Questions tagged [density-estimation]

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

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Kernel density estimation of AR(1)

I recently started playing around with estimation joint densities with Matlab using its mvksdensity function and at the moment I am fooling around with an autoregressive process of order 1 (AR(1)) ...
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31 views

DBSCAN vs Kernel Density Estimation [closed]

What is the difference between DBSCAN and Kernel Density Estimation
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Online density estimation and learning

Suppose that I have a system that at each time $t_i$ produces $N$ i.i.d samples of an unknown distribution $f(x;t)$. I want to estimate the distribution in an online manner. If I had only the ...
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46 views

Multivariate Normal density Calculation for every point in dataset

I am assuming a multivariate dataset to be normally distributed. First I calculated mean and var-covariance matrix, then to calculate density at each point in the dataset. I used the below code: ...
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How to fit a line between areas of high density? (find valley between hills in 3D)

My data are a number of points in 2 dimensions. There are areas that are more dense. I run a kernel density estimation with a Gaussian filter that gives me a result similar to the picture (of course, ...
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Empirical conditional density of continuous variables

I have a dataframe, with data of several continuous variables. The variables are not independent. My goal is to sample from the distribution that generated this data. What's a relatively easy and ...
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evaluating an empirical multivariate PDF in python

I have multivariate (bivariate in the simplest case) residuals from a VAR time series regression and I'd like to estimate the joint pdf and then be able to draw from this pdf. If I have bivariate ...
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12 views

Distance between two multivariate kernel density estimates

I tried using the ks2samp to compare two multivariate kernel density estimates. Is it the right way to compare two multivariate densities?
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Kernel density estimates comparison in a multivariate setting

I have a dataset with 64 features and binary labels (class 1 and class 2). Before I fit any classification models, I wanted to check whether the samples belonging to the two classes come from the same ...
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83 views

Kernel Density Estimation for bimodal distribution with Python

I have a bimodal distribution for the range [-0.1, 0.1] which can be viewed here: I want to train/fit a Kernel Density Estimation (KDE) on the bimodal distribution as shown in the picture and then, ...
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88 views

How to avoid smoothing to 0 at edges of R density plot

When using the density function in R, it includes smooth transitions down to 0 at both ends of the data. Is there a way to prevent this? As a trivial example, ...
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33 views

Constrained Nonparametric Density Estimation with Right Censoring

Is anyone aware if there is any available open source R (or other language) code which implements non-parametric estimation of the failure time density function subject to a monotonicity constraint on ...
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42 views

Masked Autoencoder MADE implementation in TensorFlow vs Pytorch

I am following the course CS294-158 [1] and got stuck with the first exercise that requests to implement the MADE paper (see here [2]). My implementation in TensorFlow [3] achieves results that are ...
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25 views

How to plot density for repeated k-fold cross validation?

Long story short, I conducted regression using repeated k-fold cross validation. While messing around I decided to plot the density of the R-squared distribution for the resampling. Obviously there ...
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In a lognormal distribution, is the median further left than when the variable is logged?

I created a kernel density estimate of the earnings distribution in South Africa in 2017, quarter 4, using Stata. I summarized the earnings variable, putting a sampling weight as an analytical weight ...
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How Parzen window density estimate $f_n$ converges to f

I am trying to understand how Parzen window density estimate converges to actual density function f(x).[Actually i am trying to learn machine learning on my own using available free resources. Please ...
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1answer
39 views

KDE for $h \rightarrow 0$

Let $K$ be a kernel and $X_1,\dots, X_n$ a sample drawn from some distribution with density $f$. The KDE of $f(x)$ is defined by $$\hat f_h(x) = \frac{1}{nh}\sum_{i=1}^nK\left(\frac{x - X_i}{h}\right)....
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Recentered Influence Function and Quantiles

First of all, I apologise if my question is straightforward, but I'm having some troubles understanding the concepts. If someone could help me, I would be very grateful. I am reading the Firpo et al. ...
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27 views

One shot inference with Variational Autoencoders using proposal mean

Let's say you have an already trained Variational Autoencoder where the parameters are $\phi, \theta$ for the recognition and generative models respectively. Let's also assume you have the following ...
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Alternative to Point Density

I have the coordinates of a bunch of car crashes and I reasoned that the place where they are the densest is where crashes are the most likely to occur. The solution I found when looking into this ...
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Confidence in Negative Binomial Prediction

I have predicted future demand of stock from observed historical demand projecting a negative binomial demand curve. Demand is extrapolated to multiple periods using this approach. I'm pretty happy ...
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Usefulness of MISE

I'm currently in a class on nonparametric smoothing, and, while talking about density estimation in general, the professor introduced the notion of MISE (mean integrated square error): $\text{MISE}\...
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Is it appropriate to examine the density plot for time series data?

Usually we use time plot to examine the behaviour of time series data cause it reveals the chronological characteristic. Does it make sense that one looks at the data distribution using some non-...
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176 views

Kernel density estimation and boundary bias

What sort of kernel density estimator does one use to avoid boundary bias? Consider the task of estimating the density $f_0(x)$ with bounded support and where the probability mass is not decreasing ...
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Fitting data to an exponential model with a specified rate in R

I have been using the fitdistr package in R to try and do this but with no luck so far: fit1 <- fitdistr(data1$x, "exponential", start = list(rate = 10)) I am ...
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Incremental updates for percentile estimates [duplicate]

I want to estimate percentile statistics for time-series pairs $(t, y)$ over varying granularities of time (hour, day, month, etc) For example, if I have the following pairs ...
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23 views

Classification - deterministic to probabilistic

Let $\mathcal{M} = \{X_1 , ... , X_N\}$ be a collection of objects, and assume that $x = X_i$. Imagine that we cannot observe $x$ directly, but we do have measurements $y = y(x)$ (only 1 dataset, ...
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25 views

Distribution that acts like Poisson/NegBin for small means and like a Normal distribution for large means?

I want to generate a full density probabilistic forecasting model, where I don't know a priori whether the time series I want to model are intermittent or dense. In both cases, the time series is a ...
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17 views

Comparing shapes of distributions with multiple levels

This is probably a really simple task and I'm just struggling with implementation in R. I have a simple dataset which contains three columns: Species (factor), move_direction (factor), velocity (...
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My Risk Neutral Density Curve for SPY Options looks very weird

I have created a risk neutral density curve using SPY weekly options and the RND package in R. I calculated the risk neutral density for the Feb07 options. The curve looks very weird when I look at ...
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19 views

Looking for a sample that proves that KDE behaves worse than the Dirichlet Process

I am trying to find an example that clearly shows that the kernel density estimator does worse than the Dirichlet process in terms of estimating the distribution of a sample. But eventually, I always ...
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16 views

Rescaling a Kernel Density Estimator

I want to estimate an unknown density using the Kernel Density estimator $$\hat f_h(x) = \frac{1}{nh}\sum_{i=1}^nK\left(\frac{x - X_i}{h}\right).$$ I want to apply the estimator to data with different ...
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36 views

What methods are there for estimating distributions based on histograms?

I recently worked on a consulting project where a client wanted to estimate gamma and weibull distributions based purely on histograms rather than raw-data. I have never worked with problems like that ...
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1answer
125 views

Convergence of kernel density estimate as the sample size grows

Let $X\sim\text{Normal}(0,1)$ and let $f_X$ be its probability density function. I conducted some numerical experiments in the software Mathematica to estimate $f_X$ via a kernel method. Let $\hat{f}...
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71 views

Point estimation, interval estimation, density estimation?

Frequentist statistics textbooks typically consider point and interval estimation but not density estimation of a parameter. Since the density (of the sampling distribution) of the estimator is ...
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Density estimation: the significance of smaller number of samples?

I'm reading Probabilistic Graphical Model: Principle and Techniques by Koller and Friedman. In section 18.5 Bayesian Model Averaging(p825), the author said If we are interested only in density ...
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23 views

Validity of Monte-Carlo method to estimate a probability distribution which follows a power law

I am using a Monte-Carlo method to estimate a probability distribution function (pdf). Basically, I have several input parameters following known distributions, from which I can draw samples, that I ...
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64 views

Interval and density forecast in R with both heteroskedasticity and non-normality in time-series data

We tried to get both an interval and density forecast based on time-series data, which we found to be both non-normal and heteroskedastic, in R. We know that for non-normality, forecasts can be ...
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366 views

Why is K-Means a special case of Mean-Shift algorithm?

I have read the paper of Yizong Cheng about Mean Shift, Mean shift, mode seeking, and clustering , but I didn't understand exactly, how did he concluded that KMeans is a Special case of Mean Shift ...
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What is the resulting distribution of a data set that was originally normally distributed but has been quantized and had all negative values removed?

I am trying to benchmark a seasonal forecasting model and calculate not just the point forecasts but the forecast densities from the model. To do this, I generated a simulated data set in the ...
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52 views

Expected value and variance of KDE

I need to find the expected value and variance of KDE given that $$(i) E[u] = 0 \to \int u\phi(u)du=0\\ (ii)V[u] = \sigma^2 \to \int u^2\phi(u)du=\sigma^2$$ where $\phi$ is the kernel function. I've ...
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269 views

Hellinger Distance between 2 vectors of data points using cumsum in R

I have numerous vectors of data points and I want to compute the hellinger distance between the probability distributions of every 2 vectors. I am using this version of the Hellinger distance equation:...
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23 views

How to efficiently find spikes in 2D data projected to 1 axis

I have the following points: My goal is to find the be able to differentiate the yellow points from the purple ones. We can assume that the yellow points are aligned on the vertical axis. We cannot ...
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20 views

Fitting density through regression model

I found in a paper a way to fit a density through a regression model, and i wanted to know if you have some other referenes that uses it, or maybe the source of this idea. Here it goes : Suppose ...
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1answer
53 views

Using Parzen Window approach

When is preferable using Parzen Windows approach, so a nonparametric approach, instead to a parametric approach?
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21 views

How can probability be equal to pdf times volume of area?

I'm studying pattern recognition and I'm at the part about Kernel density estimators. During the introduction of the subject, the book I'm studying (Pattern Recognition & Machine Learning by ...
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61 views

Behavior of kernel density estimation

Consider the random variable $X=YZ$, where $Y\sim\text{Normal}(0,1)$ and $Z\sim\text{log-Normal}(0,1)$ are independent. I wanted to assess the accuracy of kernel density estimates for the density ...
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36 views

Difficulties with orthogonal density estimation

I am working on an implementation of an orthogonal density estimator, using the basis $$ \psi_0(t) = 1, \quad \psi_{2j}(t) = \sqrt{2}\text{cos}(2\pi j t), \quad \psi_{2j+1}(t) = \sqrt{2}\text{sin}(2\...
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Density estimation as an optimization problem

Density estimation is the estimation of a probability density function from observed data. Can some of the common approaches to density estimation, such as kernel density estimation, be formulated as ...
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28 views

“Simple” boundary correction method in kernel density estimation

I'm new to kernel density estimation and have a rough idea on boundary bias. When correcting for boundaries, I tried to use boundary correction method as "simple" which is available in R. Once I ...

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