Questions tagged [density-estimation]
Estimation of probability density functions, whether by kernel density estimation, log-spline estimation or other methods.
342 questions
0 votes
0 answers
43 views
Estimate probability distribution of pretrained language model
Suppose you have a pretrained protein language model like and you can let it generate some sequences of a given length L. Given a number of such samples, you want to estimate the probability ...
- 101
4 votes
1 answer
196 views
Can I have some help choosing a very low-sample estimator?
I want to forecast what next semester's finances may look like, regarding my campus job. I get paid bi-weekly, and have eight past data points: ...
- 143
0 votes
0 answers
42 views
Model for predicting Species Presence Probability given some meteorological variables
I am working on a project where I want to predict the spatial distribution of a species given some variables, for example: Mean average temperature recorded through the year. Cumulative Precipitation ...
3 votes
0 answers
158 views
Evaluating resolution of a density forecast of a continuous variable
In the context of density forecasting, resolution addresses the following question: Is the conditional distribution different from the unconditional distribution? The concept is presented briefly in ...
- 71.5k
7 votes
3 answers
272 views
Radon-Nikodym derivative of the empirical measure and histograms
Is the empirical "density" distribution function the Radon-Nikodym derivative of the empirical measure w.r.t the Lebesgue measure ? I noticed a formal relationship when we were briefly ...
0 votes
1 answer
86 views
Normalizing Flows for univariate data
I am currently reading the literature on Normalizing Flow models and their ability as density estimators. It seems that the entire literature focuses on multivariate data sets and I was wondering ...
- 1
0 votes
0 answers
128 views
Normalizing Flow with Highly Negative NLL Loss
I am following the Zuko "Train From Data" tutorial to train a Neural Spline Flow. My goal is to approximate a distribution over functions. Therefore, each of my function samples are actually ...
- 1
2 votes
1 answer
88 views
$L_2$-norm consistency of kernel density estimation
The consistency results for kernel density estimation which I can find are almost all for the $L_1$-norm or $L_\infty$-norm, like in this paper or this paper. I can't simply generalize them to $L_2$-...
- 117
3 votes
1 answer
155 views
How to understand the uniform central limit theorem
In a paper from Nickl I found a theorem (Theorem 4) with a form of central limit theorem $$\sqrt{n}(P_n-P)\rightarrow G$$ in $l^\infty(F)$ where $P$ is a law on $\mathbb{R}$, $F$ is a class of ...
- 117
26 votes
2 answers
4k views
Why doesn't ML suffer from curse of dimensionality?
Disclaimer: I asked this question on Data Science Stack Exchange 3 days ago, and got no response so far. Maybe it is not the right site. I am hoping for more positive engagement here. This is a ...
- 1,845
0 votes
0 answers
68 views
Learning a probability distribution from samples drawn from unknown function
I am wanting to learn some probability distribution $p$ from data (using e.g., Kernel Density Estimation, a Normalizing Flow, whatever your favourite machine learning model is). If I had a dataset $D =...
- 91
3 votes
0 answers
87 views
How to identify hot spots in one-dimension
I am looking to identify stretches of a road along which a notably high number of accidents occur. My data can be represented as a two column table in which each row represents one accident, and the ...
- 395
4 votes
1 answer
214 views
How to accurately estimate the probability of a rare event in a large dataset?
I have a dataset of 30,155 names and out of curiosity I verified that the longest name has 68 characters, which is quite big considering the mean and SD were 24.78 and 5.64, respectively. Based on ...
- 141
0 votes
0 answers
75 views
MLE of marginal distribution for continuous random variable
Let $\mathcal{F}$ be a family of multivariate probability densities such that for a sufficiently large data sample, there always exists a unique MLE. Assume also that all marginal and conditional ...
- 213
1 vote
0 answers
83 views
How to show $\sup_{x\in [a,b]}|f_n(x)-f(x)|=O_p(\sqrt{\frac{\log n}{nh}}+h^2)$ when the kernel $K(\cdot) $ is of bounded variation?
Consider the kernel estimate $f_n$ of a real univariate density defined by $$f_n(x)=\sum_{i=1}^{n}(nh)^{-1}K\left\{h^{-1}(x-X_i)\right\}$$ where $X_1,...,X_n$ are independent and identically ...
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