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
1answer
22 views

How does TensorFlow compute gradients of nonelementary integrals?

I was reading about custom activation functions, autodiff etc, trying to understand it all. I think I have a glimpse of it now, but right after closing the book I thought "what about the ...
2
votes
0answers
41 views

Understanding the math behind linear classification [closed]

For example we have $X$ train data, $y$ and $w$ Our margin is $M = y_i \langle w, x_i \rangle$ If $M_i > 0$ classifier return True predict and otherwise, if $M_i < 0$ we get False predict. How ...
-1
votes
1answer
23 views

Why do we use 'T' when we are to say matrix-vector product? [closed]

On the first picture author uses $T$ meaning matrix-vector product But other website do not use $T$, but says that $x$ is a vector, I do not understand if it is important or not
1
vote
1answer
24 views

What are the math Prerequisite for understanding 'First Order Motion Model for Image Animation' Paper?

This is the 'First Order Motion Model for Image Animation' Paper. But I don't understand most of the mathematical things in the paper. What are the math Prerequisite for understanding this paper?
0
votes
0answers
12 views

Can transformers be used to solve for a number of independent polynomial inequalities or polynomial equations?

I'm interested in solving constraint satisfaction problems involving polynomial functions of real variables using transformers. The papers available only deal with boolean SATs in CNF format e.g., ...
0
votes
0answers
12 views

prove E[(TSS - RSS)/p] > $\sigma^2$ in multiple linear regression

In Intro to statistical learning, Chapter-3 for Linear Regression, in the subsection 3.2.2 , Unit "One: Is There a Relationship Between the Response and Predictors?" , it is mentioned that: ...
1
vote
0answers
11 views

Incorrect derivative [duplicate]

Currently I'm reading a book named "Grokking Deep Learning" and I'm confused with the way author takes derivative from function. Let me explain. We have loss function, where pred is ...
1
vote
0answers
26 views

How to compare two one hot encoded data frames based on column names?

I have two datasets with shapes (329, 159) and (26,24). Both of them are one-hot encoded. The columns in the smaller dataset are present in the larger dataset. The smaller dataset has scores that I ...
1
vote
0answers
31 views

Real distance between bounding box centers

Assume that I have a camera pointing in a specific direction. I know the Euclidean distance (Real world distance) of the camera to a fixed point, X (mm). Using ...
1
vote
1answer
50 views

Is there such thing as linear and non-linear data?

While doing machine learning projects we've heard that logistic regression works well with "Linear data" and decision tree works well with "non-linear data" However concept of ...
1
vote
0answers
15 views

What are the best methods to analyze the results of a pairwise comparison survey?

I have recently conducted as survey where I was comparing a range of different images. Due to screen size constraints I decided to display these images pairwise and ask the participants to pick one of ...
0
votes
1answer
28 views

Non-commutative distance formula

I am trying to find a distance formula or a method that can give the non-commutative distance between two points in a feature space. Suppose there are two movies represented in an R^n feature space. ...
0
votes
0answers
22 views

What Math is required to learn Policy Gradients (Part of Reinforcement Learning)?

That seems a lot of Math... So, in order for me to understand it... What topics of math should I learn? Or to summarize: What is the math prerequisite to learn Policy Gradients?
1
vote
1answer
42 views

Is there a theorem of prominent Russian mathematicians that played an important role in the development of machine learning? [closed]

I once attended a seminar in which a statement answering the question asked above was answered in the affirmative. I do not recall further specifics, however.
0
votes
1answer
61 views

Implementing the Trapezoid rule without the formula for the curve

I know that if I have some function f(x) that describes a curve, I can approximate the area under the curve using the trapezoid rule as follows: ...
1
vote
0answers
21 views

Are convolutions in deep learning associative?

Let's denote "convolution in deep learing" as "convolution-deep", and "convolution in math or signal processing" as "convolution-math". As we all know, ...
0
votes
1answer
89 views

Importance of normal Distribution

I have been reading about probability distributions lately and saw that the Normal Distribution is of great importance. A couple of the articles stated that it is advised for the data to follow normal ...
0
votes
0answers
20 views

Derivation of HiddenState wrt Output of LSTM

I'm busy trying to understand the math behind LSTM RNN's. In most of the math tutorials that I've found the derivations (Backpropagation) don't consider a dense layer before the output, instead they ...
0
votes
1answer
25 views

Math of Logistic regression cost function

In the current scikit-learn documentation for binary Logistic regression there is the minimization of the following cost function: $$\min_{w, c} \frac{1}{2}w^T w + C \sum_{i=1}^n \log(\exp(- y_i (X_i^...
1
vote
0answers
16 views

KNN with high-variance data [closed]

KNN doesn't work well with high-variance data, so how should I fit my data? Here is an example of what the data looks like:
2
votes
0answers
26 views

Geometric classification models

In class we have been presented with a Geometric classification model such that the goal is to construct a linear decision boundary $\bf{w} \cdot \bf{x} = t$; where $\bf{w}$ is the vector from the ...
0
votes
0answers
16 views

Notation of Transposed Convolution Operation in Equation

How do I notate a transposed convolution operation (as it is used in deep learning), in a math equation? A convolution operation for example is often notated as $\hat{y} = x \circledast W$ where $W$ ...
1
vote
0answers
6 views

Error term in probabilistic interpretation of least squares update rule

I have read in Stanford's CS229 course notes that to justify the least-squares update rule with probability, the following is assumed: $$y^{(i)} = \theta^Tx^{(i)}+\epsilon^{(i)}$$ , where $\epsilon^{(...
2
votes
1answer
19 views

How do you calculate the number coefficients in polynomial regression?

So I can't seem to find much on this by searching so I came here. Let's say I had 3 variables $x_1,x_2,x_3$ and the let's say the degree of the polynomial was $d=2$, I can define the length of a ...
1
vote
0answers
32 views

Custom Loss Function Equation

I am trying to reproduce a research paper, where it is a classification problem, and they have introduced a custom loss function that I am unable to understand. Now I think I have to implement the ...
0
votes
0answers
35 views

F-Value P-Value T-Value linear regression interpretation

The following is what I found and understood and put in use without really understanding the logic behind it! The t-value measures the size of the difference relative to the variation in your sample ...
1
vote
1answer
57 views

What is a distribution-wise asymmetric measure?

I was trying to understand KL-Divergence, $$D_{KL} \langle P(X) \Vert P(Y) \rangle,$$ and was going through its Wikipedia article. It says the following In contrast to variation of information, it is ...
1
vote
1answer
84 views

SVM - Making sense of distance derivation

I am studying the math behind SVM. The following question is about a small but important detail during the SVM derivation. The question Why the distance between the hyperplane $w*x+b=0$ and data ...
0
votes
1answer
19 views

Estimate the location of an object in a field using computer vision and math

I'm trying to see how to detect the location of a soccer ball in the field using the live camera. What are some ways to achieve this? At this point I'm more interested in ideas and thoughts and not ...
1
vote
0answers
15 views

Normalise the scores by small and large numbers division

I am working on a scoring problem use-case where I will score each task based on few aspects and take an average of scores of tasks in each experiment. For each experiment I will have 1 to N number of ...
1
vote
1answer
55 views

Decision boundary in a classification task

I have 1000 data points from the bivariate normal distribution $\mathcal{N}$ with mean $(0,0)$ and variance $\sigma_1^2=\sigma_2^2=10$ with the covariances being $0$. Also there are 20 more points ...
-1
votes
1answer
21 views

Trouble understanding some parts of machine learning [closed]

I am new in this field. I took one of the many courses “Introduction in Machine Learning” and realized that I have a problems with some parts of the machine learning like “Metric methods ”, “Linear ...
1
vote
0answers
188 views

Backpropagation Mathematics with Sigmoid Output Activation and Cross Entropy Loss

I am deriving a Weight update for a simple toy network with a Sigmoid Output Layer. I need some help double checking my math to make sure I did it correctly. I am using Cross-Entropy Loss as my Loss ...
1
vote
1answer
61 views

Use heading in Neural Network model

I am working on a prediction model where I must find out the destination of a boat based on its actual coordinates and heading (compass direction) : ...
1
vote
2answers
65 views

Transforming data points to match other data points

I have two sets of data points, set A and set B. Each point of both sets has two dimensions $(x, y)$. Consider the set $A$ to be the orange set on the left of the image below and $B$ to be the blue on ...
2
votes
1answer
486 views

Find periodicity of a signal using python

I have a dataset that contains occurrences of the Kettle in a single-occupancy house for the duration of a month. In this dataset, ‘ts’ column indicates the unix-timestamp (this can be converted to ...
0
votes
1answer
29 views

Understanding the algebra behind a specific partial derivative equation

I am following this article about neural networks. Given: Until here I understand everything, but then he continues to: I don't understand how he got to that conclusion. I think he skipped some ...
0
votes
0answers
38 views

What loss term might enforce interpretability?

A neural net can be interpreted as a weighted directed graph. Interpretability of this neural net could be measured using properties of that graph. In particular, "modularity" might be ...
0
votes
2answers
543 views

Python - accessing dictionary values for math operations [closed]

I have this dictionary: stocks = {'FB': 255, 'AAPL': 431, 'TSLA': 1700} and this script: ...
0
votes
1answer
36 views

What do the symbols in this image mean in relation to autoencoding? (which concepts do they represent and why?)

I'm completely new to neural nets, and am trying to get a grasp of autoencoding. I understand the function of the decoder and encoder, but what does the arg min section and beyond mean? Why is it ...
0
votes
0answers
13 views

Calculating probability from a distribution

I have a histogram/count plots of average time a property is in the market. Given this distribution, I'd like to calculate the probability that a similar property will be leased within 'x # of weeks' ...
0
votes
0answers
18 views

Weighted Conditional Expectation in AdaBoost

I am looking at "Additive logistic regression a statistical view of boosting" paper (https://web.stanford.edu/~hastie/Papers/AdditiveLogisticRegression/alr.pdf) In page 346, the authors ...
1
vote
0answers
48 views

AdaBoost.R2 learning rate from scikit learn

AdaBoost.R2 (regression), is presented in the paper "improving regressors with boosting techniques" from Drucker and is freely available on Scholar. The implementation of regression for ...
1
vote
1answer
36 views

What is lagrangian?

I'm watching an SVM tutorial. At 6:38 he mentions lagrangian, which is a term I'm not familiar with. So I googled it, hoping to find the Wikipedia article about it, ...
0
votes
0answers
80 views

How does Batch normalization help optimization? Proof

I am reading the paper How Does Batch Normalization Help Optimization found here. $\newcommand{\norm}[1]{\left\lVert#1\right\rVert}$ But I am having trouble understanding the proof of the paper. It's ...
1
vote
1answer
55 views

Why Adaboost SAMME needs f to be estimable?

I am trying to understand the mathematics behind SAMME AdaBoost: At some stage, the paper adds a constraint for f to be estimable: I do not understand why this is ...
1
vote
1answer
30 views

Mathematics: Writing down a three-class classifier confusion matrix

Confusion matrix 2A three-class classifier is evaluated on a test set of 900 samples which containsall three classes in equal proportions. ...
1
vote
1answer
36 views

Fully-Connected DNN: Compute the numbers of free parameter in a DNN

A fully-connected DNN has layer sizes of 3-3-4-2, where the first layer size represents the input layer. We assume that all layers are affine ones (no ReLU). Give the dimensions of all weight matrices ...
1
vote
1answer
44 views

Mathematics: Can the result of a derivative for the Gradient Descent consist of only one value?

I have a problem of a task using the formula of the Gradient Descent: Perform two steps of the gradient descent towards a local minimum for the function given below, using a step size of 0.1 and an ...