# Questions tagged [approximation]

Approximations to distributions, functions, or other mathematical objects. To approximate something means to find some representation of it which is simpler in some respect, but not exact.

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### Polynomials that converges pointwise to a simple function on (-1,1) and bounded by $e^{|x|}$?

I am trying to prove a theorem related to the moment generating function. I will need a sequence of polynomial that converges to a simple function $K_{(-1,1)}(x)$ pointwise on the real line while ...
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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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### Predicting Repurchase Curves next value based on usual functional form

Some definitions first: Acquired customers: Customers placing an order for their first time. Cohort: Group of customers that have been acquired during the same time period. Repurchase: An order placed ...
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### CLT theorem and Berry–Esseen bounds for this special case of sampling

Consider a finite set $S=\{s_1,s_2,..s_n\}$, where $a \leq s_i\leq b$ are integers. Each element in $S$ can be chosen to a subset $S'$ in probability $p$. We consider $n$ to be very large. My question:...
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### What are the variations of Expectation Maximization?

To explain my question better, I will use this analogy: In the case of the Gradient-Descent method, we have multiple variations/expansions for the main algorithm, like stochastic gradient descent (SGD)...
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### label set of data points

I have a set of data points in a 3-dimensional space. Points are approximately in two rows, like so(3 in secondary row and 7 in primary row): I need to label both rows separately. For example, the ...
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### Derivation of confidence interval of incidence rate ratio

I am trying to understand the confidence interval equation for a Incidence Rate Ratio (IRR) given several places: $95\text{% CL(IRR)} = \exp(\log(\text{IRR}) \pm 1.96\times \text{SE(log(IRR))})$, ...
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I am busy working my way through a paper by Guo et al. (pairwise variable selection for high dimensional model-based clustering) and I am just completely stuck. In the paper they use the EM algorithm ...
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### Nonlinear Iterative Partial Least Squares algorithm can calculate accurately all Principal Components?

I wanted to demonstrate a small example in order to understand better the $\textbf{Nonlinear Iterative Partial Least}$ $\textbf{Squares algorithm}$. My goal is to calculate all the Principal ...
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### Universal Approximation: how does a neural network handle a ratio of inputs

Related questions/background info: Universal Approximation Theorem — Neural Networks Does the universal approximation theorem for neural networks hold for any activation function? A universal ...
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### How can i find out closest lognormal distribution parameters from a GEV distributed data in R

The question is a bit weird so i'll open it up. So i have a table of return periods for different amounts of rain. The table has been made using GEV distribution on known data and then the mean and ...
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### Approximate covariance matrix while batch sampling

I have a fallowing problem: In each iteration I take samples $x^k_t, x^k_{t+1} ... x^k_{t+\tau}$ from a process from $t$ to $t+\tau$. Then I construct $k \;x\; k$ covariance matrix. Then I do it once ...
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### Approximation of a probability distribution

I have a continuous random variable $X$ that can easily be sampled. I don't have any other assumption on $X$. Let's say I have sampled $X$ and I have constructed the set $S$. We can assume that $S$ is ...
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### Predicting a value based solely on Correlation Coefficient

Let me set the stage. We are dealing with two variables; $A$ and $B$. We can easily obtain $A(x)$ for a specific data point $x$. $B(x)$, on the other hand, is very difficult to know. We know Pearson'...
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