# Questions tagged [density-estimation]

Estimation of probability density functions, whether by kernel density estimation, log-spline estimation or other methods.

299 questions
Filter by
Sorted by
Tagged with
17 views

### Density estimation on labelled data

I'm looking for a nonparametric density estimation for a particular classification. Let A={2,3,5,7,10,13} And Dens be the density of A Dens={x: x lies within the density region of A} , based on a ...
10 views

I have this example and I'm struggling to solve it Say that I have this Independent and identically distributed sample with density $f(x,\theta)= \frac{3x^2}{\theta^3} , 0 \le x \le \theta,$ $\... 3 votes 1 answer 34 views ### Estimate parameters of an unknown negative binomial distribution based on known distribution The PDF of a known NBD given in Equation (1). The parameter a and r are function of$μ$= sample mean, and$s^2$= sample variance, as given in Equation (2) and (3) respectively.$r$= number of ... 1 vote 0 answers 37 views ### Universal Approximation Capabilities of Mixture of Weibulls Can a mixture of$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 0 answers 12 views ### Kernel Density: How do the terms 'global' and 'pilot' translate? I nearly most of the articles on kernel smoothing or concepts that use kernel density estimations, authors speak of 'pilot' and 'global'. https://link.springer.com/article/10.1023/A:1008925425102 &... 1 vote 0 answers 34 views ### How to understand the density in machine learning? We can calculate the conditional density using Eq.1. $$p_{\theta, \Lambda}(y \mid \boldsymbol{x})=\frac{\exp \left(f_{\theta, \Lambda}(\boldsymbol{x})[y]\right)}{\sum_{k=1}^{n} \exp \left(f_{\... 1 vote 0 answers 66 views ### Kernel Density Estimation using a Two-Boundary-Kernel à la Jones I'm trying to understand how to perform a KDE on a bounded support, i.e. with lower and upper boundary, when using a kernel that is specifically designed to ensure consistency/h^2-bias at the ... 12 votes 2 answers 550 views ### Kernel Density Estimate for Cauchy As far as I understand, kernel density estimation does not make any assumptions on the moments of the underlying density, and just requires smoothness. The Cauchy density function is quite smooth. ... 0 votes 0 answers 63 views ### Approximation of a polynomial via histogram Note: I originally tried to pose this question generally, without discussing the specific type of stochastic process. I hope that this can still be an interesting question generally. Assume that we ... 0 votes 0 answers 17 views ### Exponentially distributed bins for viewing and analysing the tails of a histogram Is there a rule for visualising and analysing density estimates of heavy tailed observations on a log-log scale? For example, equispaced bins and exponentially distributed bins: ... 1 vote 0 answers 48 views ### How to sample from a distribution approximated by a Neural Network? There are a few models already that approximate distributions with a neural network i.e.: energy models define a density function f(x)= e^{S(x,w)}/Z where S is a neural network and Z is a ... 1 vote 1 answer 59 views ### Bandwidth Selection for Kernel Density Estimation Are there any heuristics for selecting the bandwidth for kernel density estimation? In other words, is a spiky curve better or a smooth one? 1 vote 0 answers 42 views ### I have difficulties to understand the input normalization - density estimation in the same context in ML or DL I know (by experimenting with different ML and DL algorithms) that input normalization helps to improve the performance of the model. When we do normalization in training, with the same mean and ... 0 votes 0 answers 16 views ### Understanding the methodology of evaluating density forecats I have difficulties with under understanding the idea that Diebold came up with in 1998 in his essay about the evaluation of the accuracy of forecasting density p(y), he used the probability integral ... 1 vote 0 answers 28 views ### Optimal rate of convergence of nonparametric density estimators Suppose that X_1, X_2, \dots, X_n forms an independent and identically distributed sample from some d-dimensional probability distribution with unknown probability density function f. Let x be ... 0 votes 0 answers 113 views ### Is possible to compare two density distributions 'trends'? I have responses from two groups (A and B) on a confidence rating about a distance judgment task. The participants saw pairs of stimuli and after they were asked to rate their confidence about the ... 0 votes 0 answers 15 views ### Is there a model particularly suited to predicting a discrete density function? I would like to forecast a demand density function over the 24 hours of a day. For example, consider customers at a bank with a number of tellers. I would like to forecast how the demand for tellers ... 0 votes 0 answers 14 views ### Density estimation for 50 input variables - individually or together I am a beginner to statistics and was wondering if it is possible to estimate the density where there are 50 input variables. Do I perform density estimation for each variable individually then ... 1 vote 0 answers 57 views ### Expectation of kernel density estimators using sharpened data My question regards the proof of the bias of the kernel density estimator obtained using "sharpened" data. The method comes from the paper by Choi and Hall (1999). Specifically, assume X_1, ... 0 votes 0 answers 81 views ### Estimating conditional density, each observation being conditional on belonging to some range of values I have iid observations (Y_1, X_1), (Y_2, X_2), ... , (Y_n, X_n), where the conditional density of Y_i|X_i is known to have form$$f(y|x) = \begin{cases} \frac{D(y)}{\int_{||t-x|| \leq 1} D(t)... 1 vote 0 answers 30 views ### Driver based forecasting using past distributions I have reduced my original forecasting problem (Short context : I need to forecast hotel bookings and checkins for the next 3 months. I already have a reasonable forecast for bookings and need to ... 4 votes 5 answers 115 views ### Determine traffic speed distribution while driving I assume that the vehicle speed of cars on a highway is normally distributed around the posted speed limit. I could verify this by sitting by the road with a radar gun and measure vehicle speed for a ... 1 vote 0 answers 16 views ### How is Dowd's (2007) resampling procedure supposed to mitigate the problem of autocorrelated multiple-step-ahead forecasts? Dowd "Validating multiple‐period density‐forecasting models" (2007) considers evaluation of multiple-step-ahead density forecasts. There is a know problem of dependence between forecast ... 1 vote 3 answers 145 views ### Practical Uses of Kernel Density Estimators Perhaps this question is too broad, but I would like to know - how does one use a kernel density estimate in practice? I know of course that one can use it to draw pretty pictures on top of histograms,... 1 vote 1 answer 11 views ### Gain of power by a smart choice of goodness of fit test Suppose one would like to test that a sample of observations comes from Uniform(0,1) distribution. Instead of applying the Kolmogorov-Smirnov test on the sample, one may first apply the inverse CDF (... 1 vote 0 answers 61 views ### Bayesian Parameter estimation (Pattern Classification by Duda, et al I have been trying to solve question 17 of chapter 3 (Maximum Likelihood and bayesian estimation) of the book "Pattern Classification" by Duda, et al. The question goes as follows: Now the ... 0 votes 0 answers 33 views ### Interpretation of test set negative log likelihood in neural density estimation applications I have seen people splitting a dataset into a train and test sets and learning the parameters of a mixture density network using the negative log likelihood cost function on the train set and ... 0 votes 0 answers 25 views ### Measure for evaluating a density estimation procedure Given an implementation of a multivariate density estimation scheme, what would be a suitable measure to evaluate the accuracy of the procedure? I am currently evaluating the procedure using three ... 1 vote 1 answer 86 views ### Can a neural net approximate any conditional density asymptotically? Assume that the conditional density of$ y \vert x $is a Beta distribution for all values of x. Can a Beta distribution with parameters computed by a neural net, i.e. Beta($\hat{\alpha}$,$\hat{\beta}... 18 views

### cross validation for distribution

Assume we have a linear regression model. Then, assume we have response values $y_{1}, \dots, y_{n}$ and covariates vectors $\textbf{x}_{1}, \dots, \textbf{x}_{n}$. To assess the prediction ...
1 vote
11 views

### Methods for Predicting Destination Locations based on Start Locations in 2D Space

I have location data $(x_1, x_2)$ and the associated labels $(y_1, y_2)$, which can be interpreted as origin and destination points in physical space. Now I would like to predict destination locations ...
69 views

### what is the number of bits assigned by a generative model to a K-class dataset, in theory

Consider a dataset, something like MNIST or CIFAR-10, that consists of (for example) 50000 images taken from 10 classes and balanced with an equal number in each class. For a discriminitive classifier,...
984 views

### Kernel Density Estimation for a Discrete Variable

I was tying to estimate the distribution for a discrete variable. However, suddenly I thought that "Is a simple histogram sufficient? because I have observations for every evaluation point" ...