in the pseudocode: What means $$x_{t-1}$$ under the summation sign? What do I need to ...
  • 131
1 vote
0 answers
25 views

ML techniques for mathematical inverse approximations

I have some inputs and outputs of a set of functions, and I want to be able to find/approximate any given input vector from its corresponding output vector (In other words learn the inverses of these ...
0 votes
0 answers
11 views

combining two dataset

My question is simple, is there any condition or methodology to combine two different datasets? In a nutshell, I have two different studies with different variables that I would like to combine in ...
0 votes
0 answers
11 views

How would I check the validity of covariates in my linear model on several hundred datasets?

I have this linear model with predictors that I need to prove are statistically significant and pass the necessary lm assumptions. I know for a single dataset, I can use various LM tests, but the ...
1 vote
1 answer
403 views

Understanding SGD for Binary Cross-Entropy loss

I'm trying to describe mathematically how stochastic gradient descent could be used to minimize the binary cross entropy loss. The typical description of SGD is that I can find online is: $\theta = \...
  • 13
1 vote
1 answer
269 views

Derivative of MSE Cost Function

The gradient descent: $\theta_{t+1}=\theta_t-a\frac{\partial}{\partial \theta_j}J(\theta)$ But specifically about $J$ cost function (Mean Squared Error) partial derivative: Consider that: $h_\theta(x)=...
0 votes
0 answers
35 views

Is it possible for the (Cross Entropy) test loss to increase for a few epochs while the test accuracy also increases?

I came across the question stated in the title: When training a model with the cross-entropy loss function, is it possible for the test loss to increase for a few epochs while the test accuracy also ...
0 votes
0 answers
37 views

using logsumexp in softmax

I saw this equation in somebody's code which is an alternative approach to implementing the softmax in order to avoid underflow by division by large numbers. softmax = e^(matrix - logaddexp(matrix)) = ...
  • 339
0 votes
0 answers
9 views

Growth Edge in Link Prediction

I have 2 CSV files representing edge in social networks in 2 consecutive generations. I am trying to predict future edges. My initial tough is to train a linear regression on the first generation with ...
0 votes
0 answers
22 views

Geometric Deep Learning - G-Smoothing operator on polynomials

(Note: My question resolves about a problem stated in the following lecture video: https://youtu.be/ERL17gbbSwo?t=413 Hi, I hope this is the right forum for these kind of questions. I'm currently ...
  • 1
1 vote
0 answers
16 views

Structured policies in dynamic programming: solving a toy example

I am trying to solve a dynamic programming toy example. Here is the prompt: imagine you arrive in a new city for $N$ days and every night need to pick a restaurant to get dinner at. The qualities of ...
0 votes
0 answers
9 views

Efficient Searching for a basis of information as a hyperparameter in a large possible hyperparameter space

I have a set of inputs, let's call them 'I', that can be fed through a complicated group of functions to produce/calculate a wide variety of outputs (let's call them 'O'). I want to find a subset of ...
0 votes
1 answer
44 views

Strategies for complicated inverse function approximation

I have a dataset G. There is a complicated set of mathematical functions I can use to calculated the values 'W' for any given point in G. f(G) $\rightarrow$ W To the best of my knowledge these ...
1 vote
1 answer
32 views

Confused on Naive Bayes classifier

In the last part of Andrew Ng's lectures about Gaussian Discriminant Analysis and Naive Bayes Classifier, I am confused as to how Andrew Ng derived $(2^n) - 1$ features for Naive Bayes Classifier. ...
2 votes
1 answer
24 views

How to measure statistical similarity or discrepancy between a dataset and a distribution?

Is any way to measure statistical similarity or discrepancy between a dataset and a distribution? I have do some research, but find most of method are intended to describe discrepancy between data and ...
  • 21
0 votes
1 answer
307 views

what exactly is the "order"-parameter in pandas interpolation?

what exactly is the "order"-parameter in pandas interpolation? it is mentioned in the doc: ...

1
2 3 4 5