Questions tagged [math]

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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
24 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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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 ...
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1answer
23 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 ...
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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' ...
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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 ...
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1answer
31 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, ...
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1answer
43 views

Why Adaboost SAMME needs f to be estimable?

I am trying to understand the mathematics behind SAMME AdaBoost: https://web.stanford.edu/~hastie/Papers/samme.pdf At some stage, the paper adds a constraint for f to be estimable: I do not ...
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1answer
23 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. ...
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1answer
27 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 ...
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13 views

Are the equations following equations derived for the delta of weights in back propagation correct?

Specifically, I am wondering about summing the partial derivative of error in relation to the previous node's output for all superseding layers. My network is a 4 layer feed forward network; layer one ...
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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 ...
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1answer
20 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 ...
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1answer
26 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 ...
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0answers
8 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 ...
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20 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 ...
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2answers
39 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 ...
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2answers
60 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 ...
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2answers
19 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 (...
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1answer
24 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 ...
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2answers
176 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": ...
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1answer
13 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 (...
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1answer
34 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 ...
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84 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 ...
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8 views

how to write a learning set with different element indexes?

we assume we have a set $U=\{u_1,...,u_N\}$ , a set $T=\{u_1,...,t_M\}$ and a set $E=\{e_1,...,e_P\}$. I'm going to write down the training set mathematically to a learning machine, the size of ...
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1answer
22 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 ...
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1answer
53 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 ...
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11 views

What is the difference between “letter”-dimensional vector types?

What is the difference between D-dimensional vectors and S-dimensional vectors? Are there any other "letter"-dimensional vectors which one should be aware of? I am reading about occupancy modeling ...
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1answer
28 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 ...
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1answer
32 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 ...
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1answer
250 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 ...
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0answers
25 views

How to calculate precision and recall?

There is a class-imbalanced labeled dataset with 100'000 samples. 90'000 is "0" and 10'000 is "1". There is a model that predicts the labels. It was runned on the class-balanced (10'000 of "0" and 10'...
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1answer
254 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 ...
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1answer
36 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, ...
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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 ...
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8 views

What is the best approach (and why) to identify a conic section given the the points along its cross-section and its vector magnitudes over time?

I have an N-body simulation that calculates the position, velocity, and acceleration of each body at every frame over the course of some duration. As an example, I tested the algorithm using our solar ...
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1answer
31 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 ...
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1answer
410 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 ...
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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 ...
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1answer
33 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?
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24 views

Static and Dynamic neural networks process

Neural networks can be classified into static (convention feedforward networks) and dynamic categories (RNN, LSTMs). ...
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72 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 ...
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0answers
43 views

Convergence speed of perceptron algorithm

I was reading the convergence proof for the perceptron algorithm. It says under the assumption that there are some $R$, $\theta^*$ with $|\theta^*| = 1$ and $\gamma > 0$, such that $y_t(x_t\cdot \...
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16 views

Is this interpretation of spectral normalisation mathematically correct?

Hello everyone, this is my first post. I was thinking about the mathematical interpretation for spectral normalization in neural networks the other day, and I came up with an explanation that feels ...
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1answer
40 views

SVM hyperplane margin

so that $H_0$ is equidistant from $H_1$ and $H_2$. However, here the variable $\delta$ is not necessary. So we can set $\delta=1$ to simplify the problem. $$w\cdot x+b=1 $$ and $$w\cdot x+b=−1$$ Why ...
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2answers
496 views

Solving Bayes Theorem equation -> I can't calculate proper result

I am solving questions for an edx course on Machine Learning. One particular question is giving me a problem: Assume a patient comes into the doctor’s office to test whether they have a particular ...
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2answers
420 views

Understanding REINFORCE loss

The loss used in REINFORCE algorithm is confusing me. From Pytorch documentation : loss = -m.log_prob(action) * reward We want to minimize this loss. If a ...
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2answers
150 views

Skew and Kurtosis are so similar?

I've been taking the histogram of the optical flow in videos and plotting the kurtosis and skewness of each frame. At the end of the video, I noticed that the skewness and kurtosis follow each other - ...
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2answers
78 views

How to learn certain Maths to understand machine Learning papers?

I have done the deeplearning.ai course on deep learning. But I cannot Understand equations like minGmaxDV(D,G)=Ex∼pdata(x)[logD(x)]+Ez∼pz(z)[log(1−D(G(z)))] ...
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1answer
35 views

Choose points to maximize volume of convex hull

Suppose I have N points (labeled 1, 2, ..., k, ..., N) in D dimensions. I'd like to choose ...