# 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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### Best way to approximate head point having only face keypoints

I'm using the BlazeFace model from TensorFlow which only has this few keypoints: I need those keypoints plus a head keypoint, like this one: My question is, which would be the best way to ...
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### LSA and cosine similarity approximation with large matrix

This question is the non-r related version of this one I have a tdm with 16k x 350k dimension, for which I am trying to get the document-document similarity (cosine type). With RSpectra I have found a ...
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### Distribution of the approximation error in Gaussian Process Regression (finite data setting)

I am learning about Gaussian Process Regression. I would like to have some references or results regarding the distribution of the error between a given function, and the posterior obtained in ...
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### Universal approximation of Gaussians

Can gaussian kernels reproduce non continuous L2 integrable functions? ( Do non continuous L2 integrable functions lie in the RKHS constructed by a Gaussian Kernel?) Edit: I think my question is being ...
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### Simplifying the Kullback-Leibler divergence for a sum of distributions

I want to find an approximation of a mixture of probability distributions that minimises the Kullback-Leibler divergence (KLD). I need to verify my result, as it seems suspect. We have a joint ...
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### Universal Approximation Capabilities of Mixture of Weibulls

Can a mixture of $N$ Weibull distributions approximate any continuous density with non-negative support, if $N$ is sufficiently large? (If so, a reference to the proof would be greatly appreciated). (...
1 vote
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### Is there a way to correct for degrees of freedom when using a generalized linear model with a Poisson distribution featuring random effects?

I am running a generalized linear mixed effect model with a Poisson distribution to analyse count data. The model has a random effect that takes into account multiple observation obtained by the same ...
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### Conservative coverage probability when an biased estimator is used for the variance

Suppose that $X_n\sim N(\mu, \sigma^2_n)$. Thus, to construct a 95% CI for $\mu$, we can use $X_n\pm 1.96 \sigma_n$. The coverage probability, $P(\mu\in [X_n\pm 1.96 \sigma_n])$, is equal to 95%. ...
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### Confidence interval for multiple samples of ratios of counts (in R)

Data and objective I have count data from two groups, A and B, from across multiple samples. I want to estimate the average ratio of A to B across all samples, along with a confidence interval. Issues ...
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### Mean squared value error only useful for policy evaluation?

The mean squared value error is defined as: $\overline{VE}(\mathbf{w}) \equiv \sum_{s \in \mathcal{S}} \mu (s) \left[v_{\pi}(s)- \hat{v}(s,\mathbf{w})\right]^2$ Just by looking at this metric, it ...
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### What is known, in principle, about the possibility of approximating the random discrepancy between a statistical estimate and its parameter?

The difference between the value of a statistical estimate and its parameter's value is almost never exactly $0$. For example, $r - \rho$, for a unique sample $r$, is likely to be some non-zero ...
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### A nondeterministic covariance-stationary process approximated by an ARMA process

We know that the Wold Decomposition Theorem says that any purely nondeterministic covariance-stationary process, $x = [x_t : t \in \mathbb{Z}]$, can be written as a linear combination of lagged values ...
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### Fast likelihood evaluation for Gaussian distribution with diagonal plus low rank covariance

Let's assume the likelihood $$y \sim\mathcal N_p(0, \Sigma + \Lambda\Lambda^\top)$$ where $\Sigma$ is diagonal and $\Lambda$ is a $p \times d$ matrix with $d \ll p$. What is the fastest way to ...
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### Number of points a one hidden layer neural-network can interpolate

We am trying to understand the number of points that a neural network of a particular size can interpolate. I think this may be isomorphic to its degree of freedom? We are not interested in whether ...
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### Connection between mean field inference and mean field theory (physics)

In variational inference, the mean-field family of probability distributions is the set of distributions that factors over its terms (i.e. each component is independent of all others). This allows us ...
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### Sampling marginal distribution from joint density

Suppose we know that random vectors $x, y$ have joint density $p(x, y) \propto \exp(-U(x_1, \ldots, x_m, y_1, \ldots, y_n))$, and we want to draw a random sample from the marginal $p(x)$ (i.e. we want ...
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### Why does Kullback–Leibler divergence measure information loss when approximating a probability distribution?

I've encountered a sentence: In information theory, Kullback–Leibler divergence is regarded as a measure of the information lost when probability distribution Q is used to approximate a true ...
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### Graphical construction of normal approximation to histogram

In Statistics by Freedman et al. it is described how to construct a normal approximation for a histogram, as follows: Calculate mean and SD for the histogram (in the image $63.5$ and $3$ inches). ...
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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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