Questions tagged [mathematics]

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What is the underlying difference between linear and non-linear relationship?

Study on linear correlation coefficient and nonlinear correlation coefficient in mathematical statistics WANG Ting, ZHANG Shiqiang Studies in Mathematical Sciences 3 (1), 58-63, 2011 From the above ...
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14 views

logarithmic exponential function python

The code below (I found from googling) does the trick in terms of outcome. What I need to work out is the formula for this, so for any Y point we can get corresponding X. This is part of a larger ...
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What are some modern algorithms\analysis that use Taylor Series or Lagrange multipliers?

What are some modern machine learning algorithms\analysis that use Taylor Series or Lagrange multipliers? I spent a good chunk of my weekend reading about SQP, aka SLSQP. SciPy has an implementation, ...
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20 views

How to compute Hessian matrix for log-likelihood function for Logistic Regression

I am currently studying the Elements of Statistical Learning book. The following equation is in page 120. It calculates the Hessian matrix for the log-likelihood function as follows But is the ...
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2answers
58 views

Is there a possibility that there is no relationship between some inputs and outputs?

I have a general question that comes to my mind, I'm doing machine learning projects and I took a look at many datasets and worked with, mostly there are already famous datasets that everyone uses. ...
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1answer
29 views

How to adaptively sample n-dimensional data and build an optimum training set

My input space is at least 10 dimensional (after reducing it by various component analysis such as PCA) and the output space is 4 dimensional. I am building a neural network that works something like ...
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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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24 views

LONG SHORT-TERM MEMORY Hochreiter's paper BPTT

I was trying to read paper about LSTM, and I am stuck with mathematical problem. http://www.bioinf.jku.at/publications/older/2604.pdf page 4. see, |$f'_l$$_m$($net_l$$_m$)$w_l$$_m$ $_l$$_m$$_-$$_1$...
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30 views

How does one derive the modified tanh activation proposed by LeCun?

In "Efficient Backprop" (http://yann.lecun.com/exdb/publis/pdf/lecun-98b.pdf), LeCun and others propose a modified tanh activation function of the form: $$ f(x) = 1.7159 * tanh(\frac{2}{3}*x) $$ ...
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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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29 views

Generative Model for learning Periodic solutions 3-body/N-body problems

I am tasked with finding research where a GAN or any other generative model is used to generate new shapes of 3-bodies moving under the influence of each others' gravitational pull, in a periodic ...
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20 views

intuitive understanding of (1+parameter)/parameter

When looking at a function that contains term (1+parameter)/parameter, should there be an intuitive understanding for why this term is included. For example if a function for fishing mortality ...
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9 views

Roots and discriminant of a polynomial

Intro I'm reviewing maths all the way from high school, because even though I have experience in machine learning, I have really poor maths basics. I'm currently reviewing polynomials, especially ...
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21 views

Exponentiated Gradient

I am currently trying to understand exponentiated gradient from this paper. Here is an implementation of the Algorithm in Python. So my question using exponentiated-gradient algorithm we can update ...
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1answer
89 views

How regularization helps to get rid of outliers?

I have heard regularization helps to get rid of outliers, how so? 'My intuition is, regularization shrinks parameter or even make it zero, and hence large value will have less effect on overall result'...
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75 views

ML, Statistics and Mathematics

I have just started getting my hands wet in ML and every time I try delving deeper into the concepts/code, I face the challenges of the mathematics and its cryptic notations. Coming from a Computer ...
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1answer
39 views

How do I know how to construct the layers of my CNN

I've done a CNN project with Keras and OpenCV, and I've got roughly 65% accuracy. And now I have to present this work in my University, but I'm afraid if the teachers ask me for how do I knew how to ...
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1answer
63 views

Help in understanding the maths behind Logistic Regression

I am following the lecture notes available https://www.stat.cmu.edu/~cshalizi/uADA/12/lectures/ch12.pdf I cannot understand how Eqs 12.4 and 12.5 come, why the Bernoulli probability has $1-p(x)$ in ...
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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
24 views

Kernel Trick and Inner Product Preservation

I understand that the point of using the kernel trick is to project the problem onto a higher dimensional space, where the problem is linearly separable. In this explanation, https://www.quora.com/...
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506 views

How do I calculate the range of a F1-score from a confusion matrix of 3 class,A,B,C

Is there any support function to calculate the average F1-score range?
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99 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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63 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
22 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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99 views

Updating Weight Using Updates on Related Data

Suppose $$ x=Ay $$ The $x$ is $M\times 1$, $y$ is $N \times 1$ and $A$ is $M\times N$ We have the data $x$ and would like to know what $y$ is. However, the matrix $A$ is too large for pseudo-...
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1answer
60 views

Elements of Statistical Learning - question on p. 18

In the following expression: What do $E_{X}$ and $E_{Y|X}$ mean, respectively? In case helpful, I note that the authors derived that expression from the following: Based on the above, how would one ...
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28 views

Proof MDS algorithm

I am studying this paper from Ali Ghosdi class I probably lack of knowledge in linear algebra but there are some steps that I don't understand. Like on the second page he talks about the distance ...
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8k views

What is GELU activation?

I was going through BERT paper which uses GELU (Gaussian Error Linear Unit) which states equation as $$ GELU(x) = xP(X ≤ x) = xΦ(x).$$ which in turn is approximated to $$0.5x(1 + tanh[\sqrt{ 2/π}(x + ...
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1answer
94 views

Efficient self study plan

I am hoping for a bit of guidance from experienced practitioners / academics. I want to work through the Bishop ML book, but have minimal background. What is the fastest way to get the pre-...