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Questions tagged [function]

A mapping between a set of inputs and a set of outputs.

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Correcting 'not iterable error' for def function [closed]

I am trying to plot this complex def function from a research paper that I read for a project and I keep getting that the map function is not iterable. When I run the code by itself, it's fine, but ...
Joshua Mallay's user avatar
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Finding a function for the number of people on a bus

I've been trying to pin down the function that would describe the number of people on an ideal bus ( # of stops and passengers approaches infinity/ is large enough that the function is continuous), ...
Eda Toloch's user avatar
4 votes
3 answers
233 views

Better function to fit log-like data?

I'm trying to fit a two-parameter function to data that looks like this (black dots, x scale is logarithmic): The best fit I could find is an $arctan$, measured by the MSE. All the seven functions I ...
Gabriel's user avatar
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1 vote
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Question about using the RFpredInterval Package: How to calculate the standard deviation of data points in same terminal node as test data point

I am using the RFpredInterval package (specifically the rfpi function) to obtain prediction intervals for a random forest. I ...
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Using an optimal transport map on new samples from same source distribution

I am trying to compute an optimal transport map from $p = U[0,1]^2$ to some 2D distribution $q$ given by an image, where pixel intensities represent unnormalized probabilities. My goal is to build a ...
Hubble's user avatar
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0 answers
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What Are Some Mathematical Functions that Can Represent Surge Pricing for Ride Hailing? [closed]

Consider a ride hailing service, where the fare needs to be dynamically adjusted. I know there are many machine learning driven models possible, but here I am looking for a simpler and sensible ...
Della's user avatar
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2 votes
1 answer
40 views

Understanding notation for input space

I'm taking the free Caltech machine learning course. I'm having trouble understanding the notation on one of the problems: In this problem, you will create your own target function f and data set D ...
Ben G's user avatar
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5 votes
2 answers
269 views

Sufficient/complete statistic $\leftrightarrow$ injective/surjective map?

I can't understand the paragraph in Completeness (statistics) - Wikipedia: We have an identifiable model space parameterised by $\theta$, and a statistic $T$. Then consider the map $f:p_{\theta }\...
Y.D.X.'s user avatar
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Solving integrals using incomplete gamma function (upper gamma rule)

I am attempting to integrate this function, ∫15x^(0.28) * e^(-0.21x) dx and am struggling with what techniques to apply. The lower boundary is 0 and the upper boundary is infinity. From research, I ...
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41 views

Map from Normally distributed Variable to Gamma distributed Varaible [duplicate]

I need to find some function $f:\mathbb{R} \rightarrow \mathbb{R}^+$ such that If $\; \; x \sim \mathcal{N}(x; \mu, \sigma^2) \; \;$ then $\; \; f(x) \sim \mathcal{G}(y; \alpha, rate=\beta)$ Where $\...
Snowy Baboon's user avatar
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Is it possible to learn a mapping between unpaired time-series data?

I have two time series. One is an actual recording of physiological signals, the other is a binary representation of activations (0 or 1) based on a simulation of the process underlying the ...
Clemens's user avatar
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1 answer
42 views

Transform data domain and maintain mean

I have a dataset, $y$, that is on some arbitrary range. I would like to transform this data to be on the range [-1,1]. This is accomplished using a linear transformation, such as the one described ...
Colton Campbell's user avatar
1 vote
1 answer
146 views

Standard deviation of a function of random variables

I was a bit confused recently with why two jointly distributed variables will exhibit a smaller scatter as the correlation between the random variables increases (assuming only positive values for the ...
jpcgandre's user avatar
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1 vote
1 answer
230 views

Is there a way to stretch sigmoid function output

I have an array of values and a value that lies outside of array's max value: arr = [10, 15, 20, 30] value = 150 and I want to make that value less of an outlier, ...
Cyril's user avatar
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1 answer
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Describe a geometrical shape as a piecewise function

Consider a cube filled with random particles. Let's say the particles in cube are rotated around the z-axis through the center of the cube. Here, the rotation is proportional to the height of the cube,...
Sami's user avatar
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4 votes
1 answer
234 views

Rewriting the expectation of f(x) by means of its derivative

I have a question regarding this proposition. Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be an a.e. differentiable function so that $\int \frac{\left|f^{\prime}(x)\right|}{(1+|x|)^s} d x<\infty$ ($...
Eryna's user avatar
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1 answer
296 views

Why complete data log likelihood in M-step of EM algorithm

In Bishop's Pattern Recognition and Machine Learning book(page440), it talks about the M-step in EM algorithm of Gaussian Mixture Model. I am confused about the likelihood function of M-step. By ...
user3153824's user avatar
1 vote
0 answers
60 views

Intersection of matern covariance functions with different parameters

I am trying to prove some ideas about the identifiability of covariance function parameters for small samples. From various numerical experiments, it seems that the graphs of two matern covariance ...
Tommy Tang's user avatar
0 votes
1 answer
58 views

Convergence of moment of functional of random variable

Define $X_n$ a continuous random variable that converges in distribution to $X$. Morever, we know that $E[|X_n|^p] \rightarrow E[|X|^p]$ for some $p > 0$. Then, could we prove that for any ...
Eryna's user avatar
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1 vote
0 answers
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How to train a network with multiple inputs and multiple outputs [closed]

How to train a network with multiple inputs and multiple outputs I have a dataset of (400,256) 400 examples with 256 features. and each example has its corresponding output array (400,256) 400 ...
molo32's user avatar
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Is there a substitute for an "average" which best inherently represents data, rather than reducing it to one or another aspect?

I was thinking about the arithmetic average as a type of metric or a representation of data. Maybe there is a mathematical argument for the non-arbitrariness of that function. I think something like ...
Julius Hamilton's user avatar
0 votes
1 answer
63 views

Extract the functional mapping between input and output from a machine learning model

A lot of ML models, such as neural networks, are Universal Function Approximators. But when evaluating ML models, we use usually metrics, such as MSE or accuracy, to assess the performance of a ML ...
Frank Gallagher's user avatar
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0 answers
18 views

Do error terms of a value that is part of a normal distribution also follow a normal distribution?

I asked this yesterday, but was not very concise. Hoping to get better results with different wording. I have a question related to the error term in a normal distribution. Let's assume that we are ...
GKJohn's user avatar
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1 vote
1 answer
31 views

Function that maps low values to [0,1] [closed]

I'm currently working on a predator prey simulation and have to parameters that are codependent, the attack rate and the survival rate. The attack rate is mutated within the simulation and determines ...
Marcello Zago's user avatar
1 vote
0 answers
24 views

Best way to analyse two experiments

I'm looking for help/indication on approaching a data integration problem. I have a dose-response curve that is described by a log curve. Because of measurement difficulties, the dose and response can'...
Lu_Ste's user avatar
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1 vote
0 answers
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Method to model exponential fit line coefficients based on main function parameters

I have a quite complicated trigonometric equation I was able massage into a parametric function that takes four parameters as inputs/arguments, say: $a$, $b$, $c$, and $d$. Regardless of the ...
mk1138's user avatar
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0 votes
1 answer
29 views

Problem with probabilities of functions of continuous random vector

I have problems with a true or false exercise: if the joint pdf of the continuous random vector $(X,Y)$ is $$f(x,y)= \begin{cases}2x,& 0 \le x \le 1, 0 \le y \le 1,\\ 0,& \text{otherwise} \end{...
Becker's user avatar
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-1 votes
1 answer
40 views

Function that receive two variables and decides which statistical analysis should be done

I am trying to create a function that receives two variables (dependent and independent) and figures out according to their class (numeric / factor) and number of groups, which statistical test should ...
Sari Katish's user avatar
1 vote
0 answers
35 views

I need to derivate the maximum likelihood of GLR function [closed]

I am trying to do the partial derivative of this function but I don't know how to include the $\theta$ inside my function to be able to apply the partial derivative in $\theta$. The likelihood ...
Miguel Gomez's user avatar
1 vote
0 answers
21 views

How to decompose the component that is influenced by X from time-series Y?

There is a time series Y, which is the remaining part of the initial time series after removing the trend and seasonal periodic components. And there is also a time series X, which represents the ...
Sebastien J.'s user avatar
1 vote
0 answers
43 views

How do I find a mapping f : X -> Y to characterize the relationship between 2 time-series X and Y? [closed]

I have a time series Y, and another time series X related to Y. The value of Y is affected by X and some noise. How can I separate the effect of X on Y ? That is, how do I find a mapping f : X -> Y ...
Sebastien J.'s user avatar
1 vote
1 answer
110 views

Is sequence of probability mass functions always uniformly bounded

Say that we have a sequence of discrete random variables, $\left\{X_n\right\}_{n \in \mathbb{N}}$, which converges to a random variable, $X$, with a continuous distribution, e.g., the Normal (Gaussian)...
Student_718's user avatar
1 vote
0 answers
29 views

Using output of categorical distribution in Pymc3 as index for selection of down stream parameters

The code that I would like to generate is something like: I want to have a categorical variable that maps to another value different from the index given by the categorical distribution, and fits as a ...
user359398's user avatar
1 vote
0 answers
27 views

How do you get this bifurcation diagram of this 2D discrete time model?

I want to replicate the results of "Chaos in Duopoly Pricing" by T. Puu, which can be found here: https://www.sciencedirect.com/science/article/pii/096007799190045B#section-cited-by. The ...
Ludwig Gershwin's user avatar
0 votes
0 answers
199 views

How to find expected value from cumulative distribution function?

Hello everyone, I'm currently doing research based on the model in Competitive fit-revelation sampling and mixed pricing strategy (Wu &Deng, 2021). And I don't understand how they can conclude the ...
Mai Lê's user avatar
0 votes
0 answers
61 views

Determine expected goals from two normal distributions

Assume Team A scores an average of 3 goals per game with a standard deviation of 1.0, and assuming Team B allows an average of 2 goals per game with a standard deviation of 0.5. How would you ...
Imminentfate's user avatar
1 vote
1 answer
56 views

Problem formulation classification task

I would like to know if it is correct for a classification task in a supervised learning to say the model we are looking for is a function from RxR to a discrete space $$ f:\mathbb{R}\times\mathbb{R} \...
user979974's user avatar
0 votes
1 answer
2k views

SMOTE vs Stratified Sampling in highly imbalanced dataset - classification

I am working on a project with the goal of predicting Cerebral strokes from brain arteries data (speed of blood, resistance etc. of one artery and of the neighboring ones). I have a dataset with ...
duecci's user avatar
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0 votes
1 answer
190 views

Difference between Predictive Inference and Causal Inference

I am looking for functional mathematical notation to explain the difference between Predictive Inference and Causal Inference? I list an example model. I also list links further down that give ...
L92MD14's user avatar
2 votes
1 answer
470 views

Equal intervals on log scale

I want to make a plot in which the horizontal axis is log scaled, ranging from 1 to 1000. I want to divide the horizontal axis into $n$ equal intervals, where "equal" means that it appears ...
quibble's user avatar
  • 1,694
2 votes
2 answers
392 views

distance between regression models

Consider two multivariate linear regression models (vector inputs and outputs) with the same domain observations. Namely, let: $X \in \mathcal{R}^{a \times N}$ be a matrix of domain observations (...
eretmochelys's user avatar
0 votes
0 answers
50 views

How to calculate exponential growth when the value is a percentage or probability?

I have a variable x that takes values between 1 and 0 (0<x<1). I want to calculate value of ...
Ege Can's user avatar
  • 123
0 votes
1 answer
106 views

Property of unbiased estimators

If $f(x)$ and $f(y)$ are both unbiased estimators of $\mu$, aka $E[f(x)]$ = $E[f(y)]$ = $\mu$, is it possible that $f((x+y)/2)$ is also an unbiased estimator of $\mu$? We know $f((x+y)/2)$ would be ...
VDCN's user avatar
  • 31
1 vote
1 answer
112 views

Function fit to skewed data and non-zero beginning of the function

I would like to find a function that would represent the best fit to represent this type of biological data. More precisely, I would like to estimate expected daily egg production by an insect, based ...
MIH's user avatar
  • 205
1 vote
1 answer
42 views

Prove that every linear regression predictor is a linear function

A function $f : \mathbb{R}^D \rightarrow \mathbb{R}$ is linear if both of the following conditions hold. (1) For all $\textbf{x}, \textbf{y} \in\mathbb{R}^D, f(\textbf{x} + \textbf{y}) = f(\textbf{x}) ...
xxxxxx's user avatar
  • 133
1 vote
0 answers
188 views

How to use statistics to speed up row-wise computations on a data.frame?

I have a data frame with 10,000 rows and 40 columns. I am trying to apply a function to each of these rows. For each row, I am expecting to return a scalar which is the value of the statistic I am ...
Capri's user avatar
  • 21
0 votes
0 answers
864 views

How to weight ranks?

I have a set of responses ranked by my participants. For example, they gave responses A, B, C and ranked them as 3, 2, 1 (or C, B, A). I computed relative frequencies of each responses (A, B, C) and ...
Petr Palíšek's user avatar
2 votes
1 answer
66 views

What is the equation of a line fitting a log-log model computed in R?

I am currently stuck, wanting to extract a line function from my fitted line on my log-log model. ...
Marieke de Geest's user avatar
1 vote
0 answers
26 views

Why does non-parametric approach break down when the joint distribution is estimated by a finite data sample?

I am currently reading the paper on Gradient Boosting Machines - J. H. Friedman, “Greedy function approximation: A gradient boosting machine,” Ann. Stat., vol. 29, no. 5, pp. 1189–1232, 2001, doi: 10....
Karina's user avatar
  • 85
2 votes
1 answer
79 views

replacement error when feeding data from function into matrix in R [closed]

I am trying to write a function that creates simulated datasets. The function takes the argument size, being the size of a group, and it is meant to produce a matrix with 100 columns with values 0 or ...
siso777's user avatar
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