Questions tagged [mathematics]

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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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12 views

Algorithm that predicts a next series of numbers

I have the data I want to input and see the results. It is number Data based on Marko Rodins Vortex Math. So I have these random 6 numbers from 1 to 9 it is data from the past 9 years. I need an ...
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12 views

Creating Scoring Functions

As a data scientist/analyst is there any resource I can use to solve non-conventional supervised/unsupervised learning problems, for example: Based on hotels in a city create a score for how popular ...
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11 views

Determining the degree of freedom in ridge regression | Interpretation of the head matrix

right now, I am diving into statistical learning and stumbled over the so-called "head-matrix" and the determination of the degree of freedom. I am referring to ridge regression: So the ...
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19 views

Flow System - Analysing Measurement Errors

I have a closed system with multiple flow measurement points as shown; where in theory (A1 + A2 + A3) = (B1 + B2 + B3) = C = (D1 + D2) and D1 = (E1 + E2 + E3 + E4) D2 = (F1 + F2 + F3 + F4) Some of ...
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1answer
89 views

Different activation function in same layer of a Neural network

My question is that what will happen if I arrange different activation functions in the same layer of a neural network and continue the same trend for the other hidden layers. Suppose I have 3 ...
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10 views

How to compute Fourier Transform complexity?

I would like to know what is wrong with my reasoning: 1D Transform Let suppose we have row vector with N rows I apply Fourier transform for single row I get O(log N) Then after stacking N rows to ...
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35 views

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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20 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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16 views

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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1answer
37 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 \begin{equation} ...
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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
31 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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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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25 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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50 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
24 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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1answer
23 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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33 views

Computational Complexity of Tucker decomposition

I am currently doing background reading for my Masters Thesis. I am working with tensor decompositions, whereby tensor I simply mean a multi-dimensional array. The aim of my master's project is to ...
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10 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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78 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
245 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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21 views

Is there a universal convergence rate when stacking models/experts?

It's fairly common to see people stacking different models when chasing marginal gains in contexts such as Kaggle competitions or the Netflix challenge. I would like to know about the mathematics ...
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2answers
81 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
40 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
113 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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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
29 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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2answers
705 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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0answers
35 views

Max/Min of neurons at the hidden layer of a neural network

We have a neural network with inputs $x_1,...,x_n$, a single hidden layer with neurons $y_1,\ldots,y_m$, and outputs $z_1,...,z_v$. There are no activation functions (i.e., the activation functions ...
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2answers
393 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
69 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
28 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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100 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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172 views

Formal proof of vanilla policy gradient convergence

So I stumbled upon this question, where the author asks for a proof of vanilla policy gradient procedures. The answer provided points to some literature, but the formal proof is nowhere to be included....
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1answer
67 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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99 views

When is the sum of models the model of the sum?

The response variable in a regression problem, $Y$, is modeled using a data matrix $X$. In notation, this means: $Y$ ~ $X$ However, $Y$ can be separated out into different components that can be ...
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10k 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
116 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-...
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68 views

Creating a convolutional layer with weight normalization?

This paper proposes parameterizing convolutional weights by having the primary weights normalized to unit norm plus an extra scalar weight: https://arxiv.org/pdf/1602.07868.pdf Implementations do ...