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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12 views

Finding clusters of 2D points when the metrics changes with spatial spread of points in each cluster (i.e., clustering output)

I am trying to calculate (a given number of) clusters of 2D points. However, I can't apply any conventional algorithm I'm aware of, such as k-means, as I need the clustering metrics to depend on the ...
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1answer
42 views

How do I minimizie cost for EV charging?

I want to find a charging schedule that minimize cost of charging an EV. The main objective is to have a fully charged car for the next morning, but the sub objective is to minimize cost based these ...
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1answer
34 views

Summarize 3 variables into one and calculate a „skill“value + ranking

I have a data set that looks like this: Name Top Speed Number Sprints Cumulative Sprint distance Xyz 55 300 33.3 Xyz123 45 350 32.0 Top Speed is in km/h. Cumulated Sprint distance is in km. Number ...
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1answer
39 views

Why does stochastic gradient descent lead us to a minimum at all?

Why do we think that stochastic gradient descent is going to find a minimum at all? I mean on each iteration SGD moves in the direction that reduces only current batch's error (SGD doesn't care about ...
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0answers
6 views

Sequential batch processing vs parallel batch processing?

In deep learning based model training, in general batch of inputs are passed. For example for training a deep learning model with [512] dimensional input feature vector, say for batch size= 4, we ...
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4answers
940 views

Do you actually need math for your data science job?

I am a physicist working in a data scientist role. I was told everywhere that my degree is a very good starting point because I know a lot of math and it is crucial for this job. But other than ...
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2answers
755 views

Which is meant by +/-9.2e18 years in timespan?

I was able to convert the 9.2e18 AD to a date, but I am confused about the exact date. Which date is 9.2e18 AD and and 9.2e18 BC? Time span (absolute) - [9.2e18 BC, 9.2e18 AD] i.e +/- 9.2e18 years ...
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1answer
25 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 ...
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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 ...
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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
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1answer
29 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?
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13 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., ...
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41 views

What is the purpose of defining such measure as metric or non-metric?

proximity measures can be metrics or non-metrics. the following criteria defines a metric dissimilarity measurement: here is for a metric similarity measurement I would like to know the consequences ...
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0answers
70 views

Creating neural network to solve for equations

I have a dataset like: The v1 variable is a mathematical expression. Currently, I am using hyperopt to solve for these parameters and am using v1,v2,v3 in regression to predict y and then minimize ...
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0answers
15 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: ...
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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 ...
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0answers
29 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 ...
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0answers
94 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 ...
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1answer
57 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 ...
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0answers
16 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 ...
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1answer
35 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. ...
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24 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?
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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.
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1answer
106 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: ...
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0answers
22 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, ...
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1answer
50 views

Derivative of a custom loss function with the logistic function

I have costum loss function with $\mu ,p, o, u, v$ as variables and $\sigma$ is the logistic function. I need to derive this loss function. Due to multiple variables in the loss function, I need to ...
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1answer
154 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 ...
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0answers
21 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 ...
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1answer
40 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^...
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0answers
17 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:
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27 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 ...
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20 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 $W$ ...
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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^{(...
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1answer
24 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 ...
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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 ...
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0answers
38 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 ...
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1answer
68 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 ...
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1answer
89 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 ...
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1answer
21 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 ...
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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 ...
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1answer
60 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 ...
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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 ...
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0answers
295 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 ...
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1answer
64 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) : ...
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2answers
73 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 ...
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1answer
602 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 ...
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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 ...
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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 ...
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2answers
852 views

Python - accessing dictionary values for math operations [closed]

I have this dictionary: stocks = {'FB': 255, 'AAPL': 431, 'TSLA': 1700} and this script: ...