Questions tagged [function]
A mapping between a set of inputs and a set of outputs.
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questions with no upvoted or accepted answers
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Expected entropy on output of a random function, and of $F(x)=P(x)\oplus x$ with $P$ a random permutation
Let $F$ be a function on the set $\{0,1\}^n$ of $n$-bit vectors. Let $H_F$ be the entropy (in bits) of the source $F(x)$ where $x$ is uniformly random. That is
$$\begin{align*}
H_F&=\sum_{y\in F(\{...
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50
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Minimize function curve 'length'
Given a set of points $(x_i, y_i)$, how can I find the serie of $ C^\infty $-functions for which the sum passes through all points and for which the length of the resulting curve is minimal; i.e. if ...
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reducing 2 variables of a function into one
I have an experiment where I'm measuring some physical quantity Q as a function of 3 variables which I can physically control (x,y,z). I'm collecting many samples of Q and (x,y,z) and then I can ...
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Machine Learning algorithms for multi-input/multi-output regression
I have a computationally expensive function $f(a, b, c, d, e)$ that outputs an array of size $m$ containing sorted integers. I wish to use a machine learning technique to predict, given the variables $...
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Measuring goodness of fit when making a localized average of a function with uncertainty in $x$ and $y$
I have a function $y=f(x)$ that is defined on the interval $[0, 1]$.
I would like to estimate $y_0=f(x_0)$ at some location $x_0$.
I have a procedure with multiple free parameters $\vec \alpha$ ...
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Finding a function for biomass as response variable
I would like to know how I would go about systematically finding an analytical function for biomass growth.
I have a plant production facility with lots of sensors and variables to tweek, but I need ...
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Writing monomial symmetric functions in terms of population moments about the mean
Following Sukhatme (1954, pp.35 - 36) for a univariate case, I encountered the following population monomial 'symmetric' functions for a bivariate case: $\sum_{i=1}^{N}(X_i^2Y_i^2)$ $;$ $\sum_{i\neq j=...
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Using A Time Series To "Scale" Another
I know the "average theoretical cost per impression" for Jan 13 - Dec 13. I have other monthly time series for "total # of impressions", "total # of clicks" and "total number of conversions" for Jan ...
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How can you cluster a set of functions with unknown functional forms?
Say you've $N$ functions $f_N(x)$ defined on a regular grid $x$. You don't know the form of $f(x)$, you've only got several realizations of it. The different functions are related to each other ...
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Estimating the x-intercept of an arbitrary monotonically increasing function
I have a continuous monotonically increasing function, $f(x)$, whose $x$-intercept, $x^*$, I am trying to estimate. I have a dataset of $(x_i,y_i)$ pairs, with each $y_i=f(x_i)+\varepsilon_i$, where $\...
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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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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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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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23
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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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1
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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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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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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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1
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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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1
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1
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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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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....
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Get Continuous Distribution from Discrete Variable: Problem 6.77 of Wackerly, Mendenhall, Schaeffer, 5th Ed
Problem Statement:
$\newcommand{\szdp}[1]{\!\left(#1\right)}$
Let $v$ denote the volume of a three-dimensional figure. Let $Y$
denote the number of particles observed in volume $v,$ and assume that $Y$...
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ML approach to learn function as output
I have a question on how to use ML (machine learning) methods for the following task. I have a m-dimensional (field is always over real numbers $R$) input vector $\vec{x}$, and I want to learn the ...
user311204
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A space of functions and their Fourier Transforms?
Conjugate variables and the Fourier transform are often used to analyze different states of a single object. For example in Quantum Mechanics it can be used to describe changing information about ...
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0
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124
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Cross entropy and function approximation
My overall question is: the universal approximation theorems can provide a good heuristics on defining the loss function for supervised regression problems, i.e., because universal approximation ...
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combining two second order growth functions
I have two second order growth functions of the form Y = (K1 * Yeq^2 * x) / (1 + K1 * Yeq * x) and Z = (K2 * Zeq1^2 * x) / (1 + K2 * Zeq * x), with both Y and Z having an inhibitory effect on each ...
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How to make a custom activation function in keras with a learnable parameter?
The answer to this question is generally to implement it as a new layer and do
layer = Dense(num_neurones)(previous_layer)
out = TheActivationFunction()(layer)
...
1
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0
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102
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Finding the distribution of a piecewise function of a Gamma random variable
Let random variable $X \sim \text{Gamma}(\alpha,\beta)$. I want to derive the distribution of $Y$, where:
$$
Y = \left\{
\begin{array}{ll}
a X - k & \quad X \geq \frac{k}{a} \...
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395
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Functional Forms of Independent Variables
If our objective is to ascertain the relationship (specifically, sign and significance of Beta coefficient) between independent variables and dependent variable in an OLS regression (cross sectional ...
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Limiting regression accuracy
I am currently using a LSTM Network to solve a regressional problem. The goal is to predict the payload mass using various time series as input data. For our intents and purposes estimating the mass ...
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0
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710
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Mean and std of nonlinear function
I have a gaussian random variable $\xi \sim \mathcal{N} (\mu,\sigma^2)$, and the following function $g(\xi)$:
\begin{equation}
g(\xi)=-( \xi +\textrm{b}^{\textrm{T}} x) + \left\lVert{\begin{matrix} \...
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Problems fitting a model to a variogram
I am having problems fitting a variogram model. I tried to change some parameters to estimate or fix them but I am still not achieving any improvement.
I remove trend of the data and use logarithms ...
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1
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1
answer
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Estimating the mutual information in high dimension when all but one variable are iid
I have a function $f(x_{1},\dots,x_{n})$ where $n$ is large and I would like to estimate the mutual information between the random variable $f(X_{1},\dots,X_{n})$ and the independent and identically ...
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Constant/coefficient order and naming in regression functions
This question relates to best practices in Maths and Statistics.
When looking at linear regression formulas, they are generally written as
$y = a + bx.$
However, in general algebra, the function ...
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0
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608
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Approximating a 3d function based on 3d scattered points
Hello I have many 3d points (x, y, z). I have averaged every z with a matching (x, y) value and plotted the resulting means as a surface.
The data looks pretty good:
The green indicates where the ...
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0
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Solve Multivalued function as a Multilevel model?
I have a dependent variable (y) that is bounded between 0 and 2. The ideal value of the variable is 1. Values closer to 0 or 2 are theoretically bad (not outliers). I also have a set of potential ...
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Equivalence between function of random variables and random function of random variables
All the random variables in what follows are defined on the same probability space $(S, \mathcal{A}, P)$.
Let $W, Z, Q$ be Borel measurable random variables on $[0,1]$.
Assume
(*) $X|W, Z, Q \sim ...
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What is a deterministic, non-negative, and Borel-measurable function?
May I know the intuitive understanding of a deterministic, non-negative, and Borel-measurable function?
Especially, I am not sure what the 'deterministic' and 'Borel-measurable' functions are.
Could ...
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Cost function for screening model considerring misclassifying of NSCLC and normal
How to determine the most suitable sensitivity and specificity for the lung cancer screening model, when we consider the cost functions when misclassification occurred. Any existed cost functions to ...
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Minimizer of a function containing response and predicting variables
Can anyone please give me the expression of the "minimizer" of $$\sum_{i = 1}^n \vert y_i - b x_i \vert + \sum_{i = 1}^n (y_i - b x_i)^2 \quad \quad ?$$
I am unable to find this expression on the ...
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What does this evaluation function mean?
I am solving a prediction problem where I am supposed to predict the number of clicks, given some historical Data. I am told that my predictions will be evaluated by a normalized weighted mean square ...
1
vote
1
answer
29
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Learning a spatial function
I have some observations of a variable y, that varies spatially. For each observation, I also have a lat, long tuple. I have some 50 or so observations. Besides conducting some exploratory analysis ...
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Calculate pdf of complex model
I'm trying to model the distribution of effects of mutations (let's call it s) in evolution but I'm stuck in generating the probability distribution function (pdf) for my model.
So, my model is a ...
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Question related to binomial distribution
Let $X \sim Binomial (n, p)$ with both $n$ and $p$ known.
Suppose for some non-increasing function $G:[0,1] \rightarrow [0,1]$,
and some fixed $c_0 \in [0,1]$,
we have that
\begin{align} \label{ineq}...
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1
answer
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Finding the similarity between two functions
I am a first-year grad student in Computer Science, and I need some help with a problem that I think is statistically oriented. I have taken a statistics course, but it was abysmal and I haven't had ...
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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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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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4
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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 ...
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1
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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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Estimating the sample variance and expected value of a maximization function of multiple random variables
Suppose I have three i.i.d. random variables $X$, $Y$, and $Z$. A model is used to generate $i$ outcomes for each variable that are used to estimate the sample mean and sample variance for each of the ...
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