Questions tagged [math]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1
vote
0answers
14 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
45 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
17 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, ...
1
vote
0answers
15 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
22 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
12 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^{(...
1
vote
0answers
23 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
22 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
76 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
17 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
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
86 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
2answers
46 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 ...
0
votes
1answer
27 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
37 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
1answer
26 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
17 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
1answer
35 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, ...
1
vote
1answer
53 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
25 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
34 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
43 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 ...
0
votes
1answer
23 views

How to calculate similarity between 2 users based on the images they share?

Say there are 2 users, A and B, and they each shared 10 images (in some social media site), which I have collected in 2 folders separately. I want to calculate the similarity between the 2 users based ...
0
votes
1answer
76 views

How to train neural network a math multiplication table?

I am trying to train neural network (brain.js) a multiplication table. It is not going too well: requires lots of hidden layers, iterations and very small error threshold, and the results are still ...
0
votes
0answers
9 views

Projecting 3D Chemical Data Onto a 2D Plane in Motion

I'm trying to model the rotation of two hydrogen atoms about a carbon atom. Say I have a conceptual wheel on an axle that is attached to my car. The axle is described by two points in 3D space, as ...
0
votes
0answers
149 views

How to convert google trend relative values into more “absolute” values?

Searching key words or terms on google trends provides a time series of relative search numbers. I want to be able to analyse these trends more accurately compared to general trends in the same ...
1
vote
2answers
43 views

The exact meaning of cost function ? (Machine Learning)

I'm reading the "Python Machine Learning" book by Sebastian Raschka, and we use different cost functions. For Adaline model (with a linear activation function) we use the MSE error : (Phi is the ...
2
votes
2answers
70 views

Formal math notation of masked vector

I'm struggling to write my algorithm in a concise and correct way. The following is an explanation for an optimizer's update step of part of a vector of weights (not a matrix in my case). I have a ...
2
votes
2answers
40 views

Notation for features (general notation for continuous and discrete random variables)

I'm looking for the right notation for features from different types. Let us say that my samples as $m$ features that can be modeled with $X_1,...,X_m$. The features Don't share the same distribution (...
0
votes
1answer
29 views

when x is a vector, derivative of vector diag(f'(x)) is formal notation?

https://web.stanford.edu/class/cs224n/readings/gradient-notes.pdf (4) this note says this $$ \frac{\partial \textbf{z}}{\partial \textbf{x}} = \text{diag}(f'(\textbf{x})) $$ I know this means make ...
-3
votes
2answers
261 views

Chain function in backpropagation

I'm reading a Neural Networks Tutorial. In order to answer my question you might have to take a brief look at it. I understand everything until something they declare as "chain function": ...
0
votes
1answer
15 views

Norm type in cost function of ANN

I'm reading a tutorial about ANN. They use the following cost function: As you can see this equation includes a norm. I'm new to the concept of norm. My question is what kind of norm they use here (...
1
vote
1answer
118 views

Relationship between log-odds and weighted sums in Logistic Regression

I've read several articles/tutorials on Logistic Regression and I've come across this idea of log-odds being equal to the weighted sum of features. i.e. if $p$ is the probability of a sample ...
0
votes
1answer
194 views

What is “position” in CNN (im2latex) for Positional Encoding?

I'm trying to build a model that maps images of math formulas into LaTeX markup. I found an acticle (https://arxiv.org/ftp/arxiv/papers/1908/1908.11415.pdf) that proposes an encoder-decoder ...
1
vote
1answer
88 views

Computing variance of an SGD iteration

It is known that SGD iteration has huge variance. Given the iteration update: $$ w^{k+1} := w^k - \underbrace{\alpha \ g_i(w^k)}_{p^k}, $$ where $w$ are model weights and $g_i(w^k)$ is gradient of ...
0
votes
1answer
23 views

When can you reorder log operations?

For example, you can reorder a softmax + nl (negative likelihood) to log_softmax + nll (negative log-likelihood) Essentially changing log(softmax(x)) to softmax(log(x)) However, what are the ...
1
vote
1answer
328 views

How are the channels handled in CNN? Is it independently processed or fused?

Let's assume that we are talking about 2D convolutions applied on images. In a grayscale image, the data is a matrix of dimensions $w \times h$, where $w$ is the width of the image and $h$ is its ...
1
vote
1answer
34 views

What level of math is required for machine learning research

There are several levels of math understanding: Know the math Know the intuitions behind math concepts Know the intuitions and proofs of math concepts Know the intuitions, proofs of math concepts and ...
2
votes
1answer
41 views

Encoding correlation

I have rather theory-based question as I'm not that experienced in encoders, embeddings etc. Scientifically I'm mostly oriented around novel evolutionary model-based methods. Let's assume we have ...
3
votes
1answer
769 views

Need of maxpooling layer in CNN and confusion regarding output size & number of parameters

In my CNN architecture for binary classification, I have 2 convolutional layers, 2 maxpooling layers, 2 batchnormalization operations, 1 RELu and 1 fullyconnected layer. Case1: When the number of ...
3
votes
1answer
646 views

How to find the various matrix sizes in designing a CNN

I am trying to understand CNN especially the maths and working mechanism using Matlab as the coding language. I have few confusion regarding the concept and the associated programming and will be ...
0
votes
1answer
48 views

Why multiply by 2 when calculating partial derivatives during backpropagation?

I'm wondering why we multiple by 2 when calculating partial derivatives. I'm referencing the 2's that I've circled below, from here. We also see this in the python implementation, ...
1
vote
0answers
13 views

Question regarding: Vectorization Math of Backpropagation in a Neural Network

Formula: These are the formula I use for backpropagation from Brilliant: Question: If we consider a Neural Network with the structure (3,2): And we would start calculating the derivative (for 1 ...
0
votes
1answer
51 views

Python - Appending a new Dataframe column that is a function of two separate numerical columns

I have a dataset that gives me the geographic coordinates of residential properties. My goal is to append a new column to this dataframe that shows the properties' distances to various prominent ...
0
votes
1answer
1k views

Does this line in Python indicate that KNN is weighted?

Does this line in Python indicate that KNN is weighted? clf = KNeighborsClassifier(n_neighbors=5, metric='euclidean', weights='distance') Are the weights the ...
1
vote
0answers
26 views

How to Manually Classify using SVM?

Consider points x1 = (1,1), x2=(1,0), x3=(1,-1) from class C1 and points x4 = (-1,1), x5=(-1-1) from class C2. Classify the given data with SVM How do we manually classify data by finding the ...
0
votes
1answer
72 views

Can continuous dataset have negative values? [closed]

As in the description, I want to choose continuos dataset with temperatures and the minimun value is -40 and maximum is 51. Is that OK? Can we have negative values in continuous distribution?
1
vote
0answers
93 views

Transitioning from Math PhD to ML research [closed]

I am currently a Math PhD about to defend in January. I work in a field in functional analysis that uses a lot of measure theory (but no stats). I have been considering transitioning careers since I ...