# 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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### 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 ...
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1 vote
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 ...
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1 vote
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### 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 ...
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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 ...
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 ...
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
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### 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: ...
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### 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
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
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 ...
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 ...
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 ...
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 (...
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1 vote
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### 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
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 ...
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 ...
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
123 views

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### 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 ...
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
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 ...
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 vote
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 ...
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### 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 ...
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
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. ...
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### 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 ...
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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: ...
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) . ...
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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) ...
37 views

### Understanding Kneser-Ney Formula for implementation

I am trying to implement this formula in Python $$\frac{\text{max}(c_{KN}(w^{i}_{i-n+1} - d), 0)}{c_{KN}(w^{i-1}_{i-n+1})} + \lambda(c_{KN}(w^{i-1}_{i-n+1})\mathbb{P}(c_{KN}(w_{i}|w^{i-1}_{i-n+2})$$ ...
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1 vote
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
• 109
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### 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
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 ...
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### 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 ...
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 ...
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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 ...
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 $[0, ∞]$?
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### 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 $$\bar x_i = \frac{x_i - \mu_B}{\sqrt{\sigma_B^2 + \epsilon}}$$...
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1 vote
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 ...
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 ...
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