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
-1 votes
0 answers
24 views

Difference between Classification and Feature extraction as mathematical problems

I try to understand what is the difference between Classification and Feature extraction as mathematical problems. How i think it works: Assume that we have K scenarios. In classification we try to ...
  • 1
1 vote
1 answer
18 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
49 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
24 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
8 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
7 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
11 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
9 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
17 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
20 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
7 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
14 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
20 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
10 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
8 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
123 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
120 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
15 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
16 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)) = ...
  • 309
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
14 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
31 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
23 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
20 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
113 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: ...
0 votes
0 answers
73 views

Why NMF use frobenius norm?

I read about using NMF for recommendation systems. (Non-negative matrix factorization for recommendation systems) NMF tries to minimize Frobenius norm of (V - WH) . ...
0 votes
0 answers
18 views

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) ...
3 votes
0 answers
37 views

Understanding Kneser-Ney Formula for implementation

I am trying to implement this formula in Python $$ \frac{\text{max}(c_{KN}(w^{i}_{i-n+1} - d), 0)}{c_{KN}(w^{i-1}_{i-n+1})} + \lambda(c_{KN}(w^{i-1}_{i-n+1})\mathbb{P}(c_{KN}(w_{i}|w^{i-1}_{i-n+2})$$ ...
  • 237
1 vote
1 answer
28 views

Ridge regression terms [closed]

Can anybody let me know the definition of these terms? I know we solve this for Beta but I want to have the definition
0 votes
0 answers
10 views

Random number generator and JL lemma

Suppose we are given access to a random number generator U, which generates independent random real variables distributed uniformly in the range [0,1). Show that this can be used to produce an ...
1 vote
2 answers
101 views

Does T-test requires Standard deviation or variance for calculation

Might be a novice question, but the main difference between a t-test and z-test, I was able to understand, is that the z-test calculation requires the SD value of the sample where as in a t-test, we ...
  • 183
0 votes
0 answers
5 views

straight line or going down

I want to cluster data points based on the pattern ( six points each )so if it is going down or straight line or going with ups and downs! do you have any ideas how can I achieve it accuratly, I tried ...
0 votes
0 answers
14 views

Understanding the step of SGD for binary classification

I cannot understand the step of SGD for binary classification. For example, we have $y$ - true labels $\in \{0,1\}$ and $p=f_\theta(x)$-predicted labels $\in [0,1]$. Then, the update step of SGD is ...
  • 101
2 votes
2 answers
34 views

What are the mathematical topics that I need for Machine Learning & Data Science? [duplicate]

I would like to start studying ML & DS, but I feel I am a bit lost, so I don't really know what to study, what the prerequisites are, I mean I know I should study linear algebra, calculus, and ...
0 votes
1 answer
121 views

Converting similarity value into a dissimilarity value

Suppose we have similarity values between some data point in the interval $[0, 1]$. How can I transform this similarity values into a dissimilarity values in the interval $[0, ∞]$?
  • 121
0 votes
1 answer
67 views

Equations in "Batch normalization: theory and how to use it with Tensorflow"

I read the article Batch normalization: theory and how to use it with Tensorflow by Federico Peccia. The batch normalized activation is $$ \bar x_i = \frac{x_i - \mu_B}{\sqrt{\sigma_B^2 + \epsilon}} $$...
1 vote
1 answer
36 views

How important is real analysis/measure theory to this field? [closed]

I am a college student, struggling to decide whether or not to take pure maths electives on topics such as real analysis and measure theory. If I were to take them then I would definitely have to ...
2 votes
0 answers
58 views

Deriving VIF equation from the matrix form of Least Squares equation

I have been working through the derivation of the formula used to calculate the Variance Inflation Factor associated with a model. I am hoping to start with the Least Squares equation as defined in ...
  • 81
0 votes
0 answers
54 views

Reinforcement learning policy gradient derivation

I was reading a document about Reinforcement Learning policy gradient http://web.stanford.edu/class/cs234/CS234Win2019/slides/lnotes8.pdf when I encountered this expression $ \nabla_{\theta} \mathbb{...
1 vote
0 answers
75 views

Association rules - Find 100% confidence rules [closed]

Suppose there are 100 items, numbered 1 to 100, and also 100 baskets, also numbered 1 to 100. Item i is in basket b if and only ...
1 vote
0 answers
18 views

GloVe dot product optimized for non-comutative data whilst the operation itself being commutative

To my current knowledge, GloVe word vectors dot product are optimized to be the w_i ⋅ w_j = log⁡(P(ⅈ|j)) The probability being computed from a cooccurance matrix. However, dot product is a commutative ...
  • 23
0 votes
0 answers
24 views

Is Regression Line an 1-D affine subspace of 2-D vector space?

Background I currently read a book called "Mathematics for Machine Learning" and I read chapter 2 which is about Linear Algebra, especially on subchapter 2.8 which is about Affine Space. The ...
0 votes
0 answers
7 views

Clustering features of a class based upon the difference between features of a reference class and the particular class across multiple datasets?

I want to separate (generalized separation) the features of several classes based on the difference between the features (floating point values) of the particular class and a reference class across 7 ...
1 vote
0 answers
21 views

Right way to compare model scores for Next Best Action

I have around 15 classification models for different products built in different ways (some are RF, some are Gradient Boosting, some were downsampled in one way, others in other way, some are built in ...
0 votes
1 answer
10 views

The formula of loss function uses '(i)' as power of expected and real variables. What does that mean?

In the formula below, could one understand $y^{(i)}$ as $y_i$ ? If not, what is the fundamental difference ? $$ j(\theta_0, \theta_1) = \frac{1}{2m}\sum_{i=1}^m(h_{\theta}(x^{(i)})-y^{(i)})^2 $$
0 votes
0 answers
12 views

transforms in mathematical equations

How to write transform model in mathematical equations, from the start to the end, that's include the formula of y^. instead of coding and visualizations I'm looking for the mathematical equations, as ...

1
2 3 4 5