# Questions tagged [mathematics]

Mathematics in a data science or machine learning context refers to the mathematical underpinnings for algorithms, optimization, statistics, and linear algebra etc.

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95 views

### How is Probability Used in Data Science? [closed]

This is my first Question so apologies if I do not stick to the standards. What I want to understand is how is all of the following topics: Probability Different Probability Distributions. Baye's ...
37 views

### Journals to publish a proof of a math result used for neural-network algorithms

I would like to know which journal is an appropriate outlet for the results described below. I recently came across a particular neural-network training algorithm. The algorithm is based on a result ...
1 vote
35 views

### Why there is so few research on neural code of artificial neural networks and are there alternatives to the neural code approach?

I feel that the neural code/neural coding (how neurons or biases enode the symbolic concepts of the chains of concepts, e.g. each feature is chain of symbolic functions and their parameters) is the ...
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1 vote
70 views

### What is the meaning about the $\alpha$ in TD3 algorithm

I am study the paper with TD3 algorithm. I am curious about the meaning of $\alpha$ while the paper prove that overestimation will be happened in a critical situation. The contents about mathematical ...
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44 views

### Discretize interval into fixed number of bins while minimizing error

Background I have been working on an optimization problem related to the following function: $$y = f(x) = c_{1}(1-e^{-c_{2}(x-x_{0})})^{2}$$ where $c_{1}$, $c_{2}$ and $x_{0}$ are constants. Assume ...
1 vote
25 views

### Resources for Symbolic Regression

What are some good resources/recommendations related to symbolic regression? (In terms of predicting analytic mathematical equations from neural networks)
1 vote
39 views

### How do we derive our loss function from the gradient objective?

I've been dwelling through RL theory and practice and one particular part I find hard to properly understand is the relation between the practical loss function and ...
• 111
16 views

### How can I transform or plot my data to see power consumption more easily?

I have two heating tapes installed in my setup and they provide heat to maintain the reaction at a certain setpoint temperature. Basically, the heating tapes go on a cycle of on/off to maintain the ...
1 vote
24 views

### Problem understanding the forward algorithm for HMMs

I found a recursive version of the forward algorithm on wikipedia, however I don't understand the notation given in the pseudocode: What means $$x_{t-1}$$ under the summation sign? What do I need to ...
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1 vote
39 views

### ML techniques for mathematical inverse approximations

I have some inputs and outputs of a set of functions, and I want to be able to find/approximate any given input vector from its corresponding output vector (In other words learn the inverses of these ...
1 vote
1k views

1 vote
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### Structured policies in dynamic programming: solving a toy example

I am trying to solve a dynamic programming toy example. Here is the prompt: imagine you arrive in a new city for $N$ days and every night need to pick a restaurant to get dinner at. The qualities of ...
146 views

### Strategies for complicated inverse function approximation

I have a dataset G. There is a complicated set of mathematical functions I can use to calculated the values 'W' for any given point in G. f(G) $\rightarrow$ W To the best of my knowledge these ...
1 vote
67 views

### Confused on Naive Bayes classifier

In the last part of Andrew Ng's lectures about Gaussian Discriminant Analysis and Naive Bayes Classifier, I am confused as to how Andrew Ng derived $(2^n) - 1$ features for Naive Bayes Classifier. ...
55 views

### How to measure statistical similarity or discrepancy between a dataset and a distribution?

Is any way to measure statistical similarity or discrepancy between a dataset and a distribution? I have do some research, but find most of method are intended to describe discrepancy between data and ...
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617 views

### what exactly is the "order"-parameter in pandas interpolation?

what exactly is the "order"-parameter in pandas interpolation? it is mentioned in the doc: ...
59 views

### Understanding Kneser-Ney Formula for implementation

I am trying to implement this formula in Python $$\frac{\text{max}(c_{KN}(w^{i}_{i-n+1} - d), 0)}{c_{KN}(w^{i-1}_{i-n+1})} + \lambda(c_{KN}(w^{i-1}_{i-n+1})\mathbb{P}(c_{KN}(w_{i}|w^{i-1}_{i-n+2})$$ ...
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1 vote
37 views

### Ridge regression terms [closed]

Can anybody let me know the definition of these terms? I know we solve this for Beta but I want to have the definition
• 239
172 views

### What are the mathematical topics that I need for Machine Learning & Data Science? [duplicate]

I would like to start studying ML & DS, but I feel I am a bit lost, so I don't really know what to study, what the prerequisites are, I mean I know I should study linear algebra, calculus, and ...
395 views

### Converting similarity value into a dissimilarity value

Suppose we have similarity values between some data point in the interval $[0, 1]$. How can I transform this similarity values into a dissimilarity values in the interval $[0, ∞]$?
• 121
492 views

### Equations in "Batch normalization: theory and how to use it with Tensorflow"

I read the article Batch normalization: theory and how to use it with Tensorflow by Federico Peccia. The batch normalized activation is $$\bar x_i = \frac{x_i - \mu_B}{\sqrt{\sigma_B^2 + \epsilon}}$$...
• 123
1 vote
195 views

### How important is real analysis/measure theory to this field? [closed]

I am a college student, struggling to decide whether or not to take pure maths electives on topics such as real analysis and measure theory. If I were to take them then I would definitely have to ...
103 views

### Deriving VIF equation from the matrix form of Least Squares equation

I have been working through the derivation of the formula used to calculate the Variance Inflation Factor associated with a model. I am hoping to start with the Least Squares equation as defined in ...
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1 vote
216 views

### Association rules - Find 100% confidence rules [closed]

Suppose there are 100 items, numbered 1 to 100, and also 100 baskets, also numbered 1 to 100. Item i is in basket b if and only ...
• 11
1 vote
36 views

### GloVe dot product optimized for non-comutative data whilst the operation itself being commutative

To my current knowledge, GloVe word vectors dot product are optimized to be the w_i ⋅ w_j = log⁡(P(ⅈ|j)) The probability being computed from a cooccurance matrix. However, dot product is a commutative ...
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1 vote
26 views

### Right way to compare model scores for Next Best Action

I have around 15 classification models for different products built in different ways (some are RF, some are Gradient Boosting, some were downsampled in one way, others in other way, some are built in ...
12 views

### The formula of loss function uses '(i)' as power of expected and real variables. What does that mean?

In the formula below, could one understand $y^{(i)}$ as $y_i$ ? If not, what is the fundamental difference ? $$j(\theta_0, \theta_1) = \frac{1}{2m}\sum_{i=1}^m(h_{\theta}(x^{(i)})-y^{(i)})^2$$
36 views

### What can I use to limit the range of a Cantor pairing function to 255?

I have 2 data input sets [0-20] and [0-7] and I need a pairing function like CANTOR to restrict the mapped value to [0 - 255]. Would it be feasible to use MOD(256) to restrict the result?
163 views

### How do I minimizie cost for EV charging?

I want to find a charging schedule that minimize cost of charging an EV. The main objective is to have a fully charged car for the next morning, but the sub objective is to minimize cost based these ...
142 views

### Summarize 3 variables into one and calculate a „skill“value + ranking

I have a data set that looks like this: Name Top Speed Number Sprints Cumulative Sprint distance Xyz 55 300 33.3 Xyz123 45 350 32.0 Top Speed is in km/h. Cumulated Sprint distance is in km. Number ...
1 vote
183 views

### Why does stochastic gradient descent lead us to a minimum at all?

Why do we think that stochastic gradient descent is going to find a minimum at all? I mean on each iteration SGD moves in the direction that reduces only current batch's error (SGD doesn't care about ...
• 121
2k views

### Do you actually need math for your data science job?

I am a physicist working in a data scientist role. I was told everywhere that my degree is a very good starting point because I know a lot of math and it is crucial for this job. But other than ...
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889 views

### Which is meant by +/-9.2e18 years in timespan?

I was able to convert the 9.2e18 AD to a date, but I am confused about the exact date. Which date is 9.2e18 AD and and 9.2e18 BC? Time span (absolute) - [9.2e18 BC, 9.2e18 AD] i.e +/- 9.2e18 years ...
49 views

### How does TensorFlow compute gradients of nonelementary integrals?

I was reading about custom activation functions, autodiff etc, trying to understand it all. I think I have a glimpse of it now, but right after closing the book I thought "what about the ...
72 views

### Why do we use 'T' when we are to say matrix-vector product? [closed]

On the first picture author uses $T$ meaning matrix-vector product But other website do not use $T$, but says that $x$ is a vector, I do not understand if it is important or not
70 views

### What are the math Prerequisite for understanding 'First Order Motion Model for Image Animation' Paper?

This is the 'First Order Motion Model for Image Animation' Paper. But I don't understand most of the mathematical things in the paper. What are the math Prerequisite for understanding this paper?
1 vote
255 views

### What is the purpose of defining such measure as metric or non-metric?

proximity measures can be metrics or non-metrics. the following criteria defines a metric dissimilarity measurement: here is for a metric similarity measurement I would like to know the consequences ...
122 views

### Creating neural network to solve for equations

I have a dataset like: The v1 variable is a mathematical expression. Currently, I am using hyperopt to solve for these parameters and am using v1,v2,v3 in regression to predict y and then minimize ...
55 views

### How to compare two one hot encoded data frames based on column names?

I have two datasets with shapes (329, 159) and (26,24). Both of them are one-hot encoded. The columns in the smaller dataset are present in the larger dataset. The smaller dataset has scores that I ...
1 vote
748 views

### Real distance between bounding box centers

Assume that I have a camera pointing in a specific direction. I know the Euclidean distance (Real world distance) of the camera to a fixed point, X (mm). Using ...
1 vote
163 views

### Is there such thing as linear and non-linear data?

While doing machine learning projects we've heard that logistic regression works well with "Linear data" and decision tree works well with "non-linear data" However concept of ...
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1 vote
18 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 ...
215 views

### Non-commutative distance formula

I am trying to find a distance formula or a method that can give the non-commutative distance between two points in a feature space. Suppose there are two movies represented in an R^n feature space. ...
90 views

### Is there a theorem of prominent Russian mathematicians that played an important role in the development of machine learning? [closed]

I once attended a seminar in which a statement answering the question asked above was answered in the affirmative. I do not recall further specifics, however.
1 vote
2k views

### Reinforcement Learning - PPO: Why do so many implementations calculate the returns using the GAE? (Mathematical reason)

There are so many PPO implementations that use GAE and do the following: ...
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1k 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: ...
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1 vote
53 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, ...
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1 vote
I have costum loss function with $\mu ,p, o, u, v$ as variables and $\sigma$ is the logistic function. I need to derive this loss function. Due to multiple variables in the loss function, I need to ...