Questions tagged [function]
A mapping between a set of inputs and a set of outputs.
237 questions
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Defining a general distribution over a planar curve
I'm trying to understand how to define an arbritrary distribution over a curve in $\mathbb{R}^2$. To achieve this goal I define a distribution over the unitary interval $[0,1]$ in terms of a ...
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For any pair of distinct, real-valued bivariate samples of finite size n, can one always obtain one sample by some rotational function of the other?
I'd like to define a set of functions, $F$, with the following property. For every distinct pair of real-valued, finite, bivariate samples, $(X_1,Y_1)$ and $(X_2,Y_2)$, there should be an $f$ in $F$ ...
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Loss function - computed on one data point or on all data points?
I'm trying to read Jerome H. Friedman's lecture on Gradient Boosting Decision Trees. Unfortunately I have very rudimentary understanding of statistics and mathematics and I am confused, so I hope ...
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Maximum correlation matching between 2 sets of points is creating clumps
I am describing here an issue with mapping 2 sets of points that has been bugging me for some time. Any input would be greatly appreciated!
The Task:
I have 2 sets of points living in a multivariate ...
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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), ...
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3
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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 ...
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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 ...
Rachel Tumbleson
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36
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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 ...
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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 ...
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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 ...
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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 }\...
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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 ...
user387381
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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 $\...
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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 ...
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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 ...
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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, ...
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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,...
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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 $\int \frac{\left|f^{\prime}(x)\right|}{(1+|x|)^s} d x<\infty$ ($...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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'...
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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 ...
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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{...
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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 ...
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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 ...
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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 ...
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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 ...
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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)...
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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 ...
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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 ...
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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 ...
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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 ...
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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} \...
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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 ...
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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 ...
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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 ...
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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 (...
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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 ...
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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 ...
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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 ...
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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}) ...
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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 ...
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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 ...
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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.
...
