Questions tagged [math]

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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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6 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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28 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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10 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
21 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
31 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
91 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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21 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
105 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
31 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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12 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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6 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
20 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
142 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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20 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
21 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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20 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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40 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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38 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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14 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
34 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\...
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104 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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1answer
167 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
98 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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64 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
23 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 ...
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59 views

How to determine percent contribution to classification in logistic regression?

I'm trying to understand the contribution of each feature towards a specific classification. Let's say I have clients as my data and their features are income, debt and age. We're trying to predict ...
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1answer
81 views

bias variance decomposition for classification problem

It is given that: MSE = bias$^2$ + variance I can see the mathematical relationship between MSE, bias, and variance. However, how do we understand the mathematical intuition of bias and variance for ...
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30 views

How to create an autograd library from scratch like pytorch?

I am trying to implement a deep learning library from scratch. Most common DL framework uses autograd. Unfortunately, I haven't seen a lot of resources on how to create one autograd library. Is there ...
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19 views

How to add extra constraints to an equation?

Background: I have an equation which looks like as follows: $W \times P = R$ $\left[\begin{array} &{1}&{0}&{0}&-\frac{w_{1}}{w_{o1}} &\dots &{0} &-\frac{w_{1}}{w_{0} } \\...
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2answers
52 views

Neural networks, optimization math intuition

When I look into the following partial derivative, I see it as being the key element of any optimization algorithm out there. Correct me if I'm wrong, but this gets us the slope of the loss function, ...
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1answer
124 views

Estimating the value of $\pi$ with a Monte Carlo dartboard: $<$ or $\leq$?

I'm trying to figure out which is the proper way to estimate $\pi$ using the Monte Carlo method randomly distributing points in a square that also contains an inscribed circle. Some sources say to ...
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8 views

Confidence vs. Count in association rule mining: which one is better?

I am writing a program that mines association rules from a large data set. I have an array of association rules, and I have to decide which ones are more representative of the patterns I am studying. ...
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1answer
91 views

What is the range of values of the expected percentile ranking?

I'm currently reading Hu, Koren, Volinsky: Collaborative Filtering for Implicit Feedback Datasets One thing that confuses me is the "expected percentile ranking", an function the authors define to ...
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1answer
607 views

What are CRF (Conditional Random Field)

Looking for language modeling, I have been finding CRF in a lot of places which is but looking online for the same isn't actually helping me a lot. I referred Edwin Chen's blog and Ravish Chawala's ...
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1answer
37 views

Meaning of this notion in 0-1 loss?

I am reading a paper and encountered this notion: $$1_{\{Y=1\}}$$ To me it seems to be the expression as below, but I am not entirely sure and I don't think the author explictly explained it: <...
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1answer
15 views

Looking for help calculating a probability formula

How do I put this into a calculator or a excel spreadsheet formula. I have never done this math before, but I want to figure it out.
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2answers
26 views

compare log and division of numbers

What is the difference between (a) taking the logarithm of a set of numbers (b) dividing the set of numbers by an integer. Both appear to reduce the scale of set of numbers, so can they be used ...
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1answer
15 views

What is the first tool to learn start your your data science projects? [closed]

What is the first tool to learn start your your data science projects?
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1answer
89 views

How can positional encodings including a sine operation be linearly transformable for any offset?

In the paper "Attention is all you need" the authors add a positional encoding to each token in the sequence (section 3.5). The following encoding is chosen: $ PE(pos, 2dim) = sin(pos / 10000 ^ {2dim/...
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1answer
314 views

Comparison between addition and multiplication function in deep neural network?

I designed a specific Convolution Neural Network to study in the area of image processing. The network has a part that there are two tensors which have to be transformed into a tensor in order to be ...
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1answer
44 views

What is the difference between parameters & cooficients in Machine learning?

are both terms interchangeable? I'm kinda new to machine learning field and very confused about these terms in machine learning perspective.
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2answers
53 views

Which algorithm is perfect to determine best fit analyst based on multiple factors?

Assume I have a team of 200 analyst who work on different IT tickets. I want a better ticket assignment system which considers multiple factors before ticket assignment. Outstanding Ticket with each ...
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31 views

What are the introductory mathematics courses that are most pertinent to machine learning? [closed]

To provide more context to this question, I have found the following list of courses in order to learn calculus: Course | 18.01.1x | edX Course | 18.01.2x | edX Course | 18.01.3x | edX I also have ...
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1answer
65 views

Do we need to add the sigmoid derivative term in the final layer's error value?

I have been studying professor Andrew Ng's Machine Learning course on Coursera. Currently, I am trying to prove the formulas for backpropagation, which is mentioned in Week 5 (in this document). ...
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2answers
42 views

How to tell if the “clusters” I see in my pair plots are statistically significant or occurring by random chance?

I have a data set with one row per subject. Some variables include laboratory parameters for blood chemistry, hematology, etc. I also have some flag variables: any = 1 if the subject experienced an ...
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2answers
219 views

word2vec - log in the objective softmax function

I'm reading a TensorFlow tutorial on Word2Vec models and got confused with the objective function. The base softmax function is the following: $P(w_t|h) = softmax(score(w_t, h) = \frac{exp[score(...
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2answers
594 views

Can a single-layer ANN get XOR wrong?

I'm still pretty new to artificial neural networks. While I've played around with TensorFlow, I'm now trying to get the basics straight. Since I've stumbled upon a course which explains how to ...
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2answers
30 views

Are euclidian vectors and unit vectors same thing? [closed]

Consider this statement : Let the field K be the set R of real numbers, and let the vector space V be the Euclidean space R3. Consider the vectors e1 = (1,0,0), e2 = (0,1,0) and e3 = (0,0,1). Then any ...